From 6fc0d86e1f137c6ae2d453d9e2ef3d5f4121ebe6 Mon Sep 17 00:00:00 2001 From: Georg Zhelev Date: Fri, 27 Aug 2021 16:24:08 +0200 Subject: [PATCH 01/20] Final version A/B Case Study for doubleml docs --- doc/examples/data/high42.CSV | 1001 ++++++++++ doc/examples/py_double_ml_abtest.ipynb | 2385 ++++++++++++++++++++++++ 2 files changed, 3386 insertions(+) create mode 100644 doc/examples/data/high42.CSV create mode 100644 doc/examples/py_double_ml_abtest.ipynb diff --git a/doc/examples/data/high42.CSV b/doc/examples/data/high42.CSV new file mode 100644 index 00000000..7e6e0941 --- /dev/null +++ b/doc/examples/data/high42.CSV @@ -0,0 +1,1001 @@ 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diff --git a/doc/examples/py_double_ml_abtest.ipynb b/doc/examples/py_double_ml_abtest.ipynb new file mode 100644 index 00000000..65a755cd --- /dev/null +++ b/doc/examples/py_double_ml_abtest.ipynb @@ -0,0 +1,2385 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "consecutive-cabinet", + "metadata": {}, + "source": [ + "# Python: A/B Testing with DoubleML" + ] + }, + { + "cell_type": "markdown", + "id": "opponent-indonesian", + "metadata": {}, + "source": [ + "\"An\n", + "\n", + "Image Source Freepik http://www.freepik.com, Designed by macrovector\n" + ] + }, + { + "cell_type": "markdown", + "id": "c7c96f88", + "metadata": {}, + "source": [ + "In this notebook, we illustrate how the [DoubleML](https://docs.doubleml.org/stable/index.html) package can be used to estimate the causal effect of seeing a new ad design on customers' purchases in a webshop. The [DoubleML](https://docs.doubleml.org/stable/index.html) package for Python and R provides an implementation of the double / debiased machine learning (DML) framework of [Chernozhukov et al. (2018)](https://arxiv.org/abs/1608.00060) and can be used to estimate causal effects based on machine learning (ML) methods.\n", + "\n", + "## A/B Testing\n", + "\n", + "A/B testing is a frequently used framework to perform causal inference in practice. For example, a manager of a webshop might be interested in optimally adapt the webshop design according to users' preferences. She might want to estimate the effect of a new ad design, which is displayed on the starting page, on a customer's purchases (in $100\\$$). A/B tests refer to an experimental design in which a certain treatment, for example a new ad design (called \"Version $A$\"), that is randomly assigned to groups of individuals who are otherwise assigned to \"Version $B$\". The assignment can also be randomized among subgroups, i.e., randomly displayed to visitors once one or multiple of their characteristics are taken into consideration. For example, only visitors who have already purchased a product before might be exposed to the new ad. The goal is to conclude whether the treatment (= the new ad) has an effect on an outcome of interest (= monetary value of products purchased in $100\\$$). Additional examples refer to improvement of a user experience on a website or estimation of price elasticities. Websites and apps are ideal for running A/B tests because they make it very easy to precisely direct the treatment to visitors and users (or to specific subgroups of them).\n", + "\n", + "## Scenario\n", + "\n", + "Let's consider the following stylized scenario. The manager of a webshop is performing A/B testing to estimate the effect of a new ad design $A$, on customers' purchases, $Y$. The treatment is assigned randomly conditional on the visitors' characteristics $V$. Such characteristics could be collected from a customer's shoppers account, for example. These might include the number of previous purchases, time since last purchase, length of stay on a page as well as whether a customer has a rewards card, among other characteristics. Let's assume the conditional randomization has been conducted properly, such that a tidy data set has been collected. Now, a data scientist wants to evaluate whether the new ad design causally affected the sales, by using the [DoubleML](https://docs.doubleml.org/stable/index.html) package.\n", + "\n", + "### Why control for individual characteristics?\n", + "\n", + "Before we start the case study, let us briefly address the question why we need to include individual characteristics in our analysis at all. There are mainly two reasons why we want to control for observable characteristics. First of all, so-called confounders, i.e., variables that have a causal effect on both the treatment variable and the outcome variable, possibly create a bias in our estimate. In order to uncover the true causal effect of the treatment, it is necessary that our causal framework takes all confounding variables into account. A second reason to include individual characteristics is efficiency. The more variation can be explained within our causal framework, the more precise will be the resulting estimate. In practical terms, greater efficiency leads to tighter confidence intervals and smaller standard errors and p-values.\n", + "\n", + "### Why use machine learning to analyze A/B tests?\n", + "\n", + "ML methods have turned out to be very flexible in terms of modeling complex relationships of explanatory variables and dependent variables and, thus, have exhibited a great predictive performance in many applications. In the double machine learning approach ([Chernozhukov et al. (2018)](https://arxiv.org/abs/1608.00060)), ML methods are used for modelling so-called nuisance parts. In terms of the A/B case study considered here, ML tools can be used to flexibly control for confounding variables. For example, a linear parametric specification as in a standard linear regression model might not be correct and, hence, not sufficient to address the underlying confounding. Moreover, by using powerful ML techniques, the causal model will likely be able to explain a greater share of the total variation and, hence, lead to more precise estimation." + ] + }, + { + "cell_type": "markdown", + "id": "0ec5b0cf", + "metadata": {}, + "source": [ + "## Data \n", + "\n", + "As an illustrative example we use a data set from the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge). In this challenge, a great number of data sets have been generated in a way that they mimic distributional relationships that are found in many economic real data applications. Although the data have not been generated explicitly to address an A/B testing case study, they are well-suited for demonstration purposes. We will focus on one of the many different data genereting processes (DGP) that we picked at random, in this particualar case a data set called `high42`. An advantage of using the [ACIC 2019 data](https://sites.google.com/view/acic2019datachallenge/data-challenge) is that we know the true average treatment effect which is 0.8 in our data set.\n", + "\n", + "First we load the data." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "e39d4dd0", + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "\n", + "#fetch_ACIChigh42 needs to be defined\n", + "#df = fetch_ACIChigh42(return_type='DataFrame')\n", + "\n", + "#load code locally\n", + "df = pd.read_csv('data/high42.csv', sep=',', na_values=\".\")\n", + "\n", + "#code can also be loaded using a URL of the data\n", + "#url = 'https://raw.githubusercontent.com/DoubleML/doubleml-hiwi-sandbox/master/case_studies/AB_testing/data/high42.CSV?token=AQWGKQRE57BBRGOCBPSNBJTBD57ZQ'\n", + "#df = pd.read_csv(url)" + ] + }, + { + "cell_type": "markdown", + "id": "11525056-cdec-4916-9cb4-aa4268e99175", + "metadata": {}, + "source": [ + "We see that the data set consists of 1000 observations (= website visitors) and 202 variables. The $Y$ column represents the number of page visits. The treatment variable $A$ is binary with a value 1 indicating that a customer has been exposed to the new ad design (and value 0 otherwise). The remaining 200 columns $V$ represent individual characteristics of the customers." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "10edc74d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(1000, 202)\n" + ] + } + ], + "source": [ + "print(df.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "6760c009", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " Y A V1 V2 V3 V4 V5 V6 V7 V8 ... \\\n", + "0 7.358185 1 10 0 0 7 192.793769 23.676950 8 0.185443 ... \n", + "1 8.333672 1 12 0 1 4 199.653596 19.281270 7 0.514842 ... \n", + "2 7.472758 0 14 1 1 2 194.207792 24.589331 5 0.309199 ... \n", + "3 6.502319 1 0 1 0 9 201.838024 25.513918 4 0.160160 ... \n", + "4 7.043758 1 12 0 0 9 201.360443 31.160641 6 0.291976 ... \n", + "\n", + " V191 V192 V193 V194 V195 V196 V197 V198 V199 \\\n", + "0 1.462837 1 1627.274196 0 0 4.683956 0.565667 0 3 \n", + "1 1.330522 1 1661.484439 1 0 6.766661 -0.395402 0 4 \n", + "2 1.384151 1 1658.939293 0 0 5.647794 1.112766 0 0 \n", + "3 1.220303 1 1650.801625 0 0 5.370363 -0.305842 0 4 \n", + "4 1.170094 1 1676.818876 0 0 3.446532 2.440661 0 1 \n", + "\n", + " V200 \n", + "0 0.024338 \n", + "1 0.056518 \n", + "2 0.013442 \n", + "3 0.034632 \n", + "4 0.017514 \n", + "\n", + "[5 rows x 202 columns]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.head()" + ] + }, + { + "cell_type": "markdown", + "id": "c6e32feb", + "metadata": {}, + "source": [ + "### Descriptive Statistics\n" + ] + }, + { + "cell_type": "markdown", + "id": "horizontal-hanging", + "metadata": {}, + "source": [ + "Once we loaded the data, we find that the outcome variable, $Y$, is continuous with mean around $3.44$. The treatment variable $A$ is binary with a value of $1$ indicating that a visitor was exposed to the new ad design $A$ as opposed to design $B$ (corresponding to a value of $A$ equal to $1$). The control variables $V$ are a collection of mixed data types, including continuous, discrete and binary variables." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "d14f929c-178b-47fc-8293-29a634194f21", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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25%6.4055830.0000007.0000000.0000000.0000005.000000195.94156921.2062304.0000000.204260...1.1193691.000001637.6995140.0000000.0000004.065465-0.7513550.000001.0000000.021711
50%7.3352480.00000010.0000000.0000001.0000007.000000199.87611726.2025826.0000000.282867...1.2937901.000001667.7634800.0000000.0000005.236465-0.0910560.000001.0000000.034009
75%8.2718811.00000012.0000001.0000001.0000008.000000204.39806733.0711898.0000000.374078...1.4768281.000001695.9726311.0000000.0000006.8982400.5946471.000002.0000000.049100
max13.1972601.00000020.0000001.0000001.00000015.000000220.58441095.41002014.0000000.706249...2.4486611.000001825.6970961.0000001.00000038.4279742.8326731.000009.0000000.139716
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" + ], + "text/plain": [ + " Y A V1 V2 V3 \\\n", + "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 \n", + "mean 7.331239 0.443000 9.290000 0.377000 0.616000 \n", + "std 1.379852 0.496989 3.889605 0.484877 0.486601 \n", + "min 3.435052 0.000000 0.000000 0.000000 0.000000 \n", + "25% 6.405583 0.000000 7.000000 0.000000 0.000000 \n", + "50% 7.335248 0.000000 10.000000 0.000000 1.000000 \n", + "75% 8.271881 1.000000 12.000000 1.000000 1.000000 \n", + "max 13.197260 1.000000 20.000000 1.000000 1.000000 \n", + "\n", + " V4 V5 V6 V7 V8 ... \\\n", + "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 ... \n", + "mean 6.477000 200.088758 28.066028 6.031000 0.294206 ... \n", + "std 2.870141 6.105408 9.920941 2.480361 0.119454 ... \n", + "min 0.000000 183.123067 12.020630 0.000000 0.047160 ... \n", + "25% 5.000000 195.941569 21.206230 4.000000 0.204260 ... \n", + "50% 7.000000 199.876117 26.202582 6.000000 0.282867 ... \n", + "75% 8.000000 204.398067 33.071189 8.000000 0.374078 ... \n", + "max 15.000000 220.584410 95.410020 14.000000 0.706249 ... \n", + "\n", + " V191 V192 V193 V194 V195 \\\n", + "count 1000.000000 1000.00000 1000.000000 1000.000000 1000.000000 \n", + "mean 1.318209 0.94200 1667.454561 0.254000 0.174000 \n", + "std 0.270178 0.23386 44.191913 0.435515 0.379299 \n", + "min 0.668093 0.00000 1524.291675 0.000000 0.000000 \n", + "25% 1.119369 1.00000 1637.699514 0.000000 0.000000 \n", + "50% 1.293790 1.00000 1667.763480 0.000000 0.000000 \n", + "75% 1.476828 1.00000 1695.972631 1.000000 0.000000 \n", + "max 2.448661 1.00000 1825.697096 1.000000 1.000000 \n", + "\n", + " V196 V197 V198 V199 V200 \n", + "count 1000.000000 1000.000000 1000.00000 1000.000000 1000.000000 \n", + "mean 5.804205 -0.076921 0.29400 1.629000 0.037936 \n", + "std 2.655835 1.002754 0.45582 1.388988 0.021688 \n", + "min 1.097708 -3.644652 0.00000 0.000000 0.001478 \n", + "25% 4.065465 -0.751355 0.00000 1.000000 0.021711 \n", + "50% 5.236465 -0.091056 0.00000 1.000000 0.034009 \n", + "75% 6.898240 0.594647 1.00000 2.000000 0.049100 \n", + "max 38.427974 2.832673 1.00000 9.000000 0.139716 \n", + "\n", + "[8 rows x 202 columns]" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.describe()" + ] + }, + { + "cell_type": "markdown", + "id": "d7e45649", + "metadata": {}, + "source": [ + "From the explanatory vriables $V1$ to $V200$, 107 variables are continuous, while 95 are integers. From the integer-variables 59 are binary variables. " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "bde50bfe", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "float64 107\n", + "int64 95\n", + "dtype: int64\n" + ] + }, + { + "data": { + "text/plain": [ + "59" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "print(df.dtypes.value_counts())\n", + "sum((df.max(0) == 1) & (df.min(0) == 0))" + ] + }, + { + "cell_type": "markdown", + "id": "0ce90b4b", + "metadata": {}, + "source": [ + "Let's continue with some visual inspection. First we set the graph settings for graphing." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "b4d2dfb4", + "metadata": {}, + "outputs": [], + "source": [ + "import seaborn as sns\n", + "sns.set()\n", + "colors = sns.color_palette()\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "plt.rcParams['figure.figsize'] = 5., 3.75\n", + "sns.set(font_scale=1.5)\n", + "sns.set_style('whitegrid', {'axes.spines.top': False,\n", + " 'axes.spines.bottom': False,\n", + " 'axes.spines.left': False,\n", + " 'axes.spines.right': False})" + ] + }, + { + "cell_type": "markdown", + "id": "11045894", + "metadata": {}, + "source": [ + "The first figure shows that 443 out of the 1000 customers have been exposed to the new ad design." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "2b5037d3", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "df['A'].value_counts().plot(kind='bar', color=colors)\n", + "\n", + "plt.title('Treatment')\n", + "plt.xlabel('A')\n", + "_ = plt.ylabel('count')" + ] + }, + { + "cell_type": "markdown", + "id": "8c2dc825", + "metadata": {}, + "source": [ + "### Unconditional Estimate of ATE" + ] + }, + { + "cell_type": "markdown", + "id": "8da84d00", + "metadata": {}, + "source": [ + "As a first naive estimate, we could calculate the unconditional average treatment effect (ATE). In other words, we simply take the difference between $Y$ observed for the customers who have been exposed to the treatment $(A=1)$ and those who haven't been exposed $(A=0)$. As a visualization, we plot the density of the outcome variable conditional on the treatment status to get a first impression on the descriptive relationship of $A$ and $Y$. One can see that customers-purchases Y is higher for the customers who saw the add, because the mean of the distribution $A=1$ is shifted to the right." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "57392f09", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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A
0NaN
11.117603
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" + ], + "text/plain": [ + " Y\n", + "A \n", + "0 NaN\n", + "1 1.117603" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df[['A', 'Y']].groupby('A').mean().diff()" + ] + }, + { + "cell_type": "markdown", + "id": "e6f3fa75-a5d4-480c-b627-4b99c6f6afe3", + "metadata": {}, + "source": [ + "The uncoditional effect is $1.117$. Because we use a simulated data set in this example, we know that the true effect is $0.8$. Therefore the unconditional effect overestimates the true effect, because it does not account for individual characteristics. In order to get an estimation on the ATE that explicitly takes the confounding variables $V$ into account, we apply the [DoubleML](https://docs.doubleml.org/stable/index.html) package in the next section." + ] + }, + { + "cell_type": "markdown", + "id": "9e21e9bb", + "metadata": {}, + "source": [ + "## Estimate ATE with the `DoubleML` package" + ] + }, + { + "cell_type": "markdown", + "id": "19830a0a", + "metadata": {}, + "source": [ + "Let’s use the package [DoubleML](https://docs.doubleml.org/stable/index.html) to estimate the average treatment effect of the new ad design on the value of customers' purchases. First, the required packages are imported." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "afaf4106", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import doubleml as dml\n", + "\n", + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.linear_model import LogisticRegression\n", + "\n", + "from sklearn.linear_model import LassoCV, LogisticRegressionCV\n", + "from sklearn.ensemble import RandomForestClassifier, RandomForestRegressor\n", + "from sklearn.preprocessing import StandardScaler\n", + "from sklearn.pipeline import make_pipeline\n", + "from xgboost import XGBClassifier, XGBRegressor\n", + "\n", + "import matplotlib.pyplot as plt\n", + "import scipy.stats as stats" + ] + }, + { + "cell_type": "markdown", + "id": "49242003", + "metadata": {}, + "source": [ + "### The Data Backend: `DoubleMLData`" + ] + }, + { + "cell_type": "markdown", + "id": "3653b53a", + "metadata": {}, + "source": [ + "To start our analysis, we initialize the data backend from the previously loaded data set, i.e., we create a new instance of a [DoubleMLData](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLData.html#doubleml.DoubleMLData) object. During initialization, we specify the roles of the variables in the data set, i.e., in our example the outcome variable $Y$ via the parameter `y_col`, the treatment variable $A$ via `d_cols` and the confounding variables $V$ via `x_cols`." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "abdd10b7", + "metadata": {}, + "outputs": [], + "source": [ + "# Specify explanatory variables for data-backend\n", + "features_base = list(df.columns.values)[2:]\n", + "\n", + "# Initialize DoubleMLData (data-backend of DoubleML)\n", + "data_dml = dml.DoubleMLData(df,\n", + " y_col='Y',\n", + " d_cols='A',\n", + " x_cols=features_base)" + ] + }, + { + "cell_type": "markdown", + "id": "5800ca50-c293-4266-8dd7-00fadcea8d51", + "metadata": {}, + "source": [ + "We can print the data-backend to see the variables, which we have assigned as outcome, treatment and controls." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "37b9bd8a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "================== DoubleMLData Object ==================\n", + "\n", + "------------------ Data summary ------------------\n", + "Outcome variable: Y\n", + "Treatment variable(s): ['A']\n", + "Covariates: ['V1', 'V2', 'V3', 'V4', 'V5', 'V6', 'V7', 'V8', 'V9', 'V10', 'V11', 'V12', 'V13', 'V14', 'V15', 'V16', 'V17', 'V18', 'V19', 'V20', 'V21', 'V22', 'V23', 'V24', 'V25', 'V26', 'V27', 'V28', 'V29', 'V30', 'V31', 'V32', 'V33', 'V34', 'V35', 'V36', 'V37', 'V38', 'V39', 'V40', 'V41', 'V42', 'V43', 'V44', 'V45', 'V46', 'V47', 'V48', 'V49', 'V50', 'V51', 'V52', 'V53', 'V54', 'V55', 'V56', 'V57', 'V58', 'V59', 'V60', 'V61', 'V62', 'V63', 'V64', 'V65', 'V66', 'V67', 'V68', 'V69', 'V70', 'V71', 'V72', 'V73', 'V74', 'V75', 'V76', 'V77', 'V78', 'V79', 'V80', 'V81', 'V82', 'V83', 'V84', 'V85', 'V86', 'V87', 'V88', 'V89', 'V90', 'V91', 'V92', 'V93', 'V94', 'V95', 'V96', 'V97', 'V98', 'V99', 'V100', 'V101', 'V102', 'V103', 'V104', 'V105', 'V106', 'V107', 'V108', 'V109', 'V110', 'V111', 'V112', 'V113', 'V114', 'V115', 'V116', 'V117', 'V118', 'V119', 'V120', 'V121', 'V122', 'V123', 'V124', 'V125', 'V126', 'V127', 'V128', 'V129', 'V130', 'V131', 'V132', 'V133', 'V134', 'V135', 'V136', 'V137', 'V138', 'V139', 'V140', 'V141', 'V142', 'V143', 'V144', 'V145', 'V146', 'V147', 'V148', 'V149', 'V150', 'V151', 'V152', 'V153', 'V154', 'V155', 'V156', 'V157', 'V158', 'V159', 'V160', 'V161', 'V162', 'V163', 'V164', 'V165', 'V166', 'V167', 'V168', 'V169', 'V170', 'V171', 'V172', 'V173', 'V174', 'V175', 'V176', 'V177', 'V178', 'V179', 'V180', 'V181', 'V182', 'V183', 'V184', 'V185', 'V186', 'V187', 'V188', 'V189', 'V190', 'V191', 'V192', 'V193', 'V194', 'V195', 'V196', 'V197', 'V198', 'V199', 'V200']\n", + "Instrument variable(s): None\n", + "No. Observations: 1000\n", + "\n", + "------------------ DataFrame info ------------------\n", + "\n", + "RangeIndex: 1000 entries, 0 to 999\n", + "Columns: 202 entries, Y to V200\n", + "dtypes: float64(107), int64(95)\n", + "memory usage: 1.5 MB\n", + "\n" + ] + } + ], + "source": [ + "print(data_dml)" + ] + }, + { + "cell_type": "markdown", + "id": "714346b8-90dd-4f15-b880-d71f4f60b04e", + "metadata": {}, + "source": [ + "## The Inference Problem and Choosing an Appropriate Model\n", + "\n", + "The inference problem is to determine the causal effect of seeing the new ad design $A$ on a customer's purchases $Y$ once we control for individual characteristics $V$. In our example, we are interested in the average treatment effect. Basically, there are two causal models available in [DoubleMLData](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLData.html#doubleml.DoubleMLData) that can be used to estimate the ATE.\n", + "\n", + "The so-called interactive regression model (IRM) called by [DoubleMLIRM](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLIRM.html) is a flexible model to estimate this causal quantity. The model does not impose functional form restrictions on the underlying regression relationships, for example, linearity or additivity as in a standard linear regression model. This means that the model hosts heterogeneous treatment effects, i.e., account for variation in the effect of the new ad design across customers. Moreover, it is possible to also estimate other causal parameters with the IRM, for example, the average treatment effect on the treated, which might be of interest too.\n", + "\n", + "The second causal model that can be used here is the partially linear regression model (PLR). The PLR incorporates stronger assumptions, for example, that the treatment effect is additive and linear which implies that it does not vary across individuals. We will start with the IRM and include the PLR estimates at the end of the notebook." + ] + }, + { + "cell_type": "markdown", + "id": "9e798e44-8fc8-4c93-9cfb-2d3ad7486dc0", + "metadata": {}, + "source": [ + "## 1. Interactive Regression Model (IRM)\n", + "\n", + "We briefly introduce the Interactive regression model (IRM) where the main regression relationship of interest is provided by\n", + "\n", + "$$Y = g_0(D, X) + U, \\quad E(U | X, D) = 0,$$\n", + "\n", + "where the treatment variable is binary, $D \\in \\lbrace 0,1 \\rbrace$. We consider estimation of the average treatment effects (ATE):\n", + "\n", + "$$\\theta_0 = \\mathbb{E}[g_0(1, X) - g_0(0,X)],$$\n", + "\n", + "when treatment effects are fully heterogeneous. In order to be able to use ML methods, the estimation framework generally requires a property called \"double robustness\" or \"Neyman orthogonality\". Double robustness can be achieved by including the first-stage estimation\n", + "\n", + "$$D = m_0(X) + V, \\quad E(V | X) = 0,$$\n", + "\n", + "which amounts to estimation of the propensity score, i.e., estimation the probability that a customer is exposed to the treatment provided her observed characteristics." + ] + }, + { + "cell_type": "markdown", + "id": "13a5f6f7-64c5-499b-b68a-16ca98943cd6", + "metadata": {}, + "source": [ + "Because data set was simulated we are aware of the true ATE, $\\theta_0=0.8$. The interpretation of this is that exposure to the new ad increases sales (in $100\\$$) by around $0.8$. In the following, we try to estimate this causal effect using the [DoubleML](https://docs.doubleml.org/stable/index.html) package and assess whether the estimated effect is significantly different from zero." + ] + }, + { + "cell_type": "markdown", + "id": "suburban-infrastructure", + "metadata": {}, + "source": [ + "### Benchmark: Model based on Linear Regression" + ] + }, + { + "cell_type": "markdown", + "id": "93f3af17-bcf9-429b-af9a-b90ea1153937", + "metadata": {}, + "source": [ + "Let us first start with a benchmark model that is based on linear regression. Hence, we estimate the functions $g_0(D,X)$ using a linear regrssion model and $m_0(X)$ by using an (unpenalized) logistic regression. In both cases, we include all available characteristics $V$. Later we will assess whether we can find a \"better\" estimator based on ML methods like lasso, random forests and boosting. Because we have 200 variables and 1000 observations, this is approaching a high dimentional setting, therefore the linear regression may not estimate the parameters well." + ] + }, + { + "cell_type": "markdown", + "id": "authorized-school", + "metadata": {}, + "source": [ + "We start by initializing the learners for linear regression and logistic regression. Then, we initialize a causal model object, here of the class [DoubleMLIRM](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLIRM.html). The latter is based on the data-backend we have specified above. To reduce the disproportionate impact of extreme propensity score weights in the interactive model we trim the propensity score from below and above at thresholds of 0.025 and 0.975." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "jewish-listing", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A1.4823850.6602312.2452520.0247520.1883562.776415
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 1.482385 0.660231 2.245252 0.024752 0.188356 2.776415" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize learners\n", + "linreg = make_pipeline(StandardScaler(), LinearRegression())\n", + "logreg_class = make_pipeline(StandardScaler(),LogisticRegression(penalty=\"none\"))\n", + "\n", + "np.random.seed(123)\n", + "dml_irm_regression = dml.DoubleMLIRM(data_dml,\n", + " ml_g = linreg,\n", + " ml_m = logreg_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3,\n", + " n_rep=3)\n", + "\n", + "dml_irm_regression.fit(store_predictions=True)\n", + "reg_summary = dml_irm_regression.summary\n", + "\n", + "reg_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "controlling-collapse", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.68238525]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_irm_regression.coef - 0.8)" + ] + }, + { + "cell_type": "markdown", + "id": "emerging-highlight", + "metadata": {}, + "source": [ + "We see that the causal estimate suffers from a substantial bias and is quite noisy: The ATE is overestimated by around 0.68 and the standard error is around 0.66. The corresponding confidence intervals are relatively wide, although they do not cover the value of zero. Hence, we can conclude that the average treatment effect is significantly different from zero at the 5% significance level." + ] + }, + { + "cell_type": "markdown", + "id": "neutral-converter", + "metadata": {}, + "source": [ + "Next, let us find out if we are able to use ML methods to find estimators that have a lower bias and a smaller standard error than the benchmark." + ] + }, + { + "cell_type": "markdown", + "id": "723b8e6c", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Lasso\n", + "\n", + "We estimate the nuisance components $g_0$ and $m_0$ using lasso as provided by [scikit-learn](https://scikit-learn.org). We load the learner by initializing instances from the classes [LassoCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html) and [LogisticRegressionCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegressionCV.html). Here we specify that the lasso should use the value of $\\lambda$ that minimizes the cross-validated mean squared error, which is based on 5-fold cross validation. We initialize the [DoubleMLIRM](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLIRM.html) object and use the newly defined learners." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "73cbfd4b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.8342780.07051111.8319542.668556e-320.696080.972476
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.834278 0.070511 11.831954 2.668556e-32 0.69608 0.972476" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# initialize Lasso learners\n", + "lasso = make_pipeline(StandardScaler(), LassoCV(cv=5, max_iter=20000)) \n", + "lasso_class = make_pipeline(StandardScaler(),\n", + " LogisticRegressionCV(cv=5, penalty='l1', solver='liblinear', \n", + " Cs = 4, max_iter=1000)) \n", + "\n", + "\n", + "# Initialize DoubleMLIRM model\n", + "np.random.seed(123)\n", + "dml_irm_lasso = dml.DoubleMLIRM(data_dml,\n", + " ml_g = lasso,\n", + " ml_m = lasso_class,\n", + " trimming_threshold = 0.025, \n", + " n_folds = 3)\n", + "\n", + "dml_irm_lasso.fit(store_predictions=True) \n", + "lasso_summary = dml_irm_lasso.summary\n", + "\n", + "lasso_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "stock-bookmark", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.03427819]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_irm_lasso.coef - 0.8)" + ] + }, + { + "cell_type": "markdown", + "id": "religious-algebra", + "metadata": {}, + "source": [ + "We see that the lasso-based estimate for the ATE is $0.83$ and, hence, much closer to the true value of $0.8$ than in the benchmark $1.48$. Moreover, we can achieve improvements in terms of estimation precision as can be recognized from the smaller standard error. " + ] + }, + { + "cell_type": "markdown", + "id": "33d06b0d", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Random Forest" + ] + }, + { + "cell_type": "markdown", + "id": "4d9d008a-5b6a-4acf-93b9-b26599541653", + "metadata": {}, + "source": [ + "Alternatively, we can repeat this procedure with other machine learning methods, for example a random forest learner as provided by the [RandomForestRegressor](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html) and [RandomForestClassifier](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html) class in [scikit-learn](https://scikit-learn.org)." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "2092891a", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.862030.0822910.4754551.119983e-250.7007431.023316
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.86203 0.08229 10.475455 1.119983e-25 0.700743 1.023316" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Random Forest\n", + "randomForest = RandomForestRegressor()\n", + "randomForest_class = RandomForestClassifier()\n", + "\n", + "np.random.seed(123)\n", + "dml_irm_forest = dml.DoubleMLIRM(data_dml,\n", + " ml_g = randomForest,\n", + " ml_m = randomForest_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3)\n", + "\n", + "#Set nuisance-part specific parameters\n", + "dml_irm_forest.set_ml_nuisance_params('ml_g0', 'A', {\n", + " 'max_features': 200, 'n_estimators': 250})\n", + "dml_irm_forest.set_ml_nuisance_params('ml_g1', 'A', {\n", + " 'max_features': 200, 'n_estimators': 250})\n", + "dml_irm_forest.set_ml_nuisance_params('ml_m', 'A', {\n", + " 'max_features': 200, 'n_estimators': 250})\n", + "\n", + "dml_irm_forest.fit(store_predictions=True) \n", + "forest_summary = dml_irm_forest.summary\n", + "\n", + "forest_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "vital-insight", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.0620296]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_irm_forest.coef - 0.8)" + ] + }, + { + "cell_type": "markdown", + "id": "d4b6e16b-6cb9-40d8-a4fa-c438f23b49f3", + "metadata": {}, + "source": [ + "The results are relatively similar to the one obtained by lasso with a bias and standard errors that are slightly greater than before." + ] + }, + { + "cell_type": "markdown", + "id": "9ac68b60", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Extreme Gradient Boosting" + ] + }, + { + "cell_type": "markdown", + "id": "cc71c762-8497-43e5-a151-a5239641d510", + "metadata": {}, + "source": [ + "Next, we estimate the ATE using extreme gradient boosting as provided by [xgboost](https://docs.getml.com/latest/api_reference/predictors.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "90b9ef4e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.7392250.0925117.9906481.342310e-150.5579060.920544
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.739225 0.092511 7.990648 1.342310e-15 0.557906 0.920544" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "boost = XGBRegressor(n_jobs=1, objective = \"reg:squarederror\")\n", + "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", + " objective = \"binary:logistic\", eval_metric = \"logloss\")\n", + "\n", + "np.random.seed(123)\n", + "dml_irm_boost = dml.DoubleMLIRM(data_dml,\n", + " ml_g = boost,\n", + " ml_m = boost_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3)\n", + "\n", + "#Set nuisance-part specific parameters\n", + "dml_irm_boost.set_ml_nuisance_params('ml_g0', 'A', {\n", + " 'n_estimators': 30, 'eta': 0.2})\n", + "dml_irm_boost.set_ml_nuisance_params('ml_g1', 'A', {\n", + " 'n_estimators': 30, 'eta': 0.2})\n", + "dml_irm_boost.set_ml_nuisance_params('ml_m', 'A', {\n", + " 'n_estimators': 15, 'eta': 0.2})\n", + "\n", + "dml_irm_boost.fit(store_predictions=True)\n", + "boost_summary = dml_irm_boost.summary\n", + "boost_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "traditional-ribbon", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [-0.06077519]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_irm_boost.coef - 0.8)" + ] + }, + { + "cell_type": "markdown", + "id": "9ee7f068-1ac4-4d7d-99a7-5c68c91e8b51", + "metadata": {}, + "source": [ + "The estimated coefficient is close to the true ATE of $0.8$ but has a small negative bias. The interpretation of the results obtained with lasso, random forests and boosting are very similar. In all cases we are able to reject the null hypothesis that the ad has no effect on the sales." + ] + }, + { + "cell_type": "markdown", + "id": "fba54a14-c685-4948-819d-94a99d88e94a", + "metadata": {}, + "source": [ + "### Summary of IRM Results\n", + "\n", + "We define a small function which calculates the bias from the true parameter $0.8$. Then we save the estimates, bias and confidence intervals for peresentation and comparision." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "5e16a294", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " coef Bias 2.5 % 97.5 %\n", + "regression 1.482 0.682 0.188 2.776\n", + "lasso 0.834 0.034 0.696 0.972\n", + "forest 0.862 0.062 0.701 1.023\n", + "xgboost 0.739 0.061 0.558 0.921" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def bias(x):\n", + " x=x - 0.8\n", + " x=round(abs(x),3)\n", + " return x\n", + "\n", + "irm_summary = pd.concat((reg_summary, lasso_summary, forest_summary, boost_summary))\n", + "irm_summary.index = ['regression','lasso', 'forest', 'xgboost']\n", + "irm_summary=irm_summary[['coef', '2.5 %', '97.5 %']]\n", + "irm_summary.insert(1, \"Bias\", [bias(irm_summary.loc['regression','coef']), \n", + " bias(irm_summary.loc['lasso','coef']), \n", + " bias(irm_summary.loc['forest','coef']), \n", + " bias(irm_summary.loc['xgboost','coef'])])\n", + "irm_summary.round(3)" + ] + }, + { + "cell_type": "markdown", + "id": "b29e412d-d86f-46b4-840f-cbbe082faf0b", + "metadata": {}, + "source": [ + "### Conclusion\n", + "\n", + "We conclude that the interactive regression model (IRM) estimates are close to the true coefficient value, if the nuisance components are estimated with machine learning methods. The best results in terms of the smallest bias and standard errors is achieved by the lasso-based DML estimator for the ATE. The performance of the tree-based methods: random forests and extreme gradient boosting are comparable. All of the ML-based estimators have exhibited a superior performance to the benchmark based on linear and logistic regression.\n" + ] + }, + { + "cell_type": "markdown", + "id": "f50297c5", + "metadata": {}, + "source": [ + "## 2. Partially Linear Regression Model (PLR)\n", + "\n", + "The [DoubleML](https://docs.doubleml.org/stable/index.html) package also includes the partial linear regression (PLR) Model, which assumes the data have an additive structure. Although we don't know if this structure really holds for the underlying data generating process, we can apply this model and see how the estimates compare to those from the IRM." + ] + }, + { + "cell_type": "markdown", + "id": "fa24e6e1-b878-401f-b38a-c29cc0620c2c", + "metadata": {}, + "source": [ + "We estimate the function $g_0$ and $m_0$ in the following PLR model:\n", + "\n", + "\\begin{eqnarray}\n", + "& Y = D\\theta_0 + g_0(X) + \\zeta, &\\quad E[\\zeta \\mid D,X]= 0,\\\\\n", + "& D = m_0(X) + V, &\\quad E[V \\mid X] = 0.\n", + "\\end{eqnarray}\n", + "\n", + "To estimate the causal parameter $\\theta_0$ here, we use double machine learning with 3-fold cross-fitting. The steps of our analysis are very similar to the IRM cases with the difference being that we use a model class [DoubleMLPLR](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLPLR.html) for estimation." + ] + }, + { + "cell_type": "markdown", + "id": "331a36d6", + "metadata": {}, + "source": [ + "### Benchmark: Model based on Linear Regression" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "1432e567-d221-490d-9361-39b9072cb6d4", + "metadata": { + "scrolled": true, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.7740710.07021611.0241172.923733e-280.636450.911692
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.774071 0.070216 11.024117 2.923733e-28 0.63645 0.911692" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "linreg = make_pipeline(StandardScaler(), LinearRegression())\n", + "logreg_class = make_pipeline(StandardScaler(),LogisticRegression(penalty=\"none\"))\n", + "\n", + "np.random.seed(123)\n", + "# Initialize DoubleMLPLR model\n", + "dml_plr_regression = dml.DoubleMLPLR(data_dml,\n", + " ml_g = linreg,\n", + " ml_m = logreg_class,\n", + " n_folds = 3)\n", + "\n", + "dml_plr_regression.fit(store_predictions=True)\n", + "reg_summary = dml_plr_regression.summary\n", + "\n", + "reg_summary" + ] + }, + { + "cell_type": "markdown", + "id": "4dd8948f", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Lasso" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "0bbbc3ce", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.7845790.07041411.1424197.797228e-290.646570.922587
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.784579 0.070414 11.142419 7.797228e-29 0.64657 0.922587" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.random.seed(123)\n", + "# Initialize DoubleMLPLR model\n", + "dml_plr_lasso = dml.DoubleMLPLR(data_dml,\n", + " ml_g = lasso,\n", + " ml_m = lasso_class,\n", + " n_folds = 3)\n", + "\n", + "dml_plr_lasso.fit(store_predictions=True)\n", + "lasso_summary=dml_plr_lasso.summary\n", + "\n", + "lasso_summary" + ] + }, + { + "cell_type": "markdown", + "id": "a4ed2694", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Random Forests" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "e5f3ac90", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.8238990.07347411.2135293.499555e-290.6798930.967904
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.823899 0.073474 11.213529 3.499555e-29 0.679893 0.967904" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "randomForest = RandomForestRegressor()\n", + "randomForest_class = RandomForestClassifier()\n", + "\n", + "np.random.seed(123)\n", + "dml_plr_forest = dml.DoubleMLPLR(data_dml,\n", + " ml_g = randomForest,\n", + " ml_m = randomForest_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_forest.fit(store_predictions=True)\n", + "forest_summary = dml_plr_forest.summary\n", + "\n", + "forest_summary" + ] + }, + { + "cell_type": "markdown", + "id": "6aa9af04", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Extreme Gradient Boosting" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "6fab5d3a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.8145550.07120311.4399292.641013e-300.6750.95411
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.814555 0.071203 11.439929 2.641013e-30 0.675 0.95411" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "boost = XGBRegressor(n_jobs = 1, objective = \"reg:squarederror\", #where did you get tuning params? #grid search?\n", + " eta = 0.1, n_estimators = 57, max_depth = 2)\n", + "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", + " objective = \"binary:logistic\",\n", + " eval_metric = \"logloss\",\n", + " eta = 0.1, n_estimators = 10,\n", + " max_depth = 3)\n", + "\n", + "np.random.seed(123)\n", + "dml_plr_boost = dml.DoubleMLPLR(data_dml,\n", + " ml_g = boost,\n", + " ml_m = boost_class,\n", + " n_folds = 3)\n", + "dml_plr_boost.fit()\n", + "boost_summary = dml_plr_boost.summary\n", + "\n", + "boost_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "dba8d33c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefBias2.5 %97.5 %
regression0.7740.0260.6360.912
lasso0.7850.0150.6470.923
forest0.8240.0240.6800.968
xgboost0.8150.0150.6750.954
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" + ], + "text/plain": [ + " coef Bias 2.5 % 97.5 %\n", + "regression 0.774 0.026 0.636 0.912\n", + "lasso 0.785 0.015 0.647 0.923\n", + "forest 0.824 0.024 0.680 0.968\n", + "xgboost 0.815 0.015 0.675 0.954" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plr_summary = pd.concat((reg_summary, lasso_summary, forest_summary, boost_summary))\n", + "plr_summary.index = ['regression','lasso', 'forest', 'xgboost']\n", + "plr_summary=plr_summary[['coef', '2.5 %', '97.5 %']]\n", + "plr_summary.insert(1, \"Bias\", [bias(plr_summary.loc['regression','coef']), \n", + " bias(plr_summary.loc['lasso','coef']), \n", + " bias(plr_summary.loc['forest','coef']), \n", + " bias(plr_summary.loc['xgboost','coef'])])\n", + "plr_summary.round(3) " + ] + }, + { + "cell_type": "markdown", + "id": "27d1d2a9-beed-493d-ae92-8d4e92cde8ae", + "metadata": {}, + "source": [ + "### Summary of IRM and PLR Results" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "1b4ddf50-50de-4bab-a110-767b8d50df21", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefBias2.5 %97.5 %
ModelML
IRMregression1.4820.6820.1882.776
lasso0.8340.0340.6960.972
forest0.8620.0620.7011.023
xgboost0.7390.0610.5580.921
PLRregression0.7740.0260.6360.912
lasso0.7850.0150.6470.923
forest0.8240.0240.6800.968
xgboost0.8150.0150.6750.954
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" + ], + "text/plain": [ + " coef Bias 2.5 % 97.5 %\n", + "Model ML \n", + "IRM regression 1.482 0.682 0.188 2.776\n", + " lasso 0.834 0.034 0.696 0.972\n", + " forest 0.862 0.062 0.701 1.023\n", + " xgboost 0.739 0.061 0.558 0.921\n", + "PLR regression 0.774 0.026 0.636 0.912\n", + " lasso 0.785 0.015 0.647 0.923\n", + " forest 0.824 0.024 0.680 0.968\n", + " xgboost 0.815 0.015 0.675 0.954" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df_summary = pd.concat((irm_summary,plr_summary)).reset_index().rename(columns={'index': 'ML'})\n", + "df_summary['Model'] = np.concatenate((np.repeat('IRM', 4), np.repeat('PLR', 4)))\n", + "df_summary.set_index(['Model', 'ML']).round(3)" + ] + }, + { + "cell_type": "markdown", + "id": "64aa3065-da5c-49b9-88f2-5c08c1b7e617", + "metadata": {}, + "source": [ + "### Conclusion\n", + "\n", + "As in the IRM model, the ML-based PLR models are associated with a smaller bias as compared to the model that is based on linear regression. It seems that the estimates obtained from the PLR are slightly closer to the true ATE than those from the IRM analysis. This might suggest, that the parametric assumptions (i.e., an additive and homogeneous causal effect) that are incorporated in the PLR turn out to be **not restrictive** in our example data set. However, if both models are based on appropriate ML learners, the conclusions are very similar. In all cases, the ML-based estimates were very close to the true ATE and we were always able to reject the null hypothesis of a zero-effect at all common significance levels. In terms of the A/B testing example, it can be concluded that the new ad increases customers purchases (in $100\\$$) by around 0.8 on average and that this effect is significantly different from zero at the 5% significance level. The results are summarized in the graphic below." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "c80cadcc", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(8, 9))\n", + "colors = sns.color_palette()\n", + "for ind, model in enumerate(['IRM', 'PLR']):\n", + " sns.set(font_scale=1.15)\n", + " plt.subplot(3, 1, ind+1)\n", + " this_df = df_summary.query('Model == @model')\n", + " errors = np.full((2, this_df.shape[0]), np.nan)\n", + " errors[0, :] = this_df['coef'] - this_df['2.5 %']\n", + " errors[1, :] = this_df['97.5 %'] - this_df['coef']\n", + " plt.errorbar(this_df.ML, this_df.coef, fmt='o', yerr=errors,\n", + " color=colors[ind], ecolor=colors[ind])\n", + " plt.ylim([0.5, 1.2])\n", + " plt.title(model)\n", + " plt.ylabel('Coeff. and 95%-CI')\n", + " plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", + " plt.legend(bbox_to_anchor=(1.04,0.5), loc=\"best\", borderaxespad=0)\n", + "\n", + "_ = plt.xlabel('ML method')\n" + ] + }, + { + "cell_type": "markdown", + "id": "3aa8d603-0df5-48c6-ad62-ac5ffe3e8ada", + "metadata": {}, + "source": [ + "______\n", + "\n", + "**Notes and Acknowledgement**\n", + "\n", + "We would like to thank the organizers of the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge) for setting up this data challenge and the numerous synthetic data examples that are all available online. Although the data examples in the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge) do not explicitly adress A/B testing, we put the data example here in this context to give a tractable example on the use of causal machine learning in practice. The parameters for the random forests and extreme gradient boosting learners have been tuned externally. The corresponding tuning notebook will be uploaded in the examples gallery in the future." + ] + }, + { + "cell_type": "markdown", + "id": "egyptian-platform", + "metadata": {}, + "source": [ + "## References\n", + "\n", + "Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W. and Robins, J. (2018), Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21: C1-C68. doi:10.1111/ectj.12097." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From b446cc3129134a86b679238baa72009ab9e10592 Mon Sep 17 00:00:00 2001 From: JoshuaFalke <61840730+JoshuaFalke@users.noreply.github.com> Date: Fri, 20 May 2022 23:11:33 +0200 Subject: [PATCH 02/20] Add files via upload --- doc/examples/py_double_ml_abtest.ipynb | 6408 +++++++++++------ .../py_double_ml_abtest_no_split_linreg.ipynb | 4059 +++++++++++ doc/examples/py_double_ml_abtest_tuning.ipynb | 1931 +++++ 3 files changed, 10013 insertions(+), 2385 deletions(-) create mode 100644 doc/examples/py_double_ml_abtest_no_split_linreg.ipynb create mode 100644 doc/examples/py_double_ml_abtest_tuning.ipynb diff --git a/doc/examples/py_double_ml_abtest.ipynb b/doc/examples/py_double_ml_abtest.ipynb index 65a755cd..bcf32f35 100644 --- a/doc/examples/py_double_ml_abtest.ipynb +++ b/doc/examples/py_double_ml_abtest.ipynb @@ -1,2385 +1,4023 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "consecutive-cabinet", - "metadata": {}, - "source": [ - "# Python: A/B Testing with DoubleML" - ] - }, - { - "cell_type": "markdown", - "id": "opponent-indonesian", - "metadata": {}, - "source": [ - "\"An\n", - "\n", - "Image Source Freepik http://www.freepik.com, Designed by macrovector\n" - ] - }, - { - "cell_type": "markdown", - "id": "c7c96f88", - "metadata": {}, - "source": [ - "In this notebook, we illustrate how the [DoubleML](https://docs.doubleml.org/stable/index.html) package can be used to estimate the causal effect of seeing a new ad design on customers' purchases in a webshop. The [DoubleML](https://docs.doubleml.org/stable/index.html) package for Python and R provides an implementation of the double / debiased machine learning (DML) framework of [Chernozhukov et al. (2018)](https://arxiv.org/abs/1608.00060) and can be used to estimate causal effects based on machine learning (ML) methods.\n", - "\n", - "## A/B Testing\n", - "\n", - "A/B testing is a frequently used framework to perform causal inference in practice. For example, a manager of a webshop might be interested in optimally adapt the webshop design according to users' preferences. She might want to estimate the effect of a new ad design, which is displayed on the starting page, on a customer's purchases (in $100\\$$). A/B tests refer to an experimental design in which a certain treatment, for example a new ad design (called \"Version $A$\"), that is randomly assigned to groups of individuals who are otherwise assigned to \"Version $B$\". The assignment can also be randomized among subgroups, i.e., randomly displayed to visitors once one or multiple of their characteristics are taken into consideration. For example, only visitors who have already purchased a product before might be exposed to the new ad. The goal is to conclude whether the treatment (= the new ad) has an effect on an outcome of interest (= monetary value of products purchased in $100\\$$). Additional examples refer to improvement of a user experience on a website or estimation of price elasticities. Websites and apps are ideal for running A/B tests because they make it very easy to precisely direct the treatment to visitors and users (or to specific subgroups of them).\n", - "\n", - "## Scenario\n", - "\n", - "Let's consider the following stylized scenario. The manager of a webshop is performing A/B testing to estimate the effect of a new ad design $A$, on customers' purchases, $Y$. The treatment is assigned randomly conditional on the visitors' characteristics $V$. Such characteristics could be collected from a customer's shoppers account, for example. These might include the number of previous purchases, time since last purchase, length of stay on a page as well as whether a customer has a rewards card, among other characteristics. Let's assume the conditional randomization has been conducted properly, such that a tidy data set has been collected. Now, a data scientist wants to evaluate whether the new ad design causally affected the sales, by using the [DoubleML](https://docs.doubleml.org/stable/index.html) package.\n", - "\n", - "### Why control for individual characteristics?\n", - "\n", - "Before we start the case study, let us briefly address the question why we need to include individual characteristics in our analysis at all. There are mainly two reasons why we want to control for observable characteristics. First of all, so-called confounders, i.e., variables that have a causal effect on both the treatment variable and the outcome variable, possibly create a bias in our estimate. In order to uncover the true causal effect of the treatment, it is necessary that our causal framework takes all confounding variables into account. A second reason to include individual characteristics is efficiency. The more variation can be explained within our causal framework, the more precise will be the resulting estimate. In practical terms, greater efficiency leads to tighter confidence intervals and smaller standard errors and p-values.\n", - "\n", - "### Why use machine learning to analyze A/B tests?\n", - "\n", - "ML methods have turned out to be very flexible in terms of modeling complex relationships of explanatory variables and dependent variables and, thus, have exhibited a great predictive performance in many applications. In the double machine learning approach ([Chernozhukov et al. (2018)](https://arxiv.org/abs/1608.00060)), ML methods are used for modelling so-called nuisance parts. In terms of the A/B case study considered here, ML tools can be used to flexibly control for confounding variables. For example, a linear parametric specification as in a standard linear regression model might not be correct and, hence, not sufficient to address the underlying confounding. Moreover, by using powerful ML techniques, the causal model will likely be able to explain a greater share of the total variation and, hence, lead to more precise estimation." - ] - }, - { - "cell_type": "markdown", - "id": "0ec5b0cf", - "metadata": {}, - "source": [ - "## Data \n", - "\n", - "As an illustrative example we use a data set from the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge). In this challenge, a great number of data sets have been generated in a way that they mimic distributional relationships that are found in many economic real data applications. Although the data have not been generated explicitly to address an A/B testing case study, they are well-suited for demonstration purposes. We will focus on one of the many different data genereting processes (DGP) that we picked at random, in this particualar case a data set called `high42`. An advantage of using the [ACIC 2019 data](https://sites.google.com/view/acic2019datachallenge/data-challenge) is that we know the true average treatment effect which is 0.8 in our data set.\n", - "\n", - "First we load the data." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "e39d4dd0", - "metadata": {}, - "outputs": [], - "source": [ - "import pandas as pd\n", - "\n", - "#fetch_ACIChigh42 needs to be defined\n", - "#df = fetch_ACIChigh42(return_type='DataFrame')\n", - "\n", - "#load code locally\n", - "df = pd.read_csv('data/high42.csv', sep=',', na_values=\".\")\n", - "\n", - "#code can also be loaded using a URL of the data\n", - "#url = 'https://raw.githubusercontent.com/DoubleML/doubleml-hiwi-sandbox/master/case_studies/AB_testing/data/high42.CSV?token=AQWGKQRE57BBRGOCBPSNBJTBD57ZQ'\n", - "#df = pd.read_csv(url)" - ] - }, - { - "cell_type": "markdown", - "id": "11525056-cdec-4916-9cb4-aa4268e99175", - "metadata": {}, - "source": [ - "We see that the data set consists of 1000 observations (= website visitors) and 202 variables. The $Y$ column represents the number of page visits. The treatment variable $A$ is binary with a value 1 indicating that a customer has been exposed to the new ad design (and value 0 otherwise). The remaining 200 columns $V$ represent individual characteristics of the customers." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "10edc74d", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(1000, 202)\n" - ] - } - ], - "source": [ - "print(df.shape)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "6760c009", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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YAV1V2V3V4V5V6V7V8...V191V192V193V194V195V196V197V198V199V200
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18.333672112014199.65359619.28127070.514842...1.33052211661.484439106.766661-0.395402040.056518
27.472758014112194.20779224.58933150.309199...1.38415111658.939293005.6477941.112766000.013442
36.50231910109201.83802425.51391840.160160...1.22030311650.801625005.370363-0.305842040.034632
47.043758112009201.36044331.16064160.291976...1.17009411676.818876003.4465322.440661010.017514
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5 rows × 202 columns

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" - ], - "text/plain": [ - " Y A V1 V2 V3 V4 V5 V6 V7 V8 ... \\\n", - "0 7.358185 1 10 0 0 7 192.793769 23.676950 8 0.185443 ... \n", - "1 8.333672 1 12 0 1 4 199.653596 19.281270 7 0.514842 ... \n", - "2 7.472758 0 14 1 1 2 194.207792 24.589331 5 0.309199 ... \n", - "3 6.502319 1 0 1 0 9 201.838024 25.513918 4 0.160160 ... \n", - "4 7.043758 1 12 0 0 9 201.360443 31.160641 6 0.291976 ... \n", - "\n", - " V191 V192 V193 V194 V195 V196 V197 V198 V199 \\\n", - "0 1.462837 1 1627.274196 0 0 4.683956 0.565667 0 3 \n", - "1 1.330522 1 1661.484439 1 0 6.766661 -0.395402 0 4 \n", - "2 1.384151 1 1658.939293 0 0 5.647794 1.112766 0 0 \n", - "3 1.220303 1 1650.801625 0 0 5.370363 -0.305842 0 4 \n", - "4 1.170094 1 1676.818876 0 0 3.446532 2.440661 0 1 \n", - "\n", - " V200 \n", - "0 0.024338 \n", - "1 0.056518 \n", - "2 0.013442 \n", - "3 0.034632 \n", - "4 0.017514 \n", - "\n", - "[5 rows x 202 columns]" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df.head()" - ] - }, - { - "cell_type": "markdown", - "id": "c6e32feb", - "metadata": {}, - "source": [ - "### Descriptive Statistics\n" - ] - }, - { - "cell_type": "markdown", - "id": "horizontal-hanging", - "metadata": {}, - "source": [ - "Once we loaded the data, we find that the outcome variable, $Y$, is continuous with mean around $3.44$. The treatment variable $A$ is binary with a value of $1$ indicating that a visitor was exposed to the new ad design $A$ as opposed to design $B$ (corresponding to a value of $A$ equal to $1$). The control variables $V$ are a collection of mixed data types, including continuous, discrete and binary variables." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "d14f929c-178b-47fc-8293-29a634194f21", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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YAV1V2V3V4V5V6V7V8...V191V192V193V194V195V196V197V198V199V200
count1000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.000000...1000.0000001000.000001000.0000001000.0000001000.0000001000.0000001000.0000001000.000001000.0000001000.000000
mean7.3312390.4430009.2900000.3770000.6160006.477000200.08875828.0660286.0310000.294206...1.3182090.942001667.4545610.2540000.1740005.804205-0.0769210.294001.6290000.037936
std1.3798520.4969893.8896050.4848770.4866012.8701416.1054089.9209412.4803610.119454...0.2701780.2338644.1919130.4355150.3792992.6558351.0027540.455821.3889880.021688
min3.4350520.0000000.0000000.0000000.0000000.000000183.12306712.0206300.0000000.047160...0.6680930.000001524.2916750.0000000.0000001.097708-3.6446520.000000.0000000.001478
25%6.4055830.0000007.0000000.0000000.0000005.000000195.94156921.2062304.0000000.204260...1.1193691.000001637.6995140.0000000.0000004.065465-0.7513550.000001.0000000.021711
50%7.3352480.00000010.0000000.0000001.0000007.000000199.87611726.2025826.0000000.282867...1.2937901.000001667.7634800.0000000.0000005.236465-0.0910560.000001.0000000.034009
75%8.2718811.00000012.0000001.0000001.0000008.000000204.39806733.0711898.0000000.374078...1.4768281.000001695.9726311.0000000.0000006.8982400.5946471.000002.0000000.049100
max13.1972601.00000020.0000001.0000001.00000015.000000220.58441095.41002014.0000000.706249...2.4486611.000001825.6970961.0000001.00000038.4279742.8326731.000009.0000000.139716
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8 rows × 202 columns

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" - ], - "text/plain": [ - " Y A V1 V2 V3 \\\n", - "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 \n", - "mean 7.331239 0.443000 9.290000 0.377000 0.616000 \n", - "std 1.379852 0.496989 3.889605 0.484877 0.486601 \n", - "min 3.435052 0.000000 0.000000 0.000000 0.000000 \n", - "25% 6.405583 0.000000 7.000000 0.000000 0.000000 \n", - "50% 7.335248 0.000000 10.000000 0.000000 1.000000 \n", - "75% 8.271881 1.000000 12.000000 1.000000 1.000000 \n", - "max 13.197260 1.000000 20.000000 1.000000 1.000000 \n", - "\n", - " V4 V5 V6 V7 V8 ... \\\n", - "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 ... \n", - "mean 6.477000 200.088758 28.066028 6.031000 0.294206 ... \n", - "std 2.870141 6.105408 9.920941 2.480361 0.119454 ... \n", - "min 0.000000 183.123067 12.020630 0.000000 0.047160 ... \n", - "25% 5.000000 195.941569 21.206230 4.000000 0.204260 ... \n", - "50% 7.000000 199.876117 26.202582 6.000000 0.282867 ... \n", - "75% 8.000000 204.398067 33.071189 8.000000 0.374078 ... \n", - "max 15.000000 220.584410 95.410020 14.000000 0.706249 ... \n", - "\n", - " V191 V192 V193 V194 V195 \\\n", - "count 1000.000000 1000.00000 1000.000000 1000.000000 1000.000000 \n", - "mean 1.318209 0.94200 1667.454561 0.254000 0.174000 \n", - "std 0.270178 0.23386 44.191913 0.435515 0.379299 \n", - "min 0.668093 0.00000 1524.291675 0.000000 0.000000 \n", - "25% 1.119369 1.00000 1637.699514 0.000000 0.000000 \n", - "50% 1.293790 1.00000 1667.763480 0.000000 0.000000 \n", - "75% 1.476828 1.00000 1695.972631 1.000000 0.000000 \n", - "max 2.448661 1.00000 1825.697096 1.000000 1.000000 \n", - "\n", - " V196 V197 V198 V199 V200 \n", - "count 1000.000000 1000.000000 1000.00000 1000.000000 1000.000000 \n", - "mean 5.804205 -0.076921 0.29400 1.629000 0.037936 \n", - "std 2.655835 1.002754 0.45582 1.388988 0.021688 \n", - "min 1.097708 -3.644652 0.00000 0.000000 0.001478 \n", - "25% 4.065465 -0.751355 0.00000 1.000000 0.021711 \n", - "50% 5.236465 -0.091056 0.00000 1.000000 0.034009 \n", - "75% 6.898240 0.594647 1.00000 2.000000 0.049100 \n", - "max 38.427974 2.832673 1.00000 9.000000 0.139716 \n", - "\n", - "[8 rows x 202 columns]" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df.describe()" - ] - }, - { - "cell_type": "markdown", - "id": "d7e45649", - "metadata": {}, - "source": [ - "From the explanatory vriables $V1$ to $V200$, 107 variables are continuous, while 95 are integers. From the integer-variables 59 are binary variables. " - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "bde50bfe", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "float64 107\n", - "int64 95\n", - "dtype: int64\n" - ] - }, - { - "data": { - "text/plain": [ - "59" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "print(df.dtypes.value_counts())\n", - "sum((df.max(0) == 1) & (df.min(0) == 0))" - ] - }, - { - "cell_type": "markdown", - "id": "0ce90b4b", - "metadata": {}, - "source": [ - "Let's continue with some visual inspection. First we set the graph settings for graphing." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "b4d2dfb4", - "metadata": {}, - "outputs": [], - "source": [ - "import seaborn as sns\n", - "sns.set()\n", - "colors = sns.color_palette()\n", - "\n", - "import matplotlib.pyplot as plt\n", - "\n", - "plt.rcParams['figure.figsize'] = 5., 3.75\n", - "sns.set(font_scale=1.5)\n", - "sns.set_style('whitegrid', {'axes.spines.top': False,\n", - " 'axes.spines.bottom': False,\n", - " 'axes.spines.left': False,\n", - " 'axes.spines.right': False})" - ] - }, - { - "cell_type": "markdown", - "id": "11045894", - "metadata": {}, - "source": [ - "The first figure shows that 443 out of the 1000 customers have been exposed to the new ad design." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "2b5037d3", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "df['A'].value_counts().plot(kind='bar', color=colors)\n", - "\n", - "plt.title('Treatment')\n", - "plt.xlabel('A')\n", - "_ = plt.ylabel('count')" - ] - }, - { - "cell_type": "markdown", - "id": "8c2dc825", - "metadata": {}, - "source": [ - "### Unconditional Estimate of ATE" - ] - }, - { - "cell_type": "markdown", - "id": "8da84d00", - "metadata": {}, - "source": [ - "As a first naive estimate, we could calculate the unconditional average treatment effect (ATE). In other words, we simply take the difference between $Y$ observed for the customers who have been exposed to the treatment $(A=1)$ and those who haven't been exposed $(A=0)$. As a visualization, we plot the density of the outcome variable conditional on the treatment status to get a first impression on the descriptive relationship of $A$ and $Y$. One can see that customers-purchases Y is higher for the customers who saw the add, because the mean of the distribution $A=1$ is shifted to the right." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "57392f09", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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Y
A
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" - ], - "text/plain": [ - " Y\n", - "A \n", - "0 NaN\n", - "1 1.117603" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df[['A', 'Y']].groupby('A').mean().diff()" - ] - }, - { - "cell_type": "markdown", - "id": "e6f3fa75-a5d4-480c-b627-4b99c6f6afe3", - "metadata": {}, - "source": [ - "The uncoditional effect is $1.117$. Because we use a simulated data set in this example, we know that the true effect is $0.8$. Therefore the unconditional effect overestimates the true effect, because it does not account for individual characteristics. In order to get an estimation on the ATE that explicitly takes the confounding variables $V$ into account, we apply the [DoubleML](https://docs.doubleml.org/stable/index.html) package in the next section." - ] - }, - { - "cell_type": "markdown", - "id": "9e21e9bb", - "metadata": {}, - "source": [ - "## Estimate ATE with the `DoubleML` package" - ] - }, - { - "cell_type": "markdown", - "id": "19830a0a", - "metadata": {}, - "source": [ - "Let’s use the package [DoubleML](https://docs.doubleml.org/stable/index.html) to estimate the average treatment effect of the new ad design on the value of customers' purchases. First, the required packages are imported." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "afaf4106", - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import pandas as pd\n", - "import doubleml as dml\n", - "\n", - "from sklearn.linear_model import LinearRegression\n", - "from sklearn.linear_model import LogisticRegression\n", - "\n", - "from sklearn.linear_model import LassoCV, LogisticRegressionCV\n", - "from sklearn.ensemble import RandomForestClassifier, RandomForestRegressor\n", - "from sklearn.preprocessing import StandardScaler\n", - "from sklearn.pipeline import make_pipeline\n", - "from xgboost import XGBClassifier, XGBRegressor\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import scipy.stats as stats" - ] - }, - { - "cell_type": "markdown", - "id": "49242003", - "metadata": {}, - "source": [ - "### The Data Backend: `DoubleMLData`" - ] - }, - { - "cell_type": "markdown", - "id": "3653b53a", - "metadata": {}, - "source": [ - "To start our analysis, we initialize the data backend from the previously loaded data set, i.e., we create a new instance of a [DoubleMLData](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLData.html#doubleml.DoubleMLData) object. During initialization, we specify the roles of the variables in the data set, i.e., in our example the outcome variable $Y$ via the parameter `y_col`, the treatment variable $A$ via `d_cols` and the confounding variables $V$ via `x_cols`." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "abdd10b7", - "metadata": {}, - "outputs": [], - "source": [ - "# Specify explanatory variables for data-backend\n", - "features_base = list(df.columns.values)[2:]\n", - "\n", - "# Initialize DoubleMLData (data-backend of DoubleML)\n", - "data_dml = dml.DoubleMLData(df,\n", - " y_col='Y',\n", - " d_cols='A',\n", - " x_cols=features_base)" - ] - }, - { - "cell_type": "markdown", - "id": "5800ca50-c293-4266-8dd7-00fadcea8d51", - "metadata": {}, - "source": [ - "We can print the data-backend to see the variables, which we have assigned as outcome, treatment and controls." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "37b9bd8a", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "================== DoubleMLData Object ==================\n", - "\n", - "------------------ Data summary ------------------\n", - "Outcome variable: Y\n", - "Treatment variable(s): ['A']\n", - "Covariates: ['V1', 'V2', 'V3', 'V4', 'V5', 'V6', 'V7', 'V8', 'V9', 'V10', 'V11', 'V12', 'V13', 'V14', 'V15', 'V16', 'V17', 'V18', 'V19', 'V20', 'V21', 'V22', 'V23', 'V24', 'V25', 'V26', 'V27', 'V28', 'V29', 'V30', 'V31', 'V32', 'V33', 'V34', 'V35', 'V36', 'V37', 'V38', 'V39', 'V40', 'V41', 'V42', 'V43', 'V44', 'V45', 'V46', 'V47', 'V48', 'V49', 'V50', 'V51', 'V52', 'V53', 'V54', 'V55', 'V56', 'V57', 'V58', 'V59', 'V60', 'V61', 'V62', 'V63', 'V64', 'V65', 'V66', 'V67', 'V68', 'V69', 'V70', 'V71', 'V72', 'V73', 'V74', 'V75', 'V76', 'V77', 'V78', 'V79', 'V80', 'V81', 'V82', 'V83', 'V84', 'V85', 'V86', 'V87', 'V88', 'V89', 'V90', 'V91', 'V92', 'V93', 'V94', 'V95', 'V96', 'V97', 'V98', 'V99', 'V100', 'V101', 'V102', 'V103', 'V104', 'V105', 'V106', 'V107', 'V108', 'V109', 'V110', 'V111', 'V112', 'V113', 'V114', 'V115', 'V116', 'V117', 'V118', 'V119', 'V120', 'V121', 'V122', 'V123', 'V124', 'V125', 'V126', 'V127', 'V128', 'V129', 'V130', 'V131', 'V132', 'V133', 'V134', 'V135', 'V136', 'V137', 'V138', 'V139', 'V140', 'V141', 'V142', 'V143', 'V144', 'V145', 'V146', 'V147', 'V148', 'V149', 'V150', 'V151', 'V152', 'V153', 'V154', 'V155', 'V156', 'V157', 'V158', 'V159', 'V160', 'V161', 'V162', 'V163', 'V164', 'V165', 'V166', 'V167', 'V168', 'V169', 'V170', 'V171', 'V172', 'V173', 'V174', 'V175', 'V176', 'V177', 'V178', 'V179', 'V180', 'V181', 'V182', 'V183', 'V184', 'V185', 'V186', 'V187', 'V188', 'V189', 'V190', 'V191', 'V192', 'V193', 'V194', 'V195', 'V196', 'V197', 'V198', 'V199', 'V200']\n", - "Instrument variable(s): None\n", - "No. Observations: 1000\n", - "\n", - "------------------ DataFrame info ------------------\n", - "\n", - "RangeIndex: 1000 entries, 0 to 999\n", - "Columns: 202 entries, Y to V200\n", - "dtypes: float64(107), int64(95)\n", - "memory usage: 1.5 MB\n", - "\n" - ] - } - ], - "source": [ - "print(data_dml)" - ] - }, - { - "cell_type": "markdown", - "id": "714346b8-90dd-4f15-b880-d71f4f60b04e", - "metadata": {}, - "source": [ - "## The Inference Problem and Choosing an Appropriate Model\n", - "\n", - "The inference problem is to determine the causal effect of seeing the new ad design $A$ on a customer's purchases $Y$ once we control for individual characteristics $V$. In our example, we are interested in the average treatment effect. Basically, there are two causal models available in [DoubleMLData](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLData.html#doubleml.DoubleMLData) that can be used to estimate the ATE.\n", - "\n", - "The so-called interactive regression model (IRM) called by [DoubleMLIRM](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLIRM.html) is a flexible model to estimate this causal quantity. The model does not impose functional form restrictions on the underlying regression relationships, for example, linearity or additivity as in a standard linear regression model. This means that the model hosts heterogeneous treatment effects, i.e., account for variation in the effect of the new ad design across customers. Moreover, it is possible to also estimate other causal parameters with the IRM, for example, the average treatment effect on the treated, which might be of interest too.\n", - "\n", - "The second causal model that can be used here is the partially linear regression model (PLR). The PLR incorporates stronger assumptions, for example, that the treatment effect is additive and linear which implies that it does not vary across individuals. We will start with the IRM and include the PLR estimates at the end of the notebook." - ] - }, - { - "cell_type": "markdown", - "id": "9e798e44-8fc8-4c93-9cfb-2d3ad7486dc0", - "metadata": {}, - "source": [ - "## 1. Interactive Regression Model (IRM)\n", - "\n", - "We briefly introduce the Interactive regression model (IRM) where the main regression relationship of interest is provided by\n", - "\n", - "$$Y = g_0(D, X) + U, \\quad E(U | X, D) = 0,$$\n", - "\n", - "where the treatment variable is binary, $D \\in \\lbrace 0,1 \\rbrace$. We consider estimation of the average treatment effects (ATE):\n", - "\n", - "$$\\theta_0 = \\mathbb{E}[g_0(1, X) - g_0(0,X)],$$\n", - "\n", - "when treatment effects are fully heterogeneous. In order to be able to use ML methods, the estimation framework generally requires a property called \"double robustness\" or \"Neyman orthogonality\". Double robustness can be achieved by including the first-stage estimation\n", - "\n", - "$$D = m_0(X) + V, \\quad E(V | X) = 0,$$\n", - "\n", - "which amounts to estimation of the propensity score, i.e., estimation the probability that a customer is exposed to the treatment provided her observed characteristics." - ] - }, - { - "cell_type": "markdown", - "id": "13a5f6f7-64c5-499b-b68a-16ca98943cd6", - "metadata": {}, - "source": [ - "Because data set was simulated we are aware of the true ATE, $\\theta_0=0.8$. The interpretation of this is that exposure to the new ad increases sales (in $100\\$$) by around $0.8$. In the following, we try to estimate this causal effect using the [DoubleML](https://docs.doubleml.org/stable/index.html) package and assess whether the estimated effect is significantly different from zero." - ] - }, - { - "cell_type": "markdown", - "id": "suburban-infrastructure", - "metadata": {}, - "source": [ - "### Benchmark: Model based on Linear Regression" - ] - }, - { - "cell_type": "markdown", - "id": "93f3af17-bcf9-429b-af9a-b90ea1153937", - "metadata": {}, - "source": [ - "Let us first start with a benchmark model that is based on linear regression. Hence, we estimate the functions $g_0(D,X)$ using a linear regrssion model and $m_0(X)$ by using an (unpenalized) logistic regression. In both cases, we include all available characteristics $V$. Later we will assess whether we can find a \"better\" estimator based on ML methods like lasso, random forests and boosting. Because we have 200 variables and 1000 observations, this is approaching a high dimentional setting, therefore the linear regression may not estimate the parameters well." - ] - }, - { - "cell_type": "markdown", - "id": "authorized-school", - "metadata": {}, - "source": [ - "We start by initializing the learners for linear regression and logistic regression. Then, we initialize a causal model object, here of the class [DoubleMLIRM](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLIRM.html). The latter is based on the data-backend we have specified above. To reduce the disproportionate impact of extreme propensity score weights in the interactive model we trim the propensity score from below and above at thresholds of 0.025 and 0.975." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "jewish-listing", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A1.4823850.6602312.2452520.0247520.1883562.776415
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 1.482385 0.660231 2.245252 0.024752 0.188356 2.776415" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize learners\n", - "linreg = make_pipeline(StandardScaler(), LinearRegression())\n", - "logreg_class = make_pipeline(StandardScaler(),LogisticRegression(penalty=\"none\"))\n", - "\n", - "np.random.seed(123)\n", - "dml_irm_regression = dml.DoubleMLIRM(data_dml,\n", - " ml_g = linreg,\n", - " ml_m = logreg_class,\n", - " trimming_threshold = 0.025,\n", - " n_folds = 3,\n", - " n_rep=3)\n", - "\n", - "dml_irm_regression.fit(store_predictions=True)\n", - "reg_summary = dml_irm_regression.summary\n", - "\n", - "reg_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "controlling-collapse", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [0.68238525]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_irm_regression.coef - 0.8)" - ] - }, - { - "cell_type": "markdown", - "id": "emerging-highlight", - "metadata": {}, - "source": [ - "We see that the causal estimate suffers from a substantial bias and is quite noisy: The ATE is overestimated by around 0.68 and the standard error is around 0.66. The corresponding confidence intervals are relatively wide, although they do not cover the value of zero. Hence, we can conclude that the average treatment effect is significantly different from zero at the 5% significance level." - ] - }, - { - "cell_type": "markdown", - "id": "neutral-converter", - "metadata": {}, - "source": [ - "Next, let us find out if we are able to use ML methods to find estimators that have a lower bias and a smaller standard error than the benchmark." - ] - }, - { - "cell_type": "markdown", - "id": "723b8e6c", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Lasso\n", - "\n", - "We estimate the nuisance components $g_0$ and $m_0$ using lasso as provided by [scikit-learn](https://scikit-learn.org). We load the learner by initializing instances from the classes [LassoCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html) and [LogisticRegressionCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegressionCV.html). Here we specify that the lasso should use the value of $\\lambda$ that minimizes the cross-validated mean squared error, which is based on 5-fold cross validation. We initialize the [DoubleMLIRM](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLIRM.html) object and use the newly defined learners." - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "73cbfd4b", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.834278 0.070511 11.831954 2.668556e-32 0.69608 0.972476" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# initialize Lasso learners\n", - "lasso = make_pipeline(StandardScaler(), LassoCV(cv=5, max_iter=20000)) \n", - "lasso_class = make_pipeline(StandardScaler(),\n", - " LogisticRegressionCV(cv=5, penalty='l1', solver='liblinear', \n", - " Cs = 4, max_iter=1000)) \n", - "\n", - "\n", - "# Initialize DoubleMLIRM model\n", - "np.random.seed(123)\n", - "dml_irm_lasso = dml.DoubleMLIRM(data_dml,\n", - " ml_g = lasso,\n", - " ml_m = lasso_class,\n", - " trimming_threshold = 0.025, \n", - " n_folds = 3)\n", - "\n", - "dml_irm_lasso.fit(store_predictions=True) \n", - "lasso_summary = dml_irm_lasso.summary\n", - "\n", - "lasso_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "stock-bookmark", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [0.03427819]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_irm_lasso.coef - 0.8)" - ] - }, - { - "cell_type": "markdown", - "id": "religious-algebra", - "metadata": {}, - "source": [ - "We see that the lasso-based estimate for the ATE is $0.83$ and, hence, much closer to the true value of $0.8$ than in the benchmark $1.48$. Moreover, we can achieve improvements in terms of estimation precision as can be recognized from the smaller standard error. " - ] - }, - { - "cell_type": "markdown", - "id": "33d06b0d", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Random Forest" - ] - }, - { - "cell_type": "markdown", - "id": "4d9d008a-5b6a-4acf-93b9-b26599541653", - "metadata": {}, - "source": [ - "Alternatively, we can repeat this procedure with other machine learning methods, for example a random forest learner as provided by the [RandomForestRegressor](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html) and [RandomForestClassifier](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html) class in [scikit-learn](https://scikit-learn.org)." - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "2092891a", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.86203 0.08229 10.475455 1.119983e-25 0.700743 1.023316" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Random Forest\n", - "randomForest = RandomForestRegressor()\n", - "randomForest_class = RandomForestClassifier()\n", - "\n", - "np.random.seed(123)\n", - "dml_irm_forest = dml.DoubleMLIRM(data_dml,\n", - " ml_g = randomForest,\n", - " ml_m = randomForest_class,\n", - " trimming_threshold = 0.025,\n", - " n_folds = 3)\n", - "\n", - "#Set nuisance-part specific parameters\n", - "dml_irm_forest.set_ml_nuisance_params('ml_g0', 'A', {\n", - " 'max_features': 200, 'n_estimators': 250})\n", - "dml_irm_forest.set_ml_nuisance_params('ml_g1', 'A', {\n", - " 'max_features': 200, 'n_estimators': 250})\n", - "dml_irm_forest.set_ml_nuisance_params('ml_m', 'A', {\n", - " 'max_features': 200, 'n_estimators': 250})\n", - "\n", - "dml_irm_forest.fit(store_predictions=True) \n", - "forest_summary = dml_irm_forest.summary\n", - "\n", - "forest_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "vital-insight", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [0.0620296]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_irm_forest.coef - 0.8)" - ] - }, - { - "cell_type": "markdown", - "id": "d4b6e16b-6cb9-40d8-a4fa-c438f23b49f3", - "metadata": {}, - "source": [ - "The results are relatively similar to the one obtained by lasso with a bias and standard errors that are slightly greater than before." - ] - }, - { - "cell_type": "markdown", - "id": "9ac68b60", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Extreme Gradient Boosting" - ] - }, - { - "cell_type": "markdown", - "id": "cc71c762-8497-43e5-a151-a5239641d510", - "metadata": {}, - "source": [ - "Next, we estimate the ATE using extreme gradient boosting as provided by [xgboost](https://docs.getml.com/latest/api_reference/predictors.html)." - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "90b9ef4e", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.739225 0.092511 7.990648 1.342310e-15 0.557906 0.920544" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "boost = XGBRegressor(n_jobs=1, objective = \"reg:squarederror\")\n", - "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", - " objective = \"binary:logistic\", eval_metric = \"logloss\")\n", - "\n", - "np.random.seed(123)\n", - "dml_irm_boost = dml.DoubleMLIRM(data_dml,\n", - " ml_g = boost,\n", - " ml_m = boost_class,\n", - " trimming_threshold = 0.025,\n", - " n_folds = 3)\n", - "\n", - "#Set nuisance-part specific parameters\n", - "dml_irm_boost.set_ml_nuisance_params('ml_g0', 'A', {\n", - " 'n_estimators': 30, 'eta': 0.2})\n", - "dml_irm_boost.set_ml_nuisance_params('ml_g1', 'A', {\n", - " 'n_estimators': 30, 'eta': 0.2})\n", - "dml_irm_boost.set_ml_nuisance_params('ml_m', 'A', {\n", - " 'n_estimators': 15, 'eta': 0.2})\n", - "\n", - "dml_irm_boost.fit(store_predictions=True)\n", - "boost_summary = dml_irm_boost.summary\n", - "boost_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "traditional-ribbon", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [-0.06077519]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_irm_boost.coef - 0.8)" - ] - }, - { - "cell_type": "markdown", - "id": "9ee7f068-1ac4-4d7d-99a7-5c68c91e8b51", - "metadata": {}, - "source": [ - "The estimated coefficient is close to the true ATE of $0.8$ but has a small negative bias. The interpretation of the results obtained with lasso, random forests and boosting are very similar. In all cases we are able to reject the null hypothesis that the ad has no effect on the sales." - ] - }, - { - "cell_type": "markdown", - "id": "fba54a14-c685-4948-819d-94a99d88e94a", - "metadata": {}, - "source": [ - "### Summary of IRM Results\n", - "\n", - "We define a small function which calculates the bias from the true parameter $0.8$. Then we save the estimates, bias and confidence intervals for peresentation and comparision." - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "id": "5e16a294", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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" - ], - "text/plain": [ - " coef Bias 2.5 % 97.5 %\n", - "regression 1.482 0.682 0.188 2.776\n", - "lasso 0.834 0.034 0.696 0.972\n", - "forest 0.862 0.062 0.701 1.023\n", - "xgboost 0.739 0.061 0.558 0.921" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "def bias(x):\n", - " x=x - 0.8\n", - " x=round(abs(x),3)\n", - " return x\n", - "\n", - "irm_summary = pd.concat((reg_summary, lasso_summary, forest_summary, boost_summary))\n", - "irm_summary.index = ['regression','lasso', 'forest', 'xgboost']\n", - "irm_summary=irm_summary[['coef', '2.5 %', '97.5 %']]\n", - "irm_summary.insert(1, \"Bias\", [bias(irm_summary.loc['regression','coef']), \n", - " bias(irm_summary.loc['lasso','coef']), \n", - " bias(irm_summary.loc['forest','coef']), \n", - " bias(irm_summary.loc['xgboost','coef'])])\n", - "irm_summary.round(3)" - ] - }, - { - "cell_type": "markdown", - "id": "b29e412d-d86f-46b4-840f-cbbe082faf0b", - "metadata": {}, - "source": [ - "### Conclusion\n", - "\n", - "We conclude that the interactive regression model (IRM) estimates are close to the true coefficient value, if the nuisance components are estimated with machine learning methods. The best results in terms of the smallest bias and standard errors is achieved by the lasso-based DML estimator for the ATE. The performance of the tree-based methods: random forests and extreme gradient boosting are comparable. All of the ML-based estimators have exhibited a superior performance to the benchmark based on linear and logistic regression.\n" - ] - }, - { - "cell_type": "markdown", - "id": "f50297c5", - "metadata": {}, - "source": [ - "## 2. Partially Linear Regression Model (PLR)\n", - "\n", - "The [DoubleML](https://docs.doubleml.org/stable/index.html) package also includes the partial linear regression (PLR) Model, which assumes the data have an additive structure. Although we don't know if this structure really holds for the underlying data generating process, we can apply this model and see how the estimates compare to those from the IRM." - ] - }, - { - "cell_type": "markdown", - "id": "fa24e6e1-b878-401f-b38a-c29cc0620c2c", - "metadata": {}, - "source": [ - "We estimate the function $g_0$ and $m_0$ in the following PLR model:\n", - "\n", - "\\begin{eqnarray}\n", - "& Y = D\\theta_0 + g_0(X) + \\zeta, &\\quad E[\\zeta \\mid D,X]= 0,\\\\\n", - "& D = m_0(X) + V, &\\quad E[V \\mid X] = 0.\n", - "\\end{eqnarray}\n", - "\n", - "To estimate the causal parameter $\\theta_0$ here, we use double machine learning with 3-fold cross-fitting. The steps of our analysis are very similar to the IRM cases with the difference being that we use a model class [DoubleMLPLR](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLPLR.html) for estimation." - ] - }, - { - "cell_type": "markdown", - "id": "331a36d6", - "metadata": {}, - "source": [ - "### Benchmark: Model based on Linear Regression" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "id": "1432e567-d221-490d-9361-39b9072cb6d4", - "metadata": { - "scrolled": true, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A0.7740710.07021611.0241172.923733e-280.636450.911692
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.774071 0.070216 11.024117 2.923733e-28 0.63645 0.911692" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "linreg = make_pipeline(StandardScaler(), LinearRegression())\n", - "logreg_class = make_pipeline(StandardScaler(),LogisticRegression(penalty=\"none\"))\n", - "\n", - "np.random.seed(123)\n", - "# Initialize DoubleMLPLR model\n", - "dml_plr_regression = dml.DoubleMLPLR(data_dml,\n", - " ml_g = linreg,\n", - " ml_m = logreg_class,\n", - " n_folds = 3)\n", - "\n", - "dml_plr_regression.fit(store_predictions=True)\n", - "reg_summary = dml_plr_regression.summary\n", - "\n", - "reg_summary" - ] - }, - { - "cell_type": "markdown", - "id": "4dd8948f", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Lasso" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "id": "0bbbc3ce", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A0.7845790.07041411.1424197.797228e-290.646570.922587
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.784579 0.070414 11.142419 7.797228e-29 0.64657 0.922587" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.random.seed(123)\n", - "# Initialize DoubleMLPLR model\n", - "dml_plr_lasso = dml.DoubleMLPLR(data_dml,\n", - " ml_g = lasso,\n", - " ml_m = lasso_class,\n", - " n_folds = 3)\n", - "\n", - "dml_plr_lasso.fit(store_predictions=True)\n", - "lasso_summary=dml_plr_lasso.summary\n", - "\n", - "lasso_summary" - ] - }, - { - "cell_type": "markdown", - "id": "a4ed2694", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Random Forests" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "id": "e5f3ac90", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.823899 0.073474 11.213529 3.499555e-29 0.679893 0.967904" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "randomForest = RandomForestRegressor()\n", - "randomForest_class = RandomForestClassifier()\n", - "\n", - "np.random.seed(123)\n", - "dml_plr_forest = dml.DoubleMLPLR(data_dml,\n", - " ml_g = randomForest,\n", - " ml_m = randomForest_class,\n", - " n_folds = 3,\n", - " n_rep = 3)\n", - "\n", - "dml_plr_forest.fit(store_predictions=True)\n", - "forest_summary = dml_plr_forest.summary\n", - "\n", - "forest_summary" - ] - }, - { - "cell_type": "markdown", - "id": "6aa9af04", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Extreme Gradient Boosting" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "id": "6fab5d3a", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A0.8145550.07120311.4399292.641013e-300.6750.95411
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.814555 0.071203 11.439929 2.641013e-30 0.675 0.95411" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "boost = XGBRegressor(n_jobs = 1, objective = \"reg:squarederror\", #where did you get tuning params? #grid search?\n", - " eta = 0.1, n_estimators = 57, max_depth = 2)\n", - "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", - " objective = \"binary:logistic\",\n", - " eval_metric = \"logloss\",\n", - " eta = 0.1, n_estimators = 10,\n", - " max_depth = 3)\n", - "\n", - "np.random.seed(123)\n", - "dml_plr_boost = dml.DoubleMLPLR(data_dml,\n", - " ml_g = boost,\n", - " ml_m = boost_class,\n", - " n_folds = 3)\n", - "dml_plr_boost.fit()\n", - "boost_summary = dml_plr_boost.summary\n", - "\n", - "boost_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "id": "dba8d33c", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefBias2.5 %97.5 %
regression0.7740.0260.6360.912
lasso0.7850.0150.6470.923
forest0.8240.0240.6800.968
xgboost0.8150.0150.6750.954
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" - ], - "text/plain": [ - " coef Bias 2.5 % 97.5 %\n", - "regression 0.774 0.026 0.636 0.912\n", - "lasso 0.785 0.015 0.647 0.923\n", - "forest 0.824 0.024 0.680 0.968\n", - "xgboost 0.815 0.015 0.675 0.954" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "plr_summary = pd.concat((reg_summary, lasso_summary, forest_summary, boost_summary))\n", - "plr_summary.index = ['regression','lasso', 'forest', 'xgboost']\n", - "plr_summary=plr_summary[['coef', '2.5 %', '97.5 %']]\n", - "plr_summary.insert(1, \"Bias\", [bias(plr_summary.loc['regression','coef']), \n", - " bias(plr_summary.loc['lasso','coef']), \n", - " bias(plr_summary.loc['forest','coef']), \n", - " bias(plr_summary.loc['xgboost','coef'])])\n", - "plr_summary.round(3) " - ] - }, - { - "cell_type": "markdown", - "id": "27d1d2a9-beed-493d-ae92-8d4e92cde8ae", - "metadata": {}, - "source": [ - "### Summary of IRM and PLR Results" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "id": "1b4ddf50-50de-4bab-a110-767b8d50df21", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefBias2.5 %97.5 %
ModelML
IRMregression1.4820.6820.1882.776
lasso0.8340.0340.6960.972
forest0.8620.0620.7011.023
xgboost0.7390.0610.5580.921
PLRregression0.7740.0260.6360.912
lasso0.7850.0150.6470.923
forest0.8240.0240.6800.968
xgboost0.8150.0150.6750.954
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" - ], - "text/plain": [ - " coef Bias 2.5 % 97.5 %\n", - "Model ML \n", - "IRM regression 1.482 0.682 0.188 2.776\n", - " lasso 0.834 0.034 0.696 0.972\n", - " forest 0.862 0.062 0.701 1.023\n", - " xgboost 0.739 0.061 0.558 0.921\n", - "PLR regression 0.774 0.026 0.636 0.912\n", - " lasso 0.785 0.015 0.647 0.923\n", - " forest 0.824 0.024 0.680 0.968\n", - " xgboost 0.815 0.015 0.675 0.954" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df_summary = pd.concat((irm_summary,plr_summary)).reset_index().rename(columns={'index': 'ML'})\n", - "df_summary['Model'] = np.concatenate((np.repeat('IRM', 4), np.repeat('PLR', 4)))\n", - "df_summary.set_index(['Model', 'ML']).round(3)" - ] - }, - { - "cell_type": "markdown", - "id": "64aa3065-da5c-49b9-88f2-5c08c1b7e617", - "metadata": {}, - "source": [ - "### Conclusion\n", - "\n", - "As in the IRM model, the ML-based PLR models are associated with a smaller bias as compared to the model that is based on linear regression. It seems that the estimates obtained from the PLR are slightly closer to the true ATE than those from the IRM analysis. This might suggest, that the parametric assumptions (i.e., an additive and homogeneous causal effect) that are incorporated in the PLR turn out to be **not restrictive** in our example data set. However, if both models are based on appropriate ML learners, the conclusions are very similar. In all cases, the ML-based estimates were very close to the true ATE and we were always able to reject the null hypothesis of a zero-effect at all common significance levels. In terms of the A/B testing example, it can be concluded that the new ad increases customers purchases (in $100\\$$) by around 0.8 on average and that this effect is significantly different from zero at the 5% significance level. The results are summarized in the graphic below." - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "id": "c80cadcc", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize=(8, 9))\n", - "colors = sns.color_palette()\n", - "for ind, model in enumerate(['IRM', 'PLR']):\n", - " sns.set(font_scale=1.15)\n", - " plt.subplot(3, 1, ind+1)\n", - " this_df = df_summary.query('Model == @model')\n", - " errors = np.full((2, this_df.shape[0]), np.nan)\n", - " errors[0, :] = this_df['coef'] - this_df['2.5 %']\n", - " errors[1, :] = this_df['97.5 %'] - this_df['coef']\n", - " plt.errorbar(this_df.ML, this_df.coef, fmt='o', yerr=errors,\n", - " color=colors[ind], ecolor=colors[ind])\n", - " plt.ylim([0.5, 1.2])\n", - " plt.title(model)\n", - " plt.ylabel('Coeff. and 95%-CI')\n", - " plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", - " plt.legend(bbox_to_anchor=(1.04,0.5), loc=\"best\", borderaxespad=0)\n", - "\n", - "_ = plt.xlabel('ML method')\n" - ] - }, - { - "cell_type": "markdown", - "id": "3aa8d603-0df5-48c6-ad62-ac5ffe3e8ada", - "metadata": {}, - "source": [ - "______\n", - "\n", - "**Notes and Acknowledgement**\n", - "\n", - "We would like to thank the organizers of the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge) for setting up this data challenge and the numerous synthetic data examples that are all available online. Although the data examples in the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge) do not explicitly adress A/B testing, we put the data example here in this context to give a tractable example on the use of causal machine learning in practice. The parameters for the random forests and extreme gradient boosting learners have been tuned externally. The corresponding tuning notebook will be uploaded in the examples gallery in the future." - ] - }, - { - "cell_type": "markdown", - "id": "egyptian-platform", - "metadata": {}, - "source": [ - "## References\n", - "\n", - "Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W. and Robins, J. (2018), Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21: C1-C68. doi:10.1111/ectj.12097." - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.4" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} +{ + "cells": [ + { + "cell_type": "markdown", + "id": "consecutive-cabinet", + "metadata": {}, + "source": [ + "# Python: A/B Testing with DoubleML" + ] + }, + { + "cell_type": "markdown", + "id": "opponent-indonesian", + "metadata": {}, + "source": [ + "\"An\n", + "\n", + "Image Source Freepik http://www.freepik.com, Designed by macrovector\n" + ] + }, + { + "cell_type": "markdown", + "id": "c7c96f88", + "metadata": {}, + "source": [ + "In this notebook, we demontrate exemplarily how the [DoubleML](https://docs.doubleml.org/stable/index.html) package can be used to estimate the causal effect of seeing a new ad design on customers' purchases in a webshop. The [DoubleML](https://docs.doubleml.org/stable/index.html) package for Python and R provides an implementation of the double / debiased machine learning (DML) framework of [Chernozhukov et al. (2018)](https://arxiv.org/abs/1608.00060) and can be used to estimate causal effects based on machine learning (ML) methods.\n", + "\n", + "## A/B Testing\n", + "\n", + "A/B testing is a frequently used framework to perform causal inference in practice. For example, a manager of a webshop might want to optimally adapt the webshop design according to users' preferences. For examle, she might want to estimate the effect of a new ad design, which is displayed on the starting page, on a customer's purchases (in $100\\$$). A/B tests refer to an experimental design in which a certain treatment, for example a new ad design (called \"Version $A$\"), is randomly assigned to groups of individuals, like website visitors or app users. If a user is not \"treated\", i.e., he is not exposed to Version $A$, he sees an alternative design \"Version $B$\" like the old design of the ad. The assignment of the treatment might either be unconditionally random, i.e., randomly assigned to all visitors of the online shop or directed towards specific groups of them. In the latter case, the treatment assignment would be conditional on their characteristics, like their shopping history. For example, a discount might only be granted to customers who already made some purchases in the past.\n", + "\n", + "In general, the goal of the A/B test is to assess whether the treatment has an effect on the outcome variable of interest. In our example, the manager wants to evaluate whether the new ad design changed the monetary value of products purchased (in $100\\$$). Alternative settings of A/B tests refer to improvement of a user experience on a website or estimation of price elasticities. Websites and apps are ideal for running A/B tests because they make it very easy to precisely direct the treatment to visitors and users (or to specific subgroups of them) as well as to collect the data required for evaluation of the intervention.\n", + "\n", + "## Scenario\n", + "\n", + "Let's consider the following stylized scenario. The manager of a webshop is performing an A/B test to estimate the effect a new ad design $A$ has on customers' purchases, $Y$, on average. This effect is called the **A**verage **T**reatment **E**ffect (**ATE**). The treatment is assigned randomly conditional on the visitors' characteristics, which we call $V$. Such characteristics could be collected from a customer's shoppers account, for example. These might include the number of previous purchases, time since the last purchase, length of stay on a page as well as whether a customer has a rewards card, among other characteristics.
\n", + "\n", + "In the following, we use a **D**irected **A**cyclical **G**raph (DAG) to illustrate our assumptions on the causal structure of the scenario. As not only the outcome, but also the treatment is dependent on the individuals characteristics, there are arrows going from $V$ to both $A$ and $Y$. In our example, we also assume that the treatment $A$ is a direct cause of the customers' purchases $Y$.\n", + "\n", + "\n", + "![Scenario illustration with a DAG](figures/DAG.svg)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "220997c6", + "metadata": {}, + "source": [ + "Let's assume the conditional randomization has been conducted properly, such that a tidy data set has been collected. Now, a data scientist wants to evaluate whether the new ad design causally affected the sales, by using the [DoubleML](https://docs.doubleml.org/stable/index.html) package.\n", + "\n", + "### Why control for individual characteristics?\n", + "\n", + "Before we start the case study, let us briefly address the question why we need to include individual characteristics in our analysis at all. There are mainly two reasons why we want to control for observable characteristics. First, so-called confounders, i.e., variables that have a causal effect on both the treatment variable and the outcome variable, possibly create a bias in our estimate. In order to uncover the true causal effect of the treatment, it is necessary that our causal framework takes all confounding variables into account. Otherwise, the average causal effect of the treatment on the outcome is not identified. A second reason to include individual characteristics is efficiency. The more variation can be explained within our causal framework, the more precise will be the resulting estimate. In practical terms, greater efficiency leads to tighter confidence intervals and smaller standard errors and p-values. This might help to improve the power of A/B tests even if the treatment variable is unconditionally assigned to individuals.\n", + "\n", + "### Why use machine learning to analyze A/B tests?\n", + "\n", + "ML methods have turned out to be very flexible in terms of modeling complex relationships of explanatory variables and dependent variables and, thus, have exhibited a great predictive performance in many applications. In the double machine learning approach ([Chernozhukov et al. (2018)](https://arxiv.org/abs/1608.00060)), ML methods are used for modelling so-called nuisance functions. In terms of the A/B case study considered here, ML tools can be used to flexibly control for confounding variables. For example, a linear parametric specification as in a standard linear regression model might not be correct and, hence, not sufficient to account for the underlying confounding. Moreover, by using powerful ML techniques, the causal model will likely be able to explain a greater share of the total variation and, hence, lead to more precise estimation." + ] + }, + { + "cell_type": "markdown", + "id": "0ec5b0cf", + "metadata": {}, + "source": [ + "## Data \n", + "\n", + "As an illustrative example we use a data set from the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge). In this challenge, a great number of data sets have been generated in a way that they mimic distributional relationships that are found in many economic real data applications. Although the data have not been generated explicitly to address an A/B testing case study, they are well-suited for demonstration purposes. We will focus on one of the many different data genereting processes (DGP) that we picked at random, in this particualar case a data set called `high42`. An advantage of using the synthetic [ACIC 2019 data](https://sites.google.com/view/acic2019datachallenge/data-challenge) is that we know the true average treatment effect which is 0.8 in our data set.\n", + "\n", + "First we load the data." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "e39d4dd0", + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "\n", + "#fetch_ACIChigh42 needs to be defined\n", + "#df = fetch_ACIChigh42(return_type='DataFrame')\n", + "\n", + "#load code locally\n", + "df = pd.read_csv('data/high42.csv', sep=',', na_values=\".\")\n", + "\n", + "#code can also be loaded using a URL of the data\n", + "#url = 'https://raw.githubusercontent.com/DoubleML/doubleml-hiwi-sandbox/master/case_studies/AB_testing/data/high42.CSV?token=AQWGKQRE57BBRGOCBPSNBJTBD57ZQ'\n", + "#df = pd.read_csv(url)" + ] + }, + { + "cell_type": "markdown", + "id": "11525056-cdec-4916-9cb4-aa4268e99175", + "metadata": {}, + "source": [ + "We see that the data set consists of 1000 observations (= website visitors) and 202 variables. The $Y$ column represents the customers' purchases (in $100\\$$). The treatment variable $A$ is binary with a value 1 indicating that a customer has been exposed to the new ad design (and value 0 otherwise). The remaining 200 columns $V$ represent individual characteristics of the customers." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "10edc74d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(1000, 202)\n" + ] + } + ], + "source": [ + "print(df.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "6760c009", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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5 rows × 202 columns

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" + ], + "text/plain": [ + " Y A V1 V2 V3 V4 V5 V6 V7 V8 ... \\\n", + "0 7.358185 1 10 0 0 7 192.793769 23.676950 8 0.185443 ... \n", + "1 8.333672 1 12 0 1 4 199.653596 19.281270 7 0.514842 ... \n", + "2 7.472758 0 14 1 1 2 194.207792 24.589331 5 0.309199 ... \n", + "3 6.502319 1 0 1 0 9 201.838024 25.513918 4 0.160160 ... \n", + "4 7.043758 1 12 0 0 9 201.360443 31.160641 6 0.291976 ... \n", + "\n", + " V191 V192 V193 V194 V195 V196 V197 V198 V199 \\\n", + "0 1.462837 1 1627.274196 0 0 4.683956 0.565667 0 3 \n", + "1 1.330522 1 1661.484439 1 0 6.766661 -0.395402 0 4 \n", + "2 1.384151 1 1658.939293 0 0 5.647794 1.112766 0 0 \n", + "3 1.220303 1 1650.801625 0 0 5.370363 -0.305842 0 4 \n", + "4 1.170094 1 1676.818876 0 0 3.446532 2.440661 0 1 \n", + "\n", + " V200 \n", + "0 0.024338 \n", + "1 0.056518 \n", + "2 0.013442 \n", + "3 0.034632 \n", + "4 0.017514 \n", + "\n", + "[5 rows x 202 columns]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.head()" + ] + }, + { + "cell_type": "markdown", + "id": "c6e32feb", + "metadata": {}, + "source": [ + "### Descriptive Statistics\n" + ] + }, + { + "cell_type": "markdown", + "id": "horizontal-hanging", + "metadata": {}, + "source": [ + "Once we loaded the data, we find that the outcome variable, $Y$, is continuous with mean around $7.33$. The treatment variable $A$ is binary with a value of $1$ indicating that a visitor was exposed to the new ad design $A$ as opposed to design $B$ (corresponding to a value of $A$ equal to $1$). The control variables $V$ are a collection of mixed data types, including continuous, discrete and binary variables." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "d14f929c-178b-47fc-8293-29a634194f21", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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YAV1V2V3V4V5V6V7V8...V191V192V193V194V195V196V197V198V199V200
count1000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.000000...1000.0000001000.000001000.0000001000.0000001000.0000001000.0000001000.0000001000.000001000.0000001000.000000
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std1.3798520.4969893.8896050.4848770.4866012.8701416.1054089.9209412.4803610.119454...0.2701780.2338644.1919130.4355150.3792992.6558351.0027540.455821.3889880.021688
min3.4350520.0000000.0000000.0000000.0000000.000000183.12306712.0206300.0000000.047160...0.6680930.000001524.2916750.0000000.0000001.097708-3.6446520.000000.0000000.001478
25%6.4055830.0000007.0000000.0000000.0000005.000000195.94156921.2062304.0000000.204260...1.1193691.000001637.6995140.0000000.0000004.065465-0.7513550.000001.0000000.021711
50%7.3352480.00000010.0000000.0000001.0000007.000000199.87611726.2025826.0000000.282867...1.2937901.000001667.7634800.0000000.0000005.236465-0.0910560.000001.0000000.034009
75%8.2718811.00000012.0000001.0000001.0000008.000000204.39806733.0711898.0000000.374078...1.4768281.000001695.9726311.0000000.0000006.8982400.5946471.000002.0000000.049100
max13.1972601.00000020.0000001.0000001.00000015.000000220.58441095.41002014.0000000.706249...2.4486611.000001825.6970961.0000001.00000038.4279742.8326731.000009.0000000.139716
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8 rows × 202 columns

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" + ], + "text/plain": [ + " Y A V1 V2 V3 \\\n", + "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 \n", + "mean 7.331239 0.443000 9.290000 0.377000 0.616000 \n", + "std 1.379852 0.496989 3.889605 0.484877 0.486601 \n", + "min 3.435052 0.000000 0.000000 0.000000 0.000000 \n", + "25% 6.405583 0.000000 7.000000 0.000000 0.000000 \n", + "50% 7.335248 0.000000 10.000000 0.000000 1.000000 \n", + "75% 8.271881 1.000000 12.000000 1.000000 1.000000 \n", + "max 13.197260 1.000000 20.000000 1.000000 1.000000 \n", + "\n", + " V4 V5 V6 V7 V8 ... \\\n", + "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 ... \n", + "mean 6.477000 200.088758 28.066028 6.031000 0.294206 ... \n", + "std 2.870141 6.105408 9.920941 2.480361 0.119454 ... \n", + "min 0.000000 183.123067 12.020630 0.000000 0.047160 ... \n", + "25% 5.000000 195.941569 21.206230 4.000000 0.204260 ... \n", + "50% 7.000000 199.876117 26.202582 6.000000 0.282867 ... \n", + "75% 8.000000 204.398067 33.071189 8.000000 0.374078 ... \n", + "max 15.000000 220.584410 95.410020 14.000000 0.706249 ... \n", + "\n", + " V191 V192 V193 V194 V195 \\\n", + "count 1000.000000 1000.00000 1000.000000 1000.000000 1000.000000 \n", + "mean 1.318209 0.94200 1667.454561 0.254000 0.174000 \n", + "std 0.270178 0.23386 44.191913 0.435515 0.379299 \n", + "min 0.668093 0.00000 1524.291675 0.000000 0.000000 \n", + "25% 1.119369 1.00000 1637.699514 0.000000 0.000000 \n", + "50% 1.293790 1.00000 1667.763480 0.000000 0.000000 \n", + "75% 1.476828 1.00000 1695.972631 1.000000 0.000000 \n", + "max 2.448661 1.00000 1825.697096 1.000000 1.000000 \n", + "\n", + " V196 V197 V198 V199 V200 \n", + "count 1000.000000 1000.000000 1000.00000 1000.000000 1000.000000 \n", + "mean 5.804205 -0.076921 0.29400 1.629000 0.037936 \n", + "std 2.655835 1.002754 0.45582 1.388988 0.021688 \n", + "min 1.097708 -3.644652 0.00000 0.000000 0.001478 \n", + "25% 4.065465 -0.751355 0.00000 1.000000 0.021711 \n", + "50% 5.236465 -0.091056 0.00000 1.000000 0.034009 \n", + "75% 6.898240 0.594647 1.00000 2.000000 0.049100 \n", + "max 38.427974 2.832673 1.00000 9.000000 0.139716 \n", + "\n", + "[8 rows x 202 columns]" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.describe()" + ] + }, + { + "cell_type": "markdown", + "id": "d7e45649", + "metadata": {}, + "source": [ + "From the explanatory variables $V1$ to $V200$, 107 variables are continuous, while 95 are integers. From the integer-variables 59 are binary variables. " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "bde50bfe", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "float64 107\n", + "int64 95\n", + "dtype: int64\n", + "Number of binary variables: 59\n" + ] + } + ], + "source": [ + "print(df.dtypes.value_counts())\n", + "print(\"Number of binary variables:\", len(df[df.columns[df.isin([0,1]).all()]].columns))" + ] + }, + { + "cell_type": "markdown", + "id": "0ce90b4b", + "metadata": {}, + "source": [ + "Let's continue with some visual inspection." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "b4d2dfb4", + "metadata": {}, + "outputs": [], + "source": [ + "# Define the settings for the graphs first\n", + "import seaborn as sns\n", + "sns.set()\n", + "colors = sns.color_palette()\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "plt.rcParams['figure.figsize'] = 5., 3.75\n", + "sns.set(font_scale=1.5)\n", + "sns.set_style('whitegrid', {'axes.spines.top': False,\n", + " 'axes.spines.bottom': False,\n", + " 'axes.spines.left': False,\n", + " 'axes.spines.right': False})" + ] + }, + { + "cell_type": "markdown", + "id": "11045894", + "metadata": {}, + "source": [ + "The first figure shows that 443 out of the 1000 customers have been exposed to the new ad design." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "2b5037d3", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "df['A'].value_counts().plot(kind='bar', color=colors)\n", + "\n", + "plt.title('Treatment')\n", + "plt.xlabel('A')\n", + "_ = plt.ylabel('count')" + ] + }, + { + "cell_type": "markdown", + "id": "8c2dc825", + "metadata": {}, + "source": [ + "### Unconditional Estimate of ATE" + ] + }, + { + "cell_type": "markdown", + "id": "8da84d00", + "metadata": {}, + "source": [ + "As a first naive estimate, we could calculate the unconditional average treatment effect. In other words, we simply take the difference between $Y$ observed for the customers who have been exposed to the treatment $(A=1)$ and those who haven't been exposed $(A=0)$. As a visualization, we plot the density of the outcome variable conditional on the treatment status to get a first impression on the descriptive relationship of $A$ and $Y$." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "57392f09", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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" + ], + "text/plain": [ + " Y\n", + "A \n", + "0 NaN\n", + "1 1.117603" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df[['A', 'Y']].groupby('A').mean().diff()" + ] + }, + { + "cell_type": "markdown", + "id": "e6f3fa75-a5d4-480c-b627-4b99c6f6afe3", + "metadata": {}, + "source": [ + "The uncoditional effect is around $1.118$. Because we use a simulated data set in this example, we know that the true effect is $0.8$. Therefore the unconditional ATE overestimates the true effect, because it does not account for individual characteristics. In order to get an estimation on the ATE that explicitly takes the confounding variables $V$ into account, we apply the [DoubleML](https://docs.doubleml.org/stable/index.html) package in the next section." + ] + }, + { + "cell_type": "markdown", + "id": "9e21e9bb", + "metadata": {}, + "source": [ + "## Estimate ATE with the `DoubleML` package" + ] + }, + { + "cell_type": "markdown", + "id": "19830a0a", + "metadata": {}, + "source": [ + "Let’s use the package [DoubleML](https://docs.doubleml.org/stable/index.html) to estimate the average treatment effect of the new ad design on the value of customers' purchases. First, the required packages are imported." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "afaf4106", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import doubleml as dml\n", + "\n", + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.linear_model import LogisticRegression\n", + "from sklearn.linear_model import LassoCV, LogisticRegressionCV\n", + "from sklearn.ensemble import RandomForestClassifier, RandomForestRegressor\n", + "from sklearn.preprocessing import StandardScaler\n", + "from sklearn.pipeline import make_pipeline\n", + "from sklearn.metrics import mean_squared_error\n", + "from sklearn.metrics import log_loss\n", + "from xgboost import XGBClassifier, XGBRegressor\n", + "\n", + "import matplotlib.pyplot as plt\n", + "import scipy.stats as stats" + ] + }, + { + "cell_type": "markdown", + "id": "49242003", + "metadata": {}, + "source": [ + "### The Data Backend: `DoubleMLData`" + ] + }, + { + "cell_type": "markdown", + "id": "3653b53a", + "metadata": {}, + "source": [ + "To start our analysis, we initialize the data backend from the previously loaded data set, i.e., we create a new instance of a [DoubleMLData](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLData.html#doubleml.DoubleMLData) object. During initialization, we specify the roles of the variables in the data set, i.e., in our example the outcome variable $Y$ via the parameter `y_col`, the treatment variable $A$ via `d_cols` and the confounding variables $V$ via `x_cols`." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "abdd10b7", + "metadata": {}, + "outputs": [], + "source": [ + "# Specify explanatory variables for data-backend\n", + "features_base = list(df.columns.values)[2:]\n", + "\n", + "# Initialize DoubleMLData (data-backend of DoubleML)\n", + "data_dml = dml.DoubleMLData(df,\n", + " y_col='Y',\n", + " d_cols='A',\n", + " x_cols=features_base)" + ] + }, + { + "cell_type": "markdown", + "id": "5800ca50-c293-4266-8dd7-00fadcea8d51", + "metadata": {}, + "source": [ + "We can print the data-backend to see the variables, which we have assigned as outcome, treatment and controls." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "37b9bd8a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "================== DoubleMLData Object ==================\n", + "\n", + "------------------ Data summary ------------------\n", + "Outcome variable: Y\n", + "Treatment variable(s): ['A']\n", + "Covariates: ['V1', 'V2', 'V3', 'V4', 'V5', 'V6', 'V7', 'V8', 'V9', 'V10', 'V11', 'V12', 'V13', 'V14', 'V15', 'V16', 'V17', 'V18', 'V19', 'V20', 'V21', 'V22', 'V23', 'V24', 'V25', 'V26', 'V27', 'V28', 'V29', 'V30', 'V31', 'V32', 'V33', 'V34', 'V35', 'V36', 'V37', 'V38', 'V39', 'V40', 'V41', 'V42', 'V43', 'V44', 'V45', 'V46', 'V47', 'V48', 'V49', 'V50', 'V51', 'V52', 'V53', 'V54', 'V55', 'V56', 'V57', 'V58', 'V59', 'V60', 'V61', 'V62', 'V63', 'V64', 'V65', 'V66', 'V67', 'V68', 'V69', 'V70', 'V71', 'V72', 'V73', 'V74', 'V75', 'V76', 'V77', 'V78', 'V79', 'V80', 'V81', 'V82', 'V83', 'V84', 'V85', 'V86', 'V87', 'V88', 'V89', 'V90', 'V91', 'V92', 'V93', 'V94', 'V95', 'V96', 'V97', 'V98', 'V99', 'V100', 'V101', 'V102', 'V103', 'V104', 'V105', 'V106', 'V107', 'V108', 'V109', 'V110', 'V111', 'V112', 'V113', 'V114', 'V115', 'V116', 'V117', 'V118', 'V119', 'V120', 'V121', 'V122', 'V123', 'V124', 'V125', 'V126', 'V127', 'V128', 'V129', 'V130', 'V131', 'V132', 'V133', 'V134', 'V135', 'V136', 'V137', 'V138', 'V139', 'V140', 'V141', 'V142', 'V143', 'V144', 'V145', 'V146', 'V147', 'V148', 'V149', 'V150', 'V151', 'V152', 'V153', 'V154', 'V155', 'V156', 'V157', 'V158', 'V159', 'V160', 'V161', 'V162', 'V163', 'V164', 'V165', 'V166', 'V167', 'V168', 'V169', 'V170', 'V171', 'V172', 'V173', 'V174', 'V175', 'V176', 'V177', 'V178', 'V179', 'V180', 'V181', 'V182', 'V183', 'V184', 'V185', 'V186', 'V187', 'V188', 'V189', 'V190', 'V191', 'V192', 'V193', 'V194', 'V195', 'V196', 'V197', 'V198', 'V199', 'V200']\n", + "Instrument variable(s): None\n", + "No. Observations: 1000\n", + "\n", + "------------------ DataFrame info ------------------\n", + "\n", + "RangeIndex: 1000 entries, 0 to 999\n", + "Columns: 202 entries, Y to V200\n", + "dtypes: float64(107), int64(95)\n", + "memory usage: 1.5 MB\n", + "\n" + ] + } + ], + "source": [ + "print(data_dml)" + ] + }, + { + "cell_type": "markdown", + "id": "714346b8-90dd-4f15-b880-d71f4f60b04e", + "metadata": {}, + "source": [ + "## The Inference Problem and Choosing an Appropriate Model\n", + "\n", + "The inference problem is to determine the causal effect of seeing the new ad design $A$ on a customer's purchases $Y$ once we control for individual characteristics $V$. In our example, we are interested in the average treatment effect. Basically, there are two causal models available in [DoubleMLData](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLData.html#doubleml.DoubleMLData) that can be used to estimate the ATE.\n", + "\n", + "The so-called interactive regression model (IRM) called by [DoubleMLIRM](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLIRM.html) is a flexible (nonparametric) model to estimate this causal quantity. The model does not impose functional form restrictions on the underlying regression relationships, for example, linearity or additivity as in a standard linear regression model. This means that the model hosts heterogeneous treatment effects, i.e., account for variation in the effect of the new ad design across customers. Moreover, it is possible to also estimate other causal parameters with the IRM, for example, the average treatment effect on the treated (= those customers who have been exposed to the new ad), which might be of interest too.\n", + "\n", + "The second causal model that can be used here is the partially linear regression model (PLR). The PLR incorporates stronger assumptions, for example, that the treatment effect is additive and constant, i.e., in the model it is assumed that the effect does not very across individuals. We will start with the IRM and include the PLR estimates at the end of the notebook." + ] + }, + { + "cell_type": "markdown", + "id": "9e798e44-8fc8-4c93-9cfb-2d3ad7486dc0", + "metadata": {}, + "source": [ + "## 1. Interactive Regression Model (IRM)\n", + "\n", + "We briefly introduce the [Interactive Regression Model](https://docs.doubleml.org/stable/guide/models.html#interactive-regression-model-irm) (IRM) where the main regression relationship of interest is provided by\n", + "\n", + "$$Y = g_0(D, X) + U, \\quad E(U | X, D) = 0,$$\n", + "\n", + "where the treatment variable is binary, $D \\in \\lbrace 0,1 \\rbrace$. We consider estimation of the average treatment effect (ATE):\n", + "\n", + "$$\\theta_0 = \\mathbb{E}[g_0(1, X) - g_0(0,X)],$$\n", + "\n", + "when treatment effects are fully heterogeneous. In order to be able to use ML methods, the estimation framework generally requires a property called \"double robustness\" or \"Neyman orthogonality\". In the IRM, double robustness can be achieved by including the first-stage estimation\n", + "\n", + "$$D = m_0(X) + V, \\quad E(V | X) = 0,$$\n", + "\n", + "which amounts to estimation of the propensity score, i.e., the probability that a customer is exposed to the treatment provided her observed characteristics. Both predictions are then combined in [the doubly robust score for the average treatment effect](https://docs.doubleml.org/stable/guide/scores.html#interactive-regression-model-irm) which is given by\n", + "\n", + "$$\\psi(W; \\theta, \\eta) := g(1,X) - g(0,X) + \\frac{D (Y - g(1,X))}{m(X)} - \\frac{(1 - D)(Y - g(0,X))}{1 - m(x)} - \\theta.$$" + ] + }, + { + "cell_type": "markdown", + "id": "13a5f6f7-64c5-499b-b68a-16ca98943cd6", + "metadata": {}, + "source": [ + "Because the data set was simulated we are aware of the true ATE, $\\theta_0=0.8$. The interpretation of this is that exposure to the new ad increases sales (in $100\\$$) by around $0.8$ on average. In the following, we try to estimate this causal effect using the [DoubleML](https://docs.doubleml.org/stable/index.html) package and assess whether the estimated effect is significantly different from zero." + ] + }, + { + "cell_type": "markdown", + "id": "69f0731d", + "metadata": {}, + "source": [ + "### Assess predictive performance in the IRM" + ] + }, + { + "cell_type": "markdown", + "id": "6d494c68", + "metadata": {}, + "source": [ + "In the following, we will compare the estimate of the ATE based on different learners. Moreover, we will also have a look how well the learners can predict the nuisance components of the causal model. \n", + "\n", + "To evaluate the predictive performance, we'll first define a helper function that uses a DoubleML model object and returns a summary for a predictive measure. We'll use the root mean squared error (RMSE) for the main regression and the log loss measure $L_{log}$ for the propensity score estimation.\n", + "\n", + "Estimation of the IRM delivers two arrays for the prediction function $g_0(D, X)$: `ml_g0` for $g_0(0, X)$ and `ml_g1` for $g_0(1, X)$. If we want to get the correct prediction for each observation based on the treatment realization, we pick the corresponding value of either `ml_g0` (for $D=0$) or `ml_g1` (for $D=1$). As we apply random sample splitting repeatedly in every model, the RMSE and the log loss can be calculated for each repetition. We are interested in mean and standard deviation across all repetitions." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "aa2a8f81", + "metadata": {}, + "outputs": [], + "source": [ + "def pred_acc_irm(DoubleML, prop):\n", + " \"\"\"\n", + " A function to calculate prediction accuracy values for every repetition\n", + " of a Double Machine Learning model using IRM, DoubleMLIRM\n", + " \n", + " ...\n", + " \n", + " Parameters\n", + " ----------\n", + " DoubleML : doubleml.double_ml_irm.DoubleMLIRM\n", + " The IRM Double Machine Learning model\n", + " prop : bool\n", + " Indication if RMSE values have to be computed for main regression or\n", + " log loss values for propensity score\n", + " \"\"\"\n", + " \n", + " # export data and predictions of the DoubleML model\n", + " y = DoubleML._dml_data.y\n", + " d = DoubleML._dml_data.d\n", + " g0 = DoubleML.predictions.get('ml_g0')\n", + " g1 = DoubleML.predictions.get('ml_g1') \n", + " m = DoubleML.predictions.get('ml_m')\n", + " \n", + " # dimensions of prediction array\n", + " h = g0.shape[0]\n", + " w = DoubleML.n_rep\n", + " \n", + " # check whether treatment is binary \n", + " if np.isin(d, [0,1]).all() == False:\n", + " raise ValueError(\"Treatment must be a binary variable.\")\n", + " \n", + " # prepare array to store prediction accuracy measure values\n", + " pred_acc_array = np.zeros((w,))\n", + " \n", + " # check whether to assess main regression or propensity score accuracy: \n", + " if prop == False:\n", + " \n", + " # evaluate main regression accuracy\n", + " # export an array with correctly picked prediction values \n", + " export_pred_array = np.zeros((h, w)) \n", + " for i in range(w):\n", + " for j in range(h):\n", + " if d[j] == 0:\n", + " export_pred_array[j,i] = g0[j,i]\n", + " else:\n", + " export_pred_array[j,i] = g1[j,i]\n", + " \n", + " # fill array that contains rmse of each repetition\n", + " for i in range(w):\n", + " pred_acc_array[i] = mean_squared_error(y, export_pred_array[:,i], squared=False) \n", + " else:\n", + " \n", + " # evaluate propensity score accuracy\n", + " # fill array that contains log loss of each repetition\n", + " for i in range(w):\n", + " pred_acc_array[i] = log_loss(d, m[:,i], eps=0.025)\n", + " \n", + " return pred_acc_array" + ] + }, + { + "cell_type": "markdown", + "id": "suburban-infrastructure", + "metadata": {}, + "source": [ + "### Benchmark: Model based on Linear and Logistic Regression" + ] + }, + { + "cell_type": "markdown", + "id": "93f3af17-bcf9-429b-af9a-b90ea1153937", + "metadata": {}, + "source": [ + "Let us first start with a benchmark model that is based on linear and logistic regression. Hence, we estimate the functions $g_0(D,X)$ using a linear regression model and $m_0(X)$ by using an (unpenalized) logistic regression. In both cases, we include all available characteristics $V$. Later we will assess whether we can find a \"better\" estimator based on ML methods like lasso, random forests and boosting. Because we have 200 variables and 1000 observations, this is approaching a high dimentional setting, therefore the linear and the logistic regression may not estimate the parameters well." + ] + }, + { + "cell_type": "markdown", + "id": "authorized-school", + "metadata": {}, + "source": [ + "We start by initializing the learners for linear regression and logistic regression. Then, we initialize a causal model object, here of the class [DoubleMLIRM](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLIRM.html). The latter is based on the data-backend we have specified above. To reduce the disproportionate impact of extreme propensity score weights in the interactive model we trim the propensity score from below and above at thresholds of 0.025 and 0.975." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "jewish-listing", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 1.057833 0.624814 1.693035 0.090449 -0.166781 2.282446" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Linear and Logistic Regression learners\n", + "linreg = make_pipeline(StandardScaler(), LinearRegression())\n", + "logreg_class = make_pipeline(StandardScaler(), LogisticRegression(penalty=\"none\"))\n", + "\n", + "# Initialize DoubleMLIRM model\n", + "np.random.seed(1234)\n", + "dml_irm_regression = dml.DoubleMLIRM(data_dml,\n", + " ml_g = linreg,\n", + " ml_m = logreg_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3,\n", + " n_rep=3)\n", + "\n", + "dml_irm_regression.fit(store_predictions=True)\n", + "\n", + "reg_summary = dml_irm_regression.summary\n", + "reg_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "controlling-collapse", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.25783258]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_irm_regression.coef - 0.8)" + ] + }, + { + "cell_type": "markdown", + "id": "emerging-highlight", + "metadata": {}, + "source": [ + "We see that the causal estimate suffers from a substantial bias and is quite noisy: The ATE is overestimated by around 0.26 and the standard error is around 0.62. The corresponding 95%-confidence interval is relatively wide. It even covers the value of zero. Hence, we cannot reject the null hypothesis that the average treatment effect is different from zero at the 5% significance level.\n", + "\n", + "Next, we'll calculate the RMSE and the log loss for the nuisance functions in order to find out how the benchmark compares to other ML models." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "7ad39856", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_linlog_irm = pred_acc_irm(dml_irm_regression, prop=False)\n", + "rmse_main_linlog_irm_mean = np.mean(rmse_main_linlog_irm)\n", + "rmse_main_linlog_irm_std = np.std(rmse_main_linlog_irm)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_linlog_irm = pred_acc_irm(dml_irm_regression, prop=True)\n", + "logloss_prop_linlog_irm_mean = np.mean(logloss_prop_linlog_irm)\n", + "logloss_prop_linlog_irm_std = np.std(logloss_prop_linlog_irm)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "dd39c325", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.727905012276966\n", + "Standard deviation of the RMSE is 0.026526079197961804\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_linlog_irm_mean)\n", + "print(\"Standard deviation of the RMSE is\", rmse_main_linlog_irm_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "e21456ef", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 1.0228568161263911\n", + "Standard deviation of log loss is 0.027536454508812133\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_linlog_irm_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_linlog_irm_std)" + ] + }, + { + "cell_type": "markdown", + "id": "neutral-converter", + "metadata": {}, + "source": [ + "Next, let us find out if we are able to use ML methods to find estimators that have a lower bias and a smaller standard error than the benchmark." + ] + }, + { + "cell_type": "markdown", + "id": "723b8e6c", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Lasso\n", + "\n", + "We estimate the nuisance components $g_0$ and $m_0$ using lasso as provided by [scikit-learn](https://scikit-learn.org). We load the learner by initializing instances from the classes [LassoCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html) and [LogisticRegressionCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegressionCV.html). Here we specify that the lasso should use the value of $\\lambda$ that minimizes the cross-validated mean squared error, which is based on 5-fold cross validation. We initialize the [DoubleMLIRM](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLIRM.html) object and use the newly defined learners." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "73cbfd4b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.855559 0.070928 12.062417 1.668137e-33 0.716544 0.994575" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Lasso learners\n", + "lasso = make_pipeline(StandardScaler(), LassoCV(cv=5, max_iter=20000)) \n", + "lasso_class = make_pipeline(StandardScaler(),\n", + " LogisticRegressionCV(cv=5, penalty='l1', solver='liblinear', \n", + " Cs = 4, max_iter=1000)) \n", + "\n", + "# Initialize DoubleMLIRM model\n", + "np.random.seed(1234)\n", + "dml_irm_lasso = dml.DoubleMLIRM(data_dml,\n", + " ml_g = lasso,\n", + " ml_m = lasso_class,\n", + " trimming_threshold = 0.025, \n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_irm_lasso.fit(store_predictions=True)\n", + "\n", + "lasso_summary = dml_irm_lasso.summary\n", + "lasso_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "stock-bookmark", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.05555945]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_irm_lasso.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "85c6e74e", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_lasso_irm = pred_acc_irm(dml_irm_lasso, prop=False)\n", + "rmse_main_lasso_irm_mean = np.mean(rmse_main_lasso_irm)\n", + "rmse_main_lasso_irm_std = np.std(rmse_main_lasso_irm)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_lasso_irm = pred_acc_irm(dml_irm_lasso, prop=True)\n", + "logloss_prop_lasso_irm_mean = np.mean(logloss_prop_lasso_irm)\n", + "logloss_prop_lasso_irm_std = np.std(logloss_prop_lasso_irm)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "c659681b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.1143405452234652\n", + "Standard deviation of RMSE is 0.005869688113839954\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_lasso_irm_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_lasso_irm_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "388cdfcf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.6686766530020503\n", + "Standard deviation of log loss is 0.0032543941531603953\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_lasso_irm_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_lasso_irm_std)" + ] + }, + { + "cell_type": "markdown", + "id": "religious-algebra", + "metadata": {}, + "source": [ + "We see that the lasso-based estimate for the ATE is $0.86$ and, hence, much closer to the true value of $0.8$ than in the benchmark $1.06$. Moreover, we can achieve improvements in terms of estimation precision as can be recognized from the smaller standard error. Also the prediction measures for the nuisance components are much smaller for Lasso than in the linear/logistic benchmark. Using the Lasso learners makes it now possible to conclude that the ATE is significantly different from zero at a significance level of 5%." + ] + }, + { + "cell_type": "markdown", + "id": "33d06b0d", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Random Forest" + ] + }, + { + "cell_type": "markdown", + "id": "4d9d008a-5b6a-4acf-93b9-b26599541653", + "metadata": {}, + "source": [ + "Alternatively, we can repeat this procedure with other machine learning methods, for example a random forest learner as provided by the [RandomForestRegressor](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html) and [RandomForestClassifier](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html) class in [scikit-learn](https://scikit-learn.org)." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "2092891a", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.8931760.07742111.536558.631791e-310.7414331.044919
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.893176 0.077421 11.53655 8.631791e-31 0.741433 1.044919" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Random Forest learners\n", + "randomForest = RandomForestRegressor()\n", + "randomForest_class = RandomForestClassifier()\n", + "\n", + "# Initialize DoubleMLIRM model\n", + "np.random.seed(1234)\n", + "dml_irm_forest = dml.DoubleMLIRM(data_dml,\n", + " ml_g = randomForest,\n", + " ml_m = randomForest_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "# Set nuisance-part specific parameters\n", + "dml_irm_forest.set_ml_nuisance_params('ml_g0', 'A', {\n", + " 'max_features': 200, 'n_estimators': 250})\n", + "dml_irm_forest.set_ml_nuisance_params('ml_g1', 'A', {\n", + " 'max_features': 200, 'n_estimators': 250})\n", + "dml_irm_forest.set_ml_nuisance_params('ml_m', 'A', {\n", + " 'max_features': 200, 'n_estimators': 250})\n", + "\n", + "dml_irm_forest.fit(store_predictions=True) \n", + "\n", + "forest_summary = dml_irm_forest.summary\n", + "forest_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "vital-insight", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.09317591]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_irm_forest.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "14c230b0", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_forest_irm = pred_acc_irm(dml_irm_forest, prop=False)\n", + "rmse_main_forest_irm_mean = np.mean(rmse_main_forest_irm)\n", + "rmse_main_forest_irm_std = np.std(rmse_main_forest_irm)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_forest_irm = pred_acc_irm(dml_irm_forest, prop=True)\n", + "logloss_prop_forest_irm_mean = np.mean(logloss_prop_forest_irm)\n", + "logloss_prop_forest_irm_std = np.std(logloss_prop_forest_irm)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "1d633282", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.1688034544446142\n", + "Standard deviation of RMSE is 0.00826647072034282\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_forest_irm_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_forest_irm_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "16a7a785", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.6823242335385794\n", + "Standard deviation of log loss is 0.0026223238604172463\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_forest_irm_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_forest_irm_std)" + ] + }, + { + "cell_type": "markdown", + "id": "d4b6e16b-6cb9-40d8-a4fa-c438f23b49f3", + "metadata": {}, + "source": [ + "The results are relatively similar to the one obtained by lasso with a bias and standard errors that are slightly greater than before. The predictive accuracy of the random forest learners is also slightly worse than that of Lasso." + ] + }, + { + "cell_type": "markdown", + "id": "9ac68b60", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Extreme Gradient Boosting" + ] + }, + { + "cell_type": "markdown", + "id": "cc71c762-8497-43e5-a151-a5239641d510", + "metadata": {}, + "source": [ + "Next, we estimate the ATE using extreme gradient boosting as provided by [xgboost](https://docs.getml.com/latest/api_reference/predictors.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "90b9ef4e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.7909060.1043067.5825883.387302e-140.5864710.995341
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.790906 0.104306 7.582588 3.387302e-14 0.586471 0.995341" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Extreme Gradient Boosting learners\n", + "boost = XGBRegressor(n_jobs=1, objective = \"reg:squarederror\")\n", + "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", + " objective = \"binary:logistic\", eval_metric = \"logloss\")\n", + "\n", + "# Initialize DoubleMLIRM model\n", + "np.random.seed(1234)\n", + "dml_irm_boost = dml.DoubleMLIRM(data_dml,\n", + " ml_g = boost,\n", + " ml_m = boost_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "# Set nuisance-part specific parameters\n", + "dml_irm_boost.set_ml_nuisance_params('ml_g0', 'A', {\n", + " 'n_estimators': 30, 'eta': 0.2})\n", + "dml_irm_boost.set_ml_nuisance_params('ml_g1', 'A', {\n", + " 'n_estimators': 30, 'eta': 0.2})\n", + "dml_irm_boost.set_ml_nuisance_params('ml_m', 'A', {\n", + " 'n_estimators': 15, 'eta': 0.2})\n", + "\n", + "dml_irm_boost.fit(store_predictions=True)\n", + "\n", + "boost_summary = dml_irm_boost.summary\n", + "boost_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "traditional-ribbon", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [-0.0090944]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_irm_boost.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "efd04e78", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_boost_irm = pred_acc_irm(dml_irm_boost, prop=False)\n", + "rmse_main_boost_irm_mean = np.mean(rmse_main_boost_irm)\n", + "rmse_main_boost_irm_std = np.std(rmse_main_boost_irm)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_boost_irm = pred_acc_irm(dml_irm_boost, prop=True)\n", + "logloss_prop_boost_irm_mean = np.mean(logloss_prop_boost_irm)\n", + "logloss_prop_boost_irm_std = np.std(logloss_prop_boost_irm)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "114aa5cf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.2287566646120192\n", + "Standard deviation of RMSE is 0.010275338353331828\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_boost_irm_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_boost_irm_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "c1ebde27", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.7204831015081563\n", + "Standard deviation of log loss is 0.01297502257820836\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_boost_irm_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_boost_irm_std)" + ] + }, + { + "cell_type": "markdown", + "id": "9ee7f068-1ac4-4d7d-99a7-5c68c91e8b51", + "metadata": {}, + "source": [ + "The estimated coefficient is very close to the true ATE of $0.8$ but has a small negative bias. The interpretation of the results obtained with lasso, random forests and boosting are very similar. In all cases we are able to reject the null hypothesis that the ad has no effect on the sales." + ] + }, + { + "cell_type": "markdown", + "id": "fba54a14-c685-4948-819d-94a99d88e94a", + "metadata": {}, + "source": [ + "#### IRM - Summary of coefficient estimates\n", + "\n", + "We save the estimates, bias and confidence intervals for later peresentation and comparision." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "5e16a294", + "metadata": { + "scrolled": false, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefBias2.5 %97.5 %
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\n", + "
" + ], + "text/plain": [ + " coef Bias 2.5 % 97.5 %\n", + "regression 1.058 0.258 -0.167 2.282\n", + "lasso 0.856 0.056 0.717 0.995\n", + "forest 0.893 0.093 0.741 1.045\n", + "xgboost 0.791 -0.009 0.586 0.995" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "irm_summary = pd.concat((reg_summary, lasso_summary, forest_summary, boost_summary))\n", + "irm_summary.index = ['regression','lasso', 'forest', 'xgboost']\n", + "irm_summary = irm_summary[['coef', '2.5 %', '97.5 %']]\n", + "irm_summary.insert(1, \"Bias\", [irm_summary.loc['regression','coef'] - 0.8, \n", + " irm_summary.loc['lasso','coef'] - 0.8, \n", + " irm_summary.loc['forest','coef'] - 0.8, \n", + " irm_summary.loc['xgboost','coef'] - 0.8])\n", + "irm_summary.round(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "4b478603", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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0HKX7rMwfKjk5Oe4cBD734U+bNg3+/v4oLi7mu2/zNQcHB0hJSSEqKgotWrTAlStXsGLFigr3yePxaJx1XVR65SslJcV3UgCfR4ikpaWVObC+1IsXL7Bx40b0798fQUFBfMu+7H5RUlJCgwYN8Pz5c4FtbNmyBenp6fD19RU57t69eyMwMBBRUVFISEiAuro6jIyM+I4rNzdX4JiysrJw6dKlMq/wK6KmpobFixfD29sbM2bMwP79+yEtLQ1lZWXIy8ujuLhYYH8vX75EUlIS5OXloaysjIYNG+LZs2cC2y6rXcoi6nGVjtIp/foMAAkJCRg5ciRCQ0Nhbm6Op0+fIjs7G0ZGRjAyMoKPjw8eP34MT09PbNu2rcxkXfoVPjk5GYaGhnzLnj59ioYNG6JJkybIyckR6XhEUTq6ITo6Gv3798e7d++EXliIGl/pFfWzZ8/4bmSXftMsVfr70apVK+jo6PAti42NrdRVspKSEqSlpQVGtlSGhIQElixZgjt37mDZsmUwMTGBgYGB0P2ZmJjg3LlzaN26NaSkpGBjY1PhPj58+AAVFZUqx1ge6rOuhNK/mKVXIC1atICenh7Cw8Px5s0brl5RURHmzp2LX3/9la8P8mtZWVkA+K++gc8n8rNnz7h1paWlYW1tjdjYWL4uiKysLGzZsoX7ulkaX0VXHy1atEC3bt0QERGBuLg4gcTi6OiI+/fvC/Qprlu3DtOmTRMYwiYqZ2dnuLm5ITExEVu3buWOzdbWFrGxsbh//z5f/YCAAHh7e+P9+/eQlJSEo6Mj4uLi+JJCVlYWjh8/LtL+RT2uadOmYfbs2XxP+HXp0gUyMjJcG/v7+2Py5MnIzc3l6nTo0AGNGzcWemVVOlRu06ZNfFexiYmJuHjxIuzs7L5p/LAwzs7OePPmDdasWQMdHR2hI1VEjc/JyQlSUlICQ0C/HOr65fY2bNjAt7179+5h0qRJ2LFjh8jHICEhAVVVVZG64MqjqKiIRYsWcaOFioqKhNZ1cnLCrVu3cOjQIXTv3r3cC69Sr1+/RqtWrb4pRmHoyroSSvsQN2/eDFtbWzg5OWHevHkYOXIkBg0ahJ9//hlNmzbFiRMncOvWLcycObPcIVadOnVC69atsX79ehQUFEBVVRW3b99GeHg45OTk+BLBzJkz4e7uDnd3d3h6ekJRURH79+9HXl4efvvtN7749u7di/T09HLnhujbty83LvvLLhAAmDBhAs6ePYspU6Zg6NCh6Ny5MxISEnDkyBHY2trC1ta2Su0HAH5+fjh//jzWrFmDXr16oW3btvDx8cGVK1fg6ekJT09PtG7dGjExMYiOjoaHhwc3THLatGmIjY2Fh4cHvLy8ICsri3///Zd7qrSiRCfqcY0dOxbz5s3DqFGj0KtXLzDGcOTIERQUFHBDB0ePHo1x48bB09MTAwYMgJycHCIjI5GSkoLAwMAy99+5c2d4eXkhNDQUo0ePhrOzM969e4fQ0FA0btwYM2fOrHK7lsfa2hoNGjTAhQsXMHXqVKH1RI2vbdu2GD16NDZv3oy8vDzY2NggISEBFy9e5NuepqYmt70PHz7A2dkZHz58wK5du6CgoIBp06ZV6jhKLzAYY9/0R6179+5wc3PD8ePHsWXLFqFzgTg7O2Pp0qWIj48X+pl+KSsrC8+ePau2p1bpyroS+vTpAysrKxw6dAjLli0DABgbG2Pv3r3Q09PDtm3b8PfffyM/Px8BAQEYP358uduTlZXFxo0bYWxsjJ07dyIwMBCJiYmYO3cufHx8kJOTg7t37wL4fINn37590NfXx+bNm7F69Wq0aNECe/bs4ZKZpaUlXF1dERsbi0WLFnF9n2Xp2bMn5OTkoKuryze6Avh8I3Tfvn0YOHAgTp8+DX9/f9y6dQuTJ0/G6tWrv6lPTkVFBbNmzcKnT5/wxx9/APj8y79//37Y29tj//79WLJkCVJTU+Hn58c3prtt27bYtWsXtLS0sGHDBmzcuBGOjo7w9PTk2rM8oh6Xu7s7AgMDkZubixUrVmD58uVo0KABNm3axM250r17d6xbtw7y8vJYu3YtAgICkJWVhRUrVpT7uPHvv/+O+fPnIyMjAwEBAThw4AB69OiBQ4cOCb3i/Vby8vKwtrYG8PlzL4+o8c2aNQtz585FcnIyAgICuC69sra3YMECZGZmIjAwEHv27IGpqSn27NkjcN5VxNbWFllZWVX+ZveluXPnokmTJli7di2ePn1aZh01NTVoa2tDWlpa6ANEX7p+/ToYY990MVMeCVbeXQVC6pCMjAwoKysLXFUtWrQIe/fuxa1btyo1woDUL4WFhXB0dMSgQYMwffr02g5HwMyZM5GcnIzw8PBq2T5dWZN6Y9q0aejTpw9fn3x+fj6io6Ohra1Nifo7JysrC09PTxw7dqxSo0JqQk5ODqKiojBmzJhq2wcla1Jv9O/fH0+ePMH48eOxd+9ebN++HZ6ennj9+nWdvNIi4ufl5YXi4mKRbyrXlJ07d6J9+/Z800uIG3WDkHrl6NGj2LlzJ5KTkyEpKQk9PT1MnjyZeyKSfP8iIiKwbNkynDx5ssI5rWtCdnY2evTogc2bN0NPT6/a9kPJmhBC6gHqBhFRYmJibYfw3aE2FS9qT/GrS21KyVpEnz59qu0QvjvUpuJF7Sl+dalNKVkTQkg9QMmaEELqAUrWhBBSD1CyJoSQeoCSNSGE1AOUrAkhpB4QOkVq6fSZlVE6uTchhBDxEpqsqzJzFCVrQgipHkKTdVRUVE3GUaf5rb2A7Oxs/O/F1oQQUuOEJuvS96cRQgipfSLdYPzy/YJfunHjhsB78wghhIhfucn648ePmDp1Kpydnct84/KaNWvw008/YdKkScjMzKy2IAkh5EcnNFnn5OTA09MTkZGRsLCwQF5enkCdoUOHws7ODtHR0Rg5ciTy8/OrNVhCCPlRCU3WmzZtwpMnT7BixQps3rwZLVq0EKjj7OyM9evXY9GiRXj06BG2bNlSrcESQsiPSmiyPnPmDPr06QNXV9cKN+Lu7g57e3ucOnVKrMERQgj5TGiyfvHiBUwqMVbNysoKqampYgmKEEIIP6HJukmTJmX2U5dHQUHhmwMihBAiSGiy7ty5My5evCjyhuLj46Guri6WoAghhPATmqwHDx6M+Ph4HDt2rMKNnDx5EnFxcejXr59YgyOEEPKZ0CcY+/Tpg2PHjmHOnDm4cuUKhgwZAl1dXe7V7yUlJUhMTMSBAwdw6NAh6Ovrw93dvcYCJ4SQH4nQZA0Ay5cvx19//YUDBw7g4MGDkJaWRtOmTcHj8ZCVlYWSkhIwxtC7d28sWLAAcnJyNRU3IYT8UMpN1goKCggMDMTIkSNx/PhxJCUlIT09HZKSktDW1oaxsTGcnZ2hra1dU/ESQsgPqdxkXapLly7o0qVLdcdCCCFEiCq/KSYnJwd+fn548uSJOOMhhBBShion60+fPiE8PBxv376t8s55PB727t2Lvn37cl0qS5cuLXPSqFK5ublYuHAhrK2tYWxsjHHjxuHZs2dVjoEQQuoDkbpBqsvmzZvxzz//YOzYsbC0tMTTp0+xevVqPH78WOg8I9OnT8edO3cwe/ZsKCgoICQkBCNGjMCJEyfQqFGjGj4CQgipGbWWrBlj2Lx5Mzw8PDBz5kwAnx9ZV1JSwvTp03Hv3j3o6OjwrXPt2jXExsZi06ZNsLW1BQCYmprCyckJe/fuxfjx42v8OAghpCbU2tvNc3Nz0a9fP7i5ufGVd+jQAQCQkpIisE58fDwUFBRgbW3NlSkrK8PMzAxxcXHVGzAhhNSiKl9ZN2nSBDt37qzysD1FRUXMmzdPoDwyMhIA0KlTJ4FlycnJ0NDQ4B7MKdW2bVua8Y8Q8l2rcrKWkZGBubm5OGPBrVu3sHHjRjg7O6Njx44Cy3NycqCoqChQrqCgUO5Nya8lJibi06dPItfPzs4GACQkJIi8DhENtal4UXuKX2XatDIzlVZWlZJ1YWEh1q5di5MnT+Lt27do2bIl+vTpg4kTJ0JWVrZKgSQkJGDixIlQU1ODv79/mXUYY0LXl5QUvUdHV1e3UrEduFL6dnN6vbk4JSQkUJuKEbWn+NWlNq1Ssg4KCkJMTAyGDBmCpk2bIjU1FaGhoXj//j0WLFhQ6e2dPHkSc+bMQbt27bB582YoKSmVWU9RURFpaWkC5bm5uWVecRNCyPdCaLIW1uUAfH6LzD///MP3F6dZs2ZYt25dpZP1tm3bEBgYCHNzc6xZs6bc4Xft27fHpUuXwBiDhIQEV/78+XO0b9++UvslhJD6RGjfgaOjI9avX4/c3FyBZcrKyrhw4QJ4PB4AID8/H//99x+aNWtWqZ2HhYUhICAArq6u2Lx5c4XjpLt3746PHz/yzbOdmZmJa9euwcrKqlL7JoSQ+kTolfXff/+NkJAQbNu2DWPHjsXw4cPRsGFDAMDs2bMxZcoUbN++HY0bN8b79+8hJSWF1atXi7zjjIwMLF68GG3atIGnpyeSkpL4lrdt2xbA5yF8nTp1gqKiIszMzGBubo4ZM2bAx8cHTZs2RXBwMBo1aoSff/65KsdPCCH1gtBkbWdnBzs7O5w7dw4hISHYunUrl7Stra1x7tw5REdHIyMjA82bN4eNjU2lrqzPnz+P/Px8vHjxAp6engLLg4KCUFJSAj8/P+zcuRMWFhYAgJCQEAQEBCAoKAg8Hg8mJib4559/0KRJkyocPiGE1A8SrLwhFl+IjIxESEgI3r59i19++QXDhg1DgwYNqju+OsFv7efRICG+Fb/pnYiuLt1p/x5Qe4pfXWpTkce7OTs74/Dhw5g/fz7Cw8Ph5OSE7du3o6CgoDrjI4QQggqG7qWmpuLUqVN4/fo1lJSUYGlpiV69eqFXr144efIk1q5di82bN2PcuHH4+eefqzzGmhBCSPmEXllHRkbC1dUVu3btQlJSEk6ePAkvLy8EBgYCAHr37o1jx47B19cX//77L5ycnBAaGlpjgRNCyI9EaLL++++/0a9fP8TGxuLff//FqVOnsHz5cmzfvh2vXr0CAEhISKBv3744ceIEZs6ciV27dtVY4IQQ8iMRmqzfvn2Ldu3a8T180rZtWzDG8PHjR/6NSEpiwIABNJkSIYRUE6F91n379kVISAgePHgANTU15OTk4MyZM9DX14empmaZ61Rmfg5CCCGiE5qs//zzT+jq6uLUqVNISkqCkpISBg0ahDFjxvBdbRNCCKl+QpO1pKQkPDw84OHhUZPxEEIIKUOVZt378OEDbt68iby8PKipqcHAwEDccRFCCPmC0GQ9ePBgTJs2DTY2Nnzl69evx7p161BYWMjNfqehoQF/f3+YmppWe8CEEPIjEpqs7969iw8fPvCVhYaG4p9//oGxsTGGDBkCZWVlJCcnY+fOnRg7dixCQ0PpKpsQQqpBpbpBNmzYgG7dumH79u1cmZ2dHQYPHozBgwdj1apV2LJli7hjJISQH57IY+3y8vKQnp6OQYMGCSxr1KgR3N3dcfPmTXHGRggh5H9ETtYNGzZEkyZNIC1d9sW4hIQE9zICQggh4lVuN8i///6L58+fo2PHjujUqRPc3Nywb98+uLryTxX6+vVr7Nq1C4aGhtUaLCGE/KiEJmsXFxc8efIE69evR3FxMd+DMBs3bsT48eMBAPPnz8eJEydQWFiI5cuXV3/EhBDyAxKarFetWgUAKC4uxtOnT/Ho0SM8evQIjx8/hpqaGlfvzp070NTUxNy5c6Gvr1/9ERNCyA+owtEg0tLS6Ny5Mzp37lzm8v3790NGRkbsgRFCCPl/Ig3dy8nJwYMHD5Ceno6CggJIS0ujSZMmUFdX515sSwghpPqUm6xfvHiBoKAgREVFoaSkhG9Z6dOLzZo1g6enJ0aOHMm9/ZwQQoh4CU3WL168gIeHB4qKiuDl5YW2bdviw4cPiIyMRFpaGmbNmgXGGK5evYp169YhIiIC27Zto7eME0JINRCarP/55x8oKChg7969UFZW5sonTZqEuXPn4tChQ9izZw/c3d0xatQojBkzBiEhIfj9999rJHBCCPmRCH0oJj4+Hj///DNfoi41ZswY3LhxA8+fPwcA6OrqYuTIkYiMjKy+SAkh5AcmNFnn5+cjKyurzGWfPn0CAGRkZHBlSkpKQusTQgj5NkKTtampKXbs2CEw30dBQQFWrFgBWVlZ7vVeeXl5CA8PF/q6L0IIId9GaJ/17NmzMXToUAwbNgzW1tbo3LkzcnNzERcXh1evXsHHxweKioqIiYmBn58fsrOzsWnTpioHcu/ePQwePBhRUVFQVVUVWu/IkSOYPXu2QLmnpyfmz59f5f0TQkhdJjRZd+7cGWFhYQgKCkJ8fDzOnz8PAGjfvj0CAgIwYMAArq6FhQXGjBlT5bmsk5OTMWHCBBQXF1dY9/79+9DQ0EBQUBBfuYqKSpX2TQgh9UG546w7dOiA9evXo6ioCJmZmWjYsCEaNWrEV8fe3h729vZV2nlxcTH27duH5cuXi/wU5IMHD6CrqwsjI6Mq7ZMQQuojkaZIlZGRQcuWLQUS9bdKSEjAsmXLMGbMGPj4+Ii0zv3796GlpSXWOAghpK4TeT7r6tCxY0dERkZiypQpkJKSqrD+27dvkZGRgaSkJPTq1Qu6urpwcXHB4cOHqz9YQgipRVV6u7m4VLaf+f79+wDAPUEpJyeHw4cPw9fXFyUlJWW+xaYsiYmJ3PBDUWRnZwP4/E2AiBe1qXhRe4pfZdrUxMSk2uKo1WRdWXp6eli/fj3MzMygqKgIAOjevTsyMjKwatUqkZO1rq5upfZ74MoFZGdnV+sH8SNKSEigNhUjak/xq0ttWqvdIJWlrKwMBwcHLlGXsrOzw5s3b5CZmVlLkRFCSPWqV8n6xo0bCAsLEygvnbZV3DdACSGkrhDaDeLk5FTpjUlISFTr/CA3b95EQEAA9PX1oa2tDQDg8Xg4c+YMunbtSi9BIIR8t4Qm69atWwuUJSUlITc3F1paWujQoQN4PB5SU1ORlJQEZWVldO/eXazBZWZmIiUlBZ06dYKioiIGDhyI0NBQTJkyBb/99hsUFBSwZ88ePHz4ELt37xbrvgkhpC4RmqxDQ0P5fj558iR+//137Ny5E+bm5nzLbty4gfHjx0NPT0+swZU+yr5z505YWFigSZMmCA0NxfLly7F06VLk5ORAT08P27dvpzerE0K+axKMMSZKxZ49e8LV1RXTp08vc3lISAgOHjyI6OhosQZYF/it/TwaJMTXtbZD+a7UpTvt3wNqT/GrS20q8g3Gd+/elTm3damGDRvSFKmEEFJNRE7WWlpaOHDgAPLy8gSWZWZmYvfu3dQVQQgh1UTkh2J+/fVXjB8/Hm5ubnBzc4O6ujoKCgrw7NkzHD16FEVFRVi1alV1xkoIIT8skZO1lZUVNm7ciGXLlmHjxo1cuYSEBExNTTFnzpxKPxlICCFENJV63NzKygqHDh1CZmYmXrx4AQkJCbRp0wZKSkrVFR8hhBBUcW4QZWXlcm82EkIIEa9KJeu9e/fi2LFjSE9PR0lJicDy6n6CkRBCflQiJ+uQkBCEhISgSZMmaN++PT3aTQghNUjkZH3w4EGYm5tj8+bNkJWVrc6YCCGEfEXkcdYZGRno27cvJWpCCKkFIifrzp074+nTp9UZCyGEECFETta//fYb9u/fj9jY2OqMhxBCSBlE7rPesWMHGjZsiIkTJ6JBgwZQUlKChIQEXx0aDUIIIdVD5GRdUFAADQ0NaGhoVGc8hBBCyiBysv56fmtCCCE1R6zvYExKShLn5gghhPyPyFfWRUVF2LhxI86ePYu8vDzweDxuWUlJCXJzc5GTk4N79+5VS6CEEPIjE/nK+p9//kFwcDCysrIgLy+PFy9eoFWrVpCWlsbr169RVFSE33//vTpjJYSQH5bIyfr06dMwNzfHuXPnsGnTJgDA/PnzcebMGWzYsAHFxcX0CDohhFQTkZP1mzdv0LNnT0hKSqJly5Zo1qwZbty4AQCws7PDTz/9hP3791dboIQQ8iMTOVk3aNCA78q5bdu2ePjwIfezgYEBUlNTxRsdIYQQAJVI1jo6OoiLi+N+7tChA3dlDXy+8v76IRlCCCHiIXKy9vT0RFRUFIYNG4acnBz06dMHSUlJ8PPzw6ZNm7B9+3bo6+tXZ6y1IiYhFQ+ev8fzt4UY438WMQn07YEQUvNEHrrXq1cvLFq0CNu2bYO8vDysrKwwbtw47mZj69at4efnV22B1oaYhFSEhN1CUfHnYYrv3ucjJOwWAMDeRL02QyOE/GAkGGPsWzbw8uVLZGVloWPHjt/d9Klj/M/i3ft8gfLmSvLYOq9nLUT0fUlISICJiUlth/HdoPYUv7rUpt/8BGPr1q2ho6PzzYn63r170NXVxevXr8utl5ubi4ULF8La2hrGxsYYN24cnj179k37Fia9jERdXjkhhFQXsT5uXlXJycmYMGECiouLK6w7ffp0nD59Gj4+PggMDMSbN28wYsQIZGdniz0uFSX5SpUTUlv81l7Atsi3tR0GqUa1mqyLi4uxe/duDB48GAUFBRXWv3btGmJjYxEYGIiffvoJPXv2xPbt25GdnY29e/eKPb4RrjqQk5HiK5OTkcIIVx2x74sQQspTq8k6ISEBy5Ytw5gxY+Dj41Nh/fj4eCgoKMDa2porU1ZWhpmZGd+wQnGxN1HHFHdDyEh/bqbmSvKY4m5INxcJITWuVpN1x44dERkZiSlTpkBKSqrC+snJydDQ0BCo27Zt22p75Zi9iTq0NJSg0UIWW+f1pERNCKkVIg/dK0tRURHi4+MhKSkJKysrSEtXbnMqKiqVqp+TkwNFRUWBcgUFBeTk5Ii8ncTERHz69Enk+qX94QkJCSKvQ8r3//2r1KbiQOeo+FXlHK3OkSMiZ9fCwkL4+/sjLS0NW7duRWFhITw8PHD//n0An6+Sd+zYgWbNmlVbsOWNMpSUFP1Lgq6ubqX2e+DKBWRnZ9eZITzfA2pT8aL2FL+61qYiZ7iQkBDs378frVq1AgAcPnwY9+7dg5eXF5YsWYJ3795h1apV1RYoACgqKiI3N1egPDc3t8wrbkII+V6IfGV96tQpDB48GP7+/gCAM2fOoFGjRpg9ezakpaWRmpqKsLCwagsUANq3b49Lly6BMcY3D8nz58/Rvn37at03IYTUJpGvrF+/fg0jIyMAQH5+Pv777z9YWlpy/dStWrXCx48fqyXIUt27d8fHjx9x8eJFriwzMxPXrl2DlZVVte6bEEJqk8jJWkVFBenp6QCA8+fPo7CwEPb29tzyBw8eoEWLFmINLjMzEzdv3uRuHpqZmcHc3BwzZsxAWFgYIiIiMGrUKDRq1Ag///yzWPdNSH1Bk439GERO1hYWFtixYwe2bduGoKAgyMvLw9nZGR8/fsS2bduwf/9+ODg4iDW4mJgYeHh4IDExkSsLCQmBo6MjgoKCMGfOHKiqqmL79u1o0qSJWPdNSH0gbLIxStjfH5H7rOfOnYs3b94gMDAQDRs2hL+/Pxo3boyEhAQEBgbC1NQUU6ZMqXIgAwcOxMCBAyssa9KkCZYuXYqlS5dWeV+EfC92nrqHgqISvrKCohLsPHWPngn4zoicrBs3boxt27YhMzMTioqK3MRNOjo62LdvHwwNDastSPJ9Kf3aXlTMwxj/sxjhqkOJpYposrEfh8jdIH5+frh16xaUlZX5Zthr2LAhDA0NcfnyZYwbN65agiTfD/raLl402diPQ+RkHR4eXu47Fq9cuYIrV66IJSjy/SrvazupPJps7MchtBskNTUVbm5uKCws5MpmzZqFWbNmCd3Y9/haLyJe9LVdvEq7j1bvv4miYh6aK8lTt9J3SmiyVldXx/z583Ht2jUwxnD48GGYmJhAXV3wJJCUlISysjINnyMVUlGSL/PtO/S1versTdRx5spzZGdnI8SX3mAkDnXxvkq5NxgHDRqEQYMGAQBevHiByZMnw9LSskYCI9+nEa46CAm7xdcVQl/bSV1SV9+9KvJokNDQ0OqMo0bd+X2+QJmKtRVa9e6FkoICJP21mG+Z5YssPGrWAYArij5+xP3AZQLrq/ZyQXMbaxS8S8fDf1YLLG/Tvy+Uzc2Ql/YCT9ZtEFiu7j4ITY0MkZP8FE+3bBNYrjF8GBrraOPjvft4vmuPwPL2Y0dDsUN7fLh5C6lhBwWWd5w0AQ3V2iDz6n94ceSYwHLN336FXHMVvDsfj9enzwgs1/b1gUzjxngTdQ5vz8UILO8y/3dIycnh1cnTSI+/KLBcf/FfAIDOKdfRjyXjVEkr5Eg2QFOJQrhIvYG9iRsAIHVfGD7cvsO3rkwjRWjPmQ0AeLZzF7IfPORbLtesGTRnTAMAJG/eitynz/iWy7duhU7ekwAAj9esQ/7LV3zLFdq3Q4dfxgAAHq5YhYKMDL7ljbQ00W7EcADA/YAgFGXzz/DY1EAf6h7uAIDEhf7gfdF1CADKpiZo81N/AJU/9wCghaM9Wjo5lnvuAUDDgpwyt0/n3udz70X4EWRe459BT1JWFroL5gH4/3Nvyyc9FECOr15BUQm2hl1Ds0Ob+Mq/PvdKz6PqUKk5TR8/fozjx48jPT0dJSUlAsslJCSwZMkSsQVHvk/G0u/R9M0zFJcUo3PbZpD8zl60TOq3Dyj7fHxfJAFUPO1+tRH57eanT5/GjBkzwOPxhG9MQgL37n1/d/X91l74X3+ga22H8t2gNhUvak/xGeN/tsz7Ks2V5LF1Xu3dExD5ynrNmjVo3bo1VqxYAW1t7W9+mzkhhNRFdfW+isjjrJ89e4ZRo0bBwMCAEjUh5LtVV9+9KvKVtaqqaqVehUUIqTlLJ3enV3qJUV0cDinylbWnpyd2796NzMzM6oyHEEJIGUS+si4qKoKEhAScnZ1hamoKZWVlvre1ADQahIiOrgQJqRyRk/Xy5cu5/8fFxZVZh5I1IYRUD5GTdelbzAkhhNQ8kfusv8Tj8ZCens43yRMhhJDqU6lk/fz5c0ydOhUmJiawsbFBQkICLl26BHd3d1y7dq26YiSEkB9epcZZu7u74+rVq7CxseHKpaSkkJycjDFjxuDmzZvVESMhhPzwRE7WK1asQIMGDXDy5En8+eefKH1K3dzcHCdPnoSKigpCQkKqLVBCCPmRiZysL1++jJ9//hnNmjUTGLLXsmVLDBs2DHfv3hV7gIQQQiqRrAsLC9G4cWOhy2VkZFBQUCCWoAghhPATOVlra2vj3LlzZS4rLi7G0aNHoaWlJbbACCGE/D+Rk/WECRNw8eJF+Pj44PLlywA+vz0mKioKI0aMQFJSEkaPHl1tgRJCSE1aOrk7Rju3qO0wOCI/FOPg4IDFixdjyZIlOHHiBADgjz/+AGMMcnJy8PX1hYuLS6UDOH78ONatW4fU1FS0adMGEyZMwIABA4TWP3LkCGbPni1Q7unpifnzBd+SQQgh34NKvSlm4MCB6NmzJ+Lj45Gamgoej4c2bdrAysoKSkpKld75qVOn4OPjgxEjRsDGxgaRkZHw9fVFgwYN0KtXrzLXuX//PjQ0NBAUFMRXrqKiUun9E0JIfVGpZA0AioqKVbqCLsuKFSvg6uqKuXPnAgBsbGyQlZWFVatWCU3WDx48gK6uLoyMjMQSAyGE1AdCk7Wfnx+GDh0KQ0ND7ueKVGYip9TUVKSkpGDGjBl85S4uLjh16hRSU1Ohri442ff9+/cxYsQIkfZBCCHfC6HJOjw8HFZWVlyyDg8Pr3BjlUnWycnJAID27dvzlWtoaAAAnj59KpCs3759i4yMDCQlJaFXr15ITU2FmpoaJk2aVG4/NyGE1HdCk/XXs+yJe9a97OxsAJ+7Vb6koKAAAMjJyREaU1paGmbNmgU5OTkcPnwYvr6+KCkpwaBBg8QaIyGE1BWV6rPm8Xi4cOECLCwsICcnBwCIioqCpKQk7O3tBZ5sLE/p4+pfr1NaLikpOKpQT08P69evh5mZGZfku3fvjoyMDKxatUrkZJ2YmFipV5SV/mGhyfLFj9pUvKg9xa8ybWpiYlJtcYicrN+/f48JEybgzp07OHToEHR0Pr/p99ixYzh9+jQsLS2xZs0aNGzYUKTtNWrUCIDgFXRubi7f8i8pKyvDwcFBoNzOzg4XL15EZmYmlJWVK9y3rq6uSDGWOnDlArKzs6v1g/gRJSQkUJuKEbWn+NWlNhX5oZiVK1fi0aNH+Ouvv9CxY0euPCgoCEFBQbh58yaCg4NF3nFpX3VKSgpf+fPnz/mWf+nGjRsICwsTKC8oKIC0tHSZCZ4QQr4HIifr2NhYjBo1Cu7u7pCVleXKZWVl0a9fPwwfPhxnz54VeccaGhpQU1PD6dOn+crPnj2Ldu3aoXXr1gLr3Lx5E/PmzePrP+fxeDhz5gy6du0KGRkZkfdPCCH1icjdIB8/fkSzZs2ELldVVUV6enqldu7t7Q0/Pz80adIE9vb2OHfuHE6dOoWVK1cCADIzM5GSkoJOnTpBUVERAwcORGhoKKZMmYLffvsNCgoK2LNnDx4+fIjdu3dXat+EEFKfiHxl3bFjR5w5c4a7Afi1qKioMrsuyjNw4EAsXLgQFy5cgLe3N65evYrAwED07t0bABATEwMPDw8kJiYCAJo0aYLQ0FAYGBhg6dKl+O2335CXl4ft27dzQwwJIeR7JPKVtZeXF3x9fTFx4kQMGzYMGhoakJSUxPPnz7F//35cunQJixcvrnQAQ4cOxdChQ8tcNnDgQAwcOJCvrE2bNlixYkWl90MIIfWZyMm6f//+ePv2LUJCQhAXF8e/EWlpTJs2TSCxEkIIEY9KjbMeN24cPDw8EB8fj5cvX6KkpAStW7eGlZWVSEPmCCGEVE2lJ3Jq3LgxXF1dqyMWQgghQghN1iEhIejZsyc0NTW5nysiISEBb29v8UVHCCEEQAXJWkNDg5I1IYTUAUKT9YEDB9CpUyfu56ioqBoJiBBCiCCh46zHjRuHY8eOcT+Hh4cjNzcXbdq0KfcfIYQQ8ROarPPy8pCRkcH9HBISgocPH9ZIUIQQQvgJ7QYxMDBAcHAwIiIiuDmm161bh/379wvdmISEBHbs2CH+KAkh5AcnNFkHBgYiICAADx48wPv37yEhIYHMzEzk5+fXZHyEEEJQTrKOjY3FjBkz0K5dOwCAtrY25s6di759+9ZUbIQQQv5HaJ91UFAQ3xsSWrduDWnpSj9DQwghRAyEZl9ZWVlERETA0NAQ8vLyePnyJdLT0/Hy5ctyN1jWPNSEEEK+jdBkPXjwYGzZsgWxsbFc2ZIlSyp8e/m9e/fEFx0hhBAA5STrWbNmwczMDA8ePEBhYSHWrFkDZ2dnaGlp1WR8hBBCUMFETvb29rC3twfw+aGYAQMGwMnJqSbiIoQQ8gWR7xieO3eO+/+bN2/w+vVrdOjQAXJycpCWloakpMgvnSGEEFJJlcqwCQkJGDhwIOzt7TF06FDcvXsXV69ehb29PU6ePFldMRJCyA9P5GR9+/ZtjB49Grm5uRg5ciRX3qRJE0hLS8PHx4fvZiQhhBDxETlZr1q1Cmpqajhy5AjGjx/PvThXX18fR48eRceOHbFhw4ZqC5QQQn5kIifrGzduYODAgWjQoAEkJCT4likqKmLIkCF49OiR2AMkhBBSyT5rWVlZocsKCgrA4/G+OSBCCCGCRE7WhoaGOH78eJnL8vLyEBYWBn19fbEFRggh5P+JnKx//fVXJCUlYfjw4Th8+DAkJCRw+/Zt7Ny5E/3790daWhomTpxYnbESQsgPS+Rx1sbGxtiwYQMWLFiAwMBAAMDKlSsBAM2bN8fKlSvRrVu36omSEEJ+cJWaRs/a2hoRERFISkpCSkoKeDwe2rRpAz09vSrPyHf8+HGsW7cOqampaNOmDSZMmIABAwYIrZ+bm4tly5bh7NmzyMvLg6mpKX7//XduKldCCPkeVfqxQx6Ph+LiYjDGuKcXq5qoT506BR8fH1hbW2PNmjUwNzeHr68vTp8+LXSd6dOn4/Tp0/Dx8UFgYCDevHmDESNGIDs7u0oxEEJIfVCpLBsdHY2FCxfizZs3fOUtWrTAggUL4OjoWKmdr1ixAq6urpg7dy4AwMbGBllZWVi1ahV69eolUP/atWuIjY3Fpk2bYGtrCwAwNTWFk5MT9u7di/Hjx1dq/4QQUl+IfGV97do1TJ06FYwxTJ8+HSEhIQgODsb06dMhISGBX3/9FdevXxd5x6mpqUhJSUHPnj35yl1cXJCcnIzU1FSBdeLj46GgoABra2uuTFlZGWZmZoiLixN534QQUt+IfGUdHByMNm3a4MCBA2jUqBHfsmHDhmHQoEFYt24dNm3aJNL2kpOTAQDt27fnK9fQ0AAAPH36FOrq6gLraGhoQEpKiq+8bdu2OHXqlKiHQggh9Y7Iyfr27dvw9vYWSNTA5ycYBw8eLHKiBsD1MSsqKvKVl75JPScnR2CdnJwcgfql65RVX5jExER8+vSp0rF++ZozIh7UpuJF7Sl+lWlTExOTaotDbC9VlJCQQFFRkcj1S+cW+frR9dLysqZcLV1WlspM0aqrqytyXQA4cOUCsrOzq/WD+BElJCRQm4oRtaf41aU2rdQTjAcOHEBeXp7AspycnEo/wVh6hf71FXFubi7f8i8pKipyy79ep6wrbkII+V6IfGU9ZcoUjBgxAm5ubhg+fDg3rjk5ORl79uzBmzdvsHDhQpF3XNpXnZKSwveqsOfPn/Mt/3qdS5cugTHGd0X+/PnzMusTQsj3QuQra1NTUwQHB6OkpARBQUHw9vaGt7c3li1bhqKioko/waihoQE1NTWBMdVnz55Fu3btynxLevfu3fHx40dcvHiRK8vMzMS1a9dgZWUl8r4JIaS+qVSftZOTE+zt7ZGYmIi0tDQAQJs2baCrq1ulB2O8vb3h5+eHJk2awN7eHufOncOpU6e4x9gzMzORkpKCTp06QVFREWZmZjA3N8eMGTPg4+ODpk2bIjg4GI0aNcLPP/9c6f0TQkh9UekMKyUlBQMDAxgYGCAjIwNNmzYVGEonqoEDB6KwsBBbt25FWFgY1NXVERgYiN69ewMAYmJi4Ofnh507d8LCwgIAEBISgoCAAAQFBYHH48HExAT//PMPmjRpUqUYCCGkPpBg5Q2xALBr1y7s27cP4eHhAlfPM2fOxKVLlzB+/HiMGjWqOuOsVX5rP48GCfF1re1Qvit16U7794DaU/zqUpsK7bNmjGH27Nnw9/fH27dv8fLlS4E6ampqkJSURGBgIGbMmFGtgRJCyI9MaLIOCwvD0aNHMWzYMMTFxaFt27YCdaZPn46oqCj0798fp06dwuHDh6szVkII+WGVm6zNzMwwf/58yMnJCd2AnJwclixZAm1tbfz777/VEiQhhPzohCbrx48fw8nJSbSNSErCxcUFDx48EFtghBBC/p/QZC0lJVXuC3K/pqSkVKlHvgkhhIhO6NA9DQ0N3L17V+QN3blzp8wHWb4HSyd3pwlyCCG1SuilcJ8+fXDs2DE8evSowo08evQIx44d414IQAghRLyEJmsPDw+0bt0aXl5eOHr0KEpKSgTq8Hg8HD9+HKNHj4aCggJGjhxZrcESQsiPSmg3iIKCAtatW4fJkyfD19cXCxcuhK6uLpo3bw4ej4eMjAwkJiYiLy8PrVq1wpo1a9CiRYuajJ0QQn4Y5T5u3qFDBxw9ehS7d+/GiRMncP36dRQXFwMAZGRkYGRkhJ49e8LDw6NSNyMJIYRUToVzg8jKymL06NEYPXo0gM+TK0lJSdFcHIQQUoMqPZGTsrJydcRBCCGkHDQwmhBC6gFK1oQQUg9UOEUqIYSQ2kdX1oQQUg9QsiaEkHqAkjUhhNQDlKwJIaQeoGRNCCH1ACVrQgipByhZE0JIPUDJmhBC6gFK1oQQUg9QsiaE8KGHmmuWqO1NyboGBQcHo0uXLrUdxjfR0tLC2rVrazuM78abN2/g5eUFfX19WFlZoaCgoFbjOXjwIAIDA2s1hupU134Ho6Oj4evrK1LdSk+RSqrO3d2d3lNJ+ISGhuL69ev4+++/oaqqCjk5uVqNZ/369TAxManVGH4kO3bsKPOViWWhZF2DVFVVoaqqWtthkDrkw4cPaNGiBXr37l3boZA6rk52gzg6OiIgIABeXl7o2rUrli5divfv32PevHmwtLSEgYEBfv75ZyQkJPCtl52dDT8/P1hYWMDExAR//PEHVqxYAUdHx3K3DUCk7cfHx2PIkCEwNjaGmZkZJk+ejCdPnnDLU1JSMHHiRFhYWMDQ0BAeHh6IjY3llpf1Fezw4cP46aefYGRkBFtbWwQGBuLTp0/c8jlz5mDs2LEICwtDz549oaenh/79++P8+fPf3tBicO/ePXh7e6Nbt27Q1dWFra0tFi9ezPd1/lvbDQBu3ryJ0aNHw8zMDGZmZpg2bRrS0tJq7Dirg6OjI8LCwvDy5UtoaWkhODgYr1+/xuzZs2FjYwNDQ0N4enri6tWr3DppaWnQ0tLC9u3b4eLiAgsLC5w8eRIA8ODBA4wbNw7GxsYwMTHBtGnT8Pr1a7597tixA7169YK+vj5sbGzw559/Iicnh4snJSUF4eHh0NLSqnPtGxkZCS0tLaxbt44ru3fvHvT09Ljf47CwMLi4uMDAwABDhgxBVFQUtLS0cOXKFb5tnT59Gj169ICBgQGGDx+O27dv8y1/8uQJJk+eDEtLSxgbG+OXX37B/fv3+epU9FkBwPHjx9GvXz8YGBjA0tISPj4+ePPmDQDAy8sLly5dwtWrV8uMUQCrgxwcHFiXLl1YQEAAi4uLY1evXmX9+vVj1tbWbP/+/Sw6OppNmDCB6enpsVu3bnHrDR8+nJmbm7P9+/ezqKgoNnToUKanp8ccHByEbvvWrVvs06dPFW4/JSWFGRgYsIULF7JLly6x06dPMxcXF+bk5MR4PB4rKSlhvXr1YiNGjGAxMTHswoULbPz48UxHR4c9f/6cMcbY6tWrmY6ODhfLqlWrmJaWFlu8eDE7f/4827p1KzMyMmIjR45kPB6PMcaYr68vMzExYa6uruz48eMsJiaG/fTTT8zIyIh9/PixJj4OPpqammzNmjWMMcZev37NjI2N2dixY1lMTAyLj49nS5cuZZqammzjxo2MMfG0W3x8PNPR0WG//PILi4qKYkePHmU9evRg1tbW7N27dzXeBuKSmJjIJk6cyKytrdmNGzfYy5cvmbW1NevZsyc7evQoi4qKYmPGjGFdunRhFy9eZIwxlpqayjQ1NZmBgQE7ePAgO3nyJHv37h1LTk5mxsbGzN3dnUVERLATJ06wXr16MUdHR+48OXbsGNPV1WU7d+5kV65cYXv37mVGRkZszpw5XDy2trZs3Lhx7MaNG6ygoKDW2kaYmTNnMn19ffb8+XNWUFDA+vbty9zc3FhBQQE7cOAA09TUZAsXLmRxcXEsKCiIGRgYME1NTXb58mXG2OffQU1NTWZubs727t3LIiMj2eDBg5mRkRF7+/YtY4yx+/fvMyMjIzZ48GB25swZdubMGTZw4EBmZGTEHj16xBhj7M2bNxV+VteuXWM6OjosODiYXblyhR0+fJhZW1uz4cOHM8YYe/ToERs0aBAbMGAAu3HjBsvOzi732OtssnZ0dOQS1r59+5iWlha7ffs2V6ekpIT99NNPbNSoUYwxxi5evMg0NTVZdHQ0Vyc3N5d169ZNIFl/uW1Rt3/8+HGmqanJXr9+zdW5desWW7FiBcvOzmZv375lmpqa7OjRo9zyjx8/siVLlrCHDx8yxviT9fv375menh5buHAh37GfOHGC7zh8fX2ZpqYmS0lJ4epcvXqVaWpqsoiIiEq0qnh8maxjY2OZp6cny8nJ4avj5ubGxo0bxxgTT7sNHDiQubm5sZKSEq7OixcvmJ6eHgsICKi2Y60Jc+fO5c7PgIAApq+vz16+fMktLykpYW5ubmzgwIGMsf9P1r6+vnzbmTFjBrO2tub7LN6+fcsMDAzY2rVrGWOM/fHHH8zFxYXv3D9y5AjbuXMn97Ozs7PAtuuS9+/fM2tra/bLL7+wlStXMl1dXXbv3j3GGGP29vZs6tSpfPUXLFhQZrI+e/YsVyczM5MZGRmxoKAgxhhjU6dOZZaWliw3N5erk5OTwywtLbnti/JZbdiwgRkbG/P90YuJiWHBwcHcZzBy5EgueVekTnaDAEDnzp0hISEBALh06RJatmwJHR0dFBcXo7i4GDweDw4ODvjvv/9QWFiIy5cvQ05ODnZ2dtw2GjZsCHt7+3K3Ler2DQ0NIScnh8GDB2Px4sU4f/48tLW1MX36dCgqKkJFRQWdOnXCH3/8AV9fXxw7dgw8Hg9+fn7o3LmzQAy3bt1CYWEh+vTpw1feq1cvyMjI8H0lat68OdTV1bmfS/u98/Pzq9a4YmJra4tdu3ZBVlYWjx8/RlRUFNatW4fMzEwUFRUBwDe3W15eHhITE9G7d29ISv7/6dq6dWuYmpoKfO2sz65duwYTExO0atWKK5OUlETv3r2RmJjIdVcAgKamJt+6ly9fRrdu3SAnJ8edw0pKSjAwMMDFixcBAN26dcPTp0/x008/ISQkBHfu3EHfvn3h5eVVMwcoBk2bNsXChQsRFxeHDRs2YNq0adDW1sbz58/x8uVLuLi48NUv616AjIwMnJycuJ+VlJTQtWtXrivk2rVrcHR0RMOGDbk6CgoKcHR05M43UT4rMzMz5Ofno2/fvli+fDmuXbuG7t27Y8qUKXz5R1R19gZjs2bNuP9/+PABr1+/hq6ubpl1379/j/fv30NJSUmgEVRUVMrdtqjbV1NTw65du7Bx40YcOHAAO3fuROPGjTFs2DD89ttvkJCQwNatW7Fu3TpERETg8OHDkJGRgbOzMxYuXCjwNvisrCwAnxPxlyQlJaGsrMz3iykvL89Xp/QYeTxemfHWFB6PhxUrVmD37t3Iy8tDq1atYGBgADk5OW7s6Le226dPn8AYE/o5vnz5sqYPu9pkZWWhXbt2AuUqKipgjCE3N5crK+scPnbsGI4dOyawfuk2e/fuDR6Phz179mDt2rUIDg5GmzZt4OPjU69ucNrY2EBFRQXp6encxVhmZiYAwRd6l3XeKCkp8f3hL12vNFlnZWUJPd9Kfy9F+ayMjY2xceNGbN++Hdu2bcPGjRuhoqKCiRMnVukPZJ1N1l9q1KgROnbsKHT8p5KSElq0aIHMzEwwxvgSdkZGhli2DwAGBgYICQlBYWEhEhISsG/fPqxfvx5dunSBi4sLWrZsiT///BMLFizA/fv3cfr0aWzatAnNmjXDH3/8wbfN0uT97t07tG3blivn8XjIzMzk9lmXlZ6If/31F3r06IFGjRoBAAYPHsxX71vabcaMGZCQkEB6errA/t+9e1cv2klUjRs3LvM43759C+DzeVj6/68pKirC1tYWI0aMEFgmKyvL/d/NzQ1ubm7Izs7GhQsXsGnTJsyaNQvm5uZlJqi6aNWqVcjJyUG7du3w+++/Y+/evWjZsiUAwd/30iT+pezsbIE8kZ6ezp1Lwj6Hd+/eoWnTpuXW+fKzAj7/YbGxsUF+fj4uX76MnTt3wt/fH8bGxtDT06vUcdfZbpAvmZmZ4eXLl2jRogX09fW5f1FRUQgNDYWMjAzMzMxQWFjIN0ri65+/ZfuhoaFwdHREYWEhZGVlYWlpiUWLFgEAXr16hdu3b8PKygq3b9+GhIQEdHR0MH36dGhqauLVq1cC+zQ0NISsrCxOnDjBV3769GkUFRXVi7GuCQkJ0NLSwsCBA7lE/ebNGzx8+JC76v/WdlNQUICuri5OnjzJ903i1atXuH79Orp27VrzB15NzMzMkJCQwDeCg8fj4fTp09DX1+dLul8zNzfHkydPoKury52/Xbp0wcaNGxEXFwcAmDlzJqZMmQLg8wWKq6srJk+ejOLiYrx79w4ABK4465pbt25h27ZtmDp1KpYuXYrbt29j27ZtaNWqFdTU1BAVFcVXPzIyUmAb+fn5uHbtGvfzu3fvkJCQAAsLCwCfP4fo6Gjk5eVxdfLy8hAdHc39XoryWf39998YPHgwGGOQl5eHg4MD9wBM6XpSUlIiH3vd/mT+Z+DAgWjZsiVGjx6NI0eO4PLlywgICMC6deugrq4OCQkJWFhYwMLCAnPmzEFYWBhiYmIwYcIEpKenV9g/JMr2u3Xrhnfv3sHb2xuxsbG4cOEC/Pz8ICcnBwcHB2hra6Nhw4aYPXs2Tpw4gStXrmDlypW4d++eQD8a8LnvbezYsdizZw+WLFmC+Ph4bN++HX/88QfMzc1hY2NTXc0pNgYGBkhKSsKmTZtw9epVhIWFwdPTE4WFhVx/ujjabfr06Xj8+DEmTpyI6OhoHD9+HKNGjYKioiJGjRpViy0gXqNHj4aioiJGjhyJ48ePIzo6GhMmTMCTJ08wffr0ctf19vbG48ePMWnSJERFRSE2NhYTJ07EuXPnuO69bt26ISIiAoGBgbh06RLOnDmDVatWoX379tx9lcaNGyMpKQlXr17lG0JaFxQUFMDPzw+ampoYNWoUunbtiiFDhmD16tVITk7G1KlTcfLkSfj7+yM+Ph7BwcHYtWsXAP4/QjIyMvD19cXJkycRGRmJsWPHolGjRty3Em9vb+Tk5GDUqFGIiIjA2bNnMWrUKOTl5cHb2xuAaJ+VlZUV7t69izlz5iA+Ph4xMTHw9/eHkpISzM3NAXz+o/n06VNcunSJ6xoVSqTbkDXMwcGBzZ07l6/s3bt3bM6cOaxbt25MX1+f9e7dm4WGhvLVyczMZD4+Pqxr167MxMSE/fnnn2zq1KnMzc2t3G2Luv34+Hg2dOhQ1rVrV2ZoaMg8PT3Zf//9xy1/9uwZdydZV1eX9enTh+3bt49b/vXQPcYYCw0NZS4uLkxXV5fZ2dmxwMBAlpeXxy339fVlzs7OfOuUjgg4fPhwRU0pdl+OBikoKGALFy5k1tbWzMDAgLm4uLDVq1ez4OBgpq+vzw1F+tZ2K92Gh4cH09fXZ+bm5uy3335jaWlpNXfg1eTL0SCMfW6LKVOmsK5duzIjIyM2fPhwbiQDY+V/9rdv32ZjxoxhRkZGzNjYmP3888/swoULfHV27drFevfuzQwMDJi5uTmbNm0ae/HiBbc8MjKSWVpaMj09PZaQkFANR1x1gYGBTEdHh2/UVlZWFrO2tmZDhgxhxcXFbNeuXczR0ZHp6uqyoUOHsm3btjFNTU129+5dxtjn30EbGxt2+PBhZm9vz/T19dmYMWNYcnIy377u3LnDRo8ezYyMjFjXrl3Z+PHjuVEnpSr6rBj7PLqrdKitsbEx++WXX9iDBw+45Tdv3mT29vZMV1eXnThxotzjl2Ds+5i15cWLF7h16xacnZ35vi4OHjwYqqqqCAkJqcXoCCHV7fjx49DX14eGhgZXtnv3bvj7++PKlSto3LhxLUb37erFDUZR+fr6wtXVFQMGDABjDKdOncLdu3cxc+bM2g6NEFLNwsPDERwcjGnTpqF58+Z49OgRVq1ahf79+9f7RA0A382VNfD5seY1a9bgwYMH4PF40NbWxuTJk+tF/y8h5NtkZGRg2bJlOH/+PD58+ABVVVX0798fEydOhIyMTG2H982+q2RNCCHfq3oxGoQQQn50lKwJIaQeoGRNCCH1ACVrUuPmzJkDLS0t6OjolPk4cKl+/fpBS0sLc+bMEVi3rs21XIrH4/HFdujQIdHmKv5GNbUfUnsoWZNaw+PxEB0dXeay1NRUPHjwoIYj+jY5OTkYMmQIwsPDazsU8h2iZE1qTVlzOZSKjIwUmEGtrvvw4QPu3LlT22GQ7xQla1JrnJyccPHixTLnoIiIiOB7HRshPzpK1qTWODs7Iz8/n5scv1RGRgZu3LiBnj17im1fpX269+/fx6+//gpjY2N069YNgYGBKCkpQXh4OFxcXGBkZIShQ4cKvG8vKysLixYtgo2NDfT09ODq6oodO3Zw83ZfuXKFm9A+JCREoF89IyMDPj4+MDU1RdeuXeHt7S0wF3d+fj6WL18OR0dH6OnpwdHREcuWLRN4yURGRgb8/PzQrVs3mJiYYP78+SgsLBRbW5G66bt63JzULyYmJlBSUkJUVBTfVXRUVBTk5eVhaWkp9n2OHz8eJiYmmDNnDs6ePYutW7fi4cOHePDgAUaOHAnGGNatW4dff/0VJ0+ehLS0NPLy8jB8+HC8evUKw4YNg6qqKi5fvowlS5bg2bNnWLBgATp27Ag/Pz8sXboUPXr0QI8ePfi6cebOnQtTU1P4+Pjg8ePH2LNnD9LS0nDkyBEAn6fzHT16NG7evImBAwdCT08Pt2/fxqZNm5CQkICdO3dCRkYGBQUFGD58ONLS0jBixAg0b94c4eHh3EtzyfeLkjWpNVJSUnBwcEB0dDR4PB43jWVERATs7e3Lnb+5qoyMjLBy5UoAn9+cYmlpiYsXL+Lo0aPcNKG5ublYv3490tLS0K5dO2zZsgVPnz7FwYMHoaWlBQAYNmwYVqxYgQ0bNsDDwwPa2tpwdnbG0qVLoaWlhf79+/Pt18rKCmvXruV+zs3NxaFDh5Camgp1dXUcPHgQN27cgJ+fHzft67Bhw9CpUyf8/fffCAsLw7BhwxAWFobk5GSsWbMGzs7OAIAhQ4bA3d0d2dnZYm8vUndQNwipVU5OTsjIyMDNmzcBfB5RcenSJS4RiduX223UqBGUlZXRrl07vvdkqqmpAQA3If/Zs2ehqamJ5s2bIzMzk/tXui1hI1q+9PW7NvX19fn2ce7cOSgqKsLT05Ov3ogRI6CoqMjdiI2Li4OKigrfcTRs2BDu7u6iNQCpt+jKmtSq7t27Q15eHufOnUPXrl0RGxsLSUlJvhcfi9PXr66SlpYWeJ9h6ds7St9Mk5KSgk+fPgntlinrTUBf+3pkS4MGDQCAe7FwWloa1NXVBSYckpWVhbq6Ol68eAHg81TAX748uVT79u0rjIHUb5SsSa1q0KABrKysEBUVBR8fH0RERMDKygoKCgrVsr+yXqNU0ZuESkpKYGJiwr0S62stWrSocL8VvS6rvPnUeDwel8QlJCRQUFBQqfXJ94G6QUitc3Z2RnJyMh4+fIi4uDj06NGjtkPi06ZNG+Tm5sLKyorvn66uLj5+/Cjw9vmq7iM1NZW70i5VWFiItLQ0tGrVCsDnLprU1FQUFxfz1UtNTf3mGEjdRsma1DoHBwdISUkhMDAQnz59qnPjqx0dHXH//n3ExMTwla9btw7Tpk3Do0ePAAh2n1R2Hzk5Odi9ezdf+Z49e5Cbmwt7e3sAQM+ePZGdnY2wsDCuTlFREfbv31/pfZL6hbpBSK1TUlKCiYkJLly4AAsLCygpKVW4zsqVK8vsKnF1dRX7kL8JEybg7NmzmDJlCoYOHYrOnTsjISEBR44cga2tLWxtbQF8fgmypKQkzp07h9atW1dqnLi7uzvCw8MREBCAhw8fQk9PD3fv3sWhQ4dgaGjI3UDs378/9u/fj0WLFuHJkydo164djh49yt2oJN8vStakTnBycsLVq1dFTnDHjx8vs7xDhw5iT9ZNmzbFvn37sHr1apw+fRr79u1D69atMXnyZIwfP57rj5aXl8f06dOxZcsW+Pv7o23btiLvQ1ZWFtu3b8eaNWtw6tQpHD16FKqqqpgwYQImTZrE9VlLSUlh8+bNWLlyJU6dOoW8vDzY2tpi1KhRFb4BndRv9KYYQgipB6jPmhBC6gFK1oQQUg9QsiaEkHqAkjUhhNQDlKwJIaQeoGRNCCH1ACVrQgipByhZE0JIPUDJmhBC6oH/AydTQt5rSEBKAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "errors = np.full((2, irm_summary.shape[0]), np.nan)\n", + "errors[0, :] = irm_summary['coef'] - irm_summary['2.5 %']\n", + "errors[1, :] = irm_summary['97.5 %'] - irm_summary['coef']\n", + "plt.errorbar(irm_summary.index, irm_summary.coef, fmt='o', yerr=errors)\n", + "plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", + "\n", + "plt.title('Interactive Regression Model (IRM)')\n", + "plt.xlabel('ML method')\n", + "_ = plt.ylabel('Coefficients and 95%-CI')" + ] + }, + { + "cell_type": "markdown", + "id": "8c891e02", + "metadata": {}, + "source": [ + "#### IRM - Summary of prediction assessment metric's mean values" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "6790aad8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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main RMSEmain RMSE (sd)prop log lossprop log loss (sd)
regression1.7280.0271.0230.028
lasso1.1140.0060.6690.003
forest1.1690.0080.6820.003
xgboost1.2290.0100.7200.013
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" + ], + "text/plain": [ + " main RMSE main RMSE (sd) prop log loss prop log loss (sd)\n", + "regression 1.728 0.027 1.023 0.028\n", + "lasso 1.114 0.006 0.669 0.003\n", + "forest 1.169 0.008 0.682 0.003\n", + "xgboost 1.229 0.010 0.720 0.013" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "irm_rmse_index = ['regression','lasso', 'forest', 'xgboost']\n", + "irm_rmse = pd.DataFrame([[rmse_main_linlog_irm_mean, rmse_main_linlog_irm_std, \n", + " logloss_prop_linlog_irm_mean, logloss_prop_linlog_irm_std],\n", + " [rmse_main_lasso_irm_mean, rmse_main_lasso_irm_std,\n", + " logloss_prop_lasso_irm_mean, logloss_prop_lasso_irm_std],\n", + " [rmse_main_forest_irm_mean, rmse_main_forest_irm_std,\n", + " logloss_prop_forest_irm_mean, logloss_prop_forest_irm_std],\n", + " [rmse_main_boost_irm_mean, rmse_main_boost_irm_std,\n", + " logloss_prop_boost_irm_mean, logloss_prop_boost_irm_std]],\n", + " index=irm_rmse_index,\n", + " columns=['main RMSE', 'main RMSE (sd)',\n", + " 'prop log loss', 'prop log loss (sd)'])\n", + "irm_rmse.round(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "a5be2641", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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AU6ZMwdmzZwEAw4cPx44dO7B79+7r1liD3ETv3r2la9euMnfuXNmyZYvs3r1b+vXrJ4GBgfLpp59KZmamjBs3Tjw9PSUnJ8fyumHDhomfn598+umnkpGRIUOGDBFPT0/p3bv3H/adk5Mj5eXlN+0/Pz9fjEajzJo1S3bs2CFpaWkSEhIijz76qFRVVcnVq1clNDRUnn32Wdm0aZNs27ZNnn/+efHw8JATJ06IiMjChQvFw8PDUkt8fLy4u7vLnDlzZOvWrbJ06VIxmUzy3HPPSVVVlYiIxMTEiI+Pj/Tt21dSU1Nl06ZNMnDgQDGZTPLLL7/cbCjrhE6nk/fee09ERAoKCsTLy0tGjx4tmzZtkqysLHnrrbdEp9NJYmKiiGgzdllZWeLh4SFjxoyRjIwM+eqrr+Sxxx6TwMBAKSwsrJdxsFVubq5ERUVJYGCg7Nu3T86cOSOBgYHy+OOPy1dffSUZGRkyatQo6dq1q2zfvl1ERE6ePCk6nU6MRqN8/vnnsn79eiksLJS8vDzx8vKSQYMGycaNG2XdunUSGhoqwcHBlv1k7dq1otfrZfny5bJr1y755JNPxGQySWxsrKWenj17ytixY2Xfvn1SUVFRb2NzI5MnTxaDwSAnTpyQiooKefLJJyU8PFwqKirks88+E51OJ7NmzZItW7bI/PnzxWg0ik6nk507d4rItfehTqcTPz8/+eSTTyQ9PV0iIyPFZDLJuXPnRETkxx9/FJPJJJGRkfLNN9/IN998IxEREWIymeTIkSMiInL27Nmbbq+9e/eKh4eHJCQkyK5duyQlJUUCAwNl2LBhIiJy5MgR+fvf/y4DBgyQffv2SUlJyQ3XvVbhGRwcbAmQ1atXi7u7u+zfv9/S5urVqzJw4EAZMWKEiIhs375ddDqdZGZmWtqUlpaKv79/jfD8fd+17T81NVV0Op0UFBRY2uTk5MiCBQukpKREzp07JzqdTr766ivL/F9++UXefPNN+emnn0TEOjwvXrwonp6eMmvWLKt1X7dundV6xMTEiE6nk/z8fEub3bt3i06nk40bN95sKOvE78Nz8+bNMnToUDGbzVZtwsPDZezYsSKizdhFRERIeHi4XL161dLm9OnT4unpKXPnzq2zda1rr7zyimX/nDt3rhgMBjlz5oxl/tWrVyU8PFwiIiJE5LfwjImJsern5ZdflsDAQKvtcO7cOTEajfL++++LiMiMGTMkJCTEat//8ssvZfny5Zaf+/TpU6Nve3Px4kUJDAyUMWPGyDvvvCN6vV4OHTokIiK9evWS6Ohoq/avv/76dcNzw4YNljZFRUViMplk/vz5IiISHR0tAQEBUlpaamljNpslICDA0n9tttfixYvFy8vL6oNo06ZNkpCQYNkOzz33nCVMb6ZWd9s7d+4MBwcHAMCOHTvQvn17eHh44MqVK7hy5QqqqqrQu3dv7NmzB5WVldi5cyeaNWuGRx55xNLHXXfdhV69et2w79r2361bNzRr1gyRkZGYM2cOtm7dii5dumDSpElwcnKCi4sLHn74YcyYMQMxMTFYu3YtqqqqMH36dHTu3LlGDTk5OaisrMQTTzxhNT00NBSOjo5Wh+9333033NzcLD9XXze9fPlybYayTvXs2RMrV65E06ZNcfToUWRkZGDRokUoKirCr7/+CgA2j11ZWRlyc3MRFhaGJk1+233uuece/O1vf6txmtRQ7d27Fz4+PujQoYNlWpMmTRAWFobc3FzL6TUA6HQ6q9fu3LkT/v7+aNasmWUfdnZ2htFoxPbt2wEA/v7+OH78OAYOHIh3330XBw4cwJNPPonhw4ffnhXUSOvWrTFr1ixs2bIFixcvxsSJE9GlSxecOHECZ86cQUhIiFX7611PdnR0xKOPPmr52dnZGd7e3pZT97179yI4OBh33XWXpU3z5s0RHBxs2d9qs718fX1x+fJlPPnkk/jXv/6FvXv34v/+7//w4osvWmVQbdXqhlHbtm0t/7906RIKCgqg1+uv2/bixYu4ePEinJ2daxTk4uJyw75r23/Hjh2xcuVKJCYm4rPPPsPy5cvRsmVLPPPMM3jppZfg4OCApUuXYtGiRdi4cSNSUlLg6OiIPn36YNasWWjVqpVVn8XFxQCuBePvNWnSBG3atLF6o9x5551WbarXsaqq6rr13k5VVVVYsGABVq1ahbKyMnTo0AFGoxHNmjWzPLtm69iVl5dDRP5wW545c+Z2r3adKC4uRqdOnWpMd3FxgYigtLTUMu16+/DatWuxdu3aGq+v7jMsLAxVVVX4+OOP8f777yMhIQH33nsvpkyZ0uBuWAUFBcHFxQXnz5+3HCAVFRUBANq0aWPV9nr7jbOzs9UHcfXrqsOzuLj4D/e36vdmbbaXl5cXEhMTsWzZMiQlJSExMREuLi6IiopS+tC65bvtLVq0wEMPPfSHz585OzujXbt2KCoqgohYBeiFCxc06R8AjEYj3n33XVRWViI7OxurV6/GBx98gK5duyIkJATt27fHzJkz8frrr+PHH39EWloaPvzwQ7Rt2xYzZsyw6rM6TAsLC3HfffdZpldVVaGoqMiyTHtXvWO88cYbeOyxx9CiRQsAQGRkpFU7W8bu5ZdfhoODA86fP19j+YWFhQ1mrG6mZcuW113Hc+fOAbi2H1b//385OTmhZ8+eePbZZ2vMa9q0qeX/4eHhCA8PR0lJCbZt24YPP/wQU6dOhZ+f33XDwl7Fx8fDbDajU6dOePXVV/HJJ5+gffv2AGq+56tD9fdKSkpqZMX58+ct+9IfbYvCwkK0bt36hm1+v72Aa0EfFBSEy5cvY+fOnVi+fDlmz54NLy8veHp63tJ63/JD8r6+vjhz5gzatWsHg8Fg+ZeRkYEVK1bA0dERvr6+qKystLoL/b8/29L/ihUrEBwcjMrKSjRt2hQBAQH45z//CQD4+eefsX//fvTo0QP79++Hg4MDPDw8MGnSJOh0Ovz88881ltmtWzc0bdoU69ats5qelpaGX3/9tcE8a5ednQ13d3dERERYgvPs2bP46aefLEfGto5d8+bNodfrsX79equj7Z9//hnfffcdvL29b/+K1wFfX19kZ2db3SGvqqpCWloaDAaDVQj+Lz8/Pxw7dgx6vd6y/3bt2hWJiYnYsmULAGDy5Ml48cUXAVw7YOjbty/Gjx+PK1euoLCwEABqHI3Zo5ycHCQlJSE6OhpvvfUW9u/fj6SkJHTo0AEdO3ZERkaGVfv09PQafVy+fBl79+61/FxYWIjs7Gx0794dwLVtkZmZibKyMkubsrIyZGZmWt6btdlecXFxiIyMhIjgzjvvRO/evS0PxFe/7o477qj1ut/y1omIiED79u0xcuRIfPnll9i5cyfmzp2LRYsWwc3NDQ4ODujevTu6d++O2NhYJCcnY9OmTRg3bhzOnz9/02sLtenf398fhYWFmDBhAjZv3oxt27Zh+vTpaNasGXr37o0uXbrgrrvuwrRp07Bu3Trs2rUL77zzDg4dOlTjGgxw7brN6NGj8fHHH+PNN99EVlYWli1bhhkzZsDPzw9BQUG3Okz1wmg04ocffsCHH36I3bt3Izk5GUOHDkVlZaXlmqwWYzdp0iQcPXoUUVFRyMzMRGpqKkaMGAEnJyeMGDGiHkdAOyNHjoSTkxOee+45pKamIjMzE+PGjcOxY8cwadKkG752woQJOHr0KF544QVkZGRg8+bNiIqKwrfffmu5HOXv74+NGzdi3rx52LFjB7755hvEx8fjgQcesFyXb9myJX744Qfs3r3b6pE5e1FRUYHp06dDp9NhxIgR8Pb2xuDBg7Fw4ULk5eUhOjoa69evx+zZs5GVlYWEhASsXLkSgPUHg6OjI2JiYrB+/Xqkp6dj9OjRaNGiheXIfcKECTCbzRgxYgQ2btyIDRs2YMSIESgrK8OECRMA1G579ejRAwcPHkRsbCyysrKwadMmzJ49G87OzvDz8wNw7YPs+PHj2LFjh+Vy3h+62R2l3r17yyuvvGI1rbCwUGJjY8Xf318MBoOEhYXJihUrrNoUFRXJlClTxNvbW3x8fGTmzJkSHR0t4eHhN+y7tv1nZWXJkCFDxNvbW7p16yZDhw6VPXv2WOb/97//tdyl0+v18sQTT8jq1ast8//3USURkRUrVkhISIjo9Xp55JFHZN68eVJWVmaZHxMTI3369LF6TfUd15SUlJsNZZ34/d32iooKmTVrlgQGBorRaJSQkBBZuHChJCQkiMFgsDx6YevYVffx1FNPicFgED8/P3nppZfk1KlTt2/F68Dv77aLXBuHF198Uby9vcVkMsmwYcMsd4lFbrzt9+/fL6NGjRKTySReXl7y9NNPy7Zt26zarFy5UsLCwsRoNIqfn59MnDhRTp8+bZmfnp4uAQEB4unpKdnZ2XWwxraZN2+eeHh4WD0ZU1xcLIGBgTJ48GC5cuWKrFy5UoKDg0Wv18uQIUMkKSlJdDqdHDx4UESuvQ+DgoIkJSVFevXqJQaDQUaNGiV5eXlWyzpw4ICMHDlSTCaTeHt7y/PPP2+5q1/tZttL5NoTNNWPF3p5ecmYMWPk8OHDlvnff/+99OrVS/R6vaxbt+6G618nXz18+vRp5OTkoE+fPlanN5GRkXB1dcW7776r9SKJyM6kpqbCYDDg/vvvt0xbtWoVZs+ejV27dqFly5b1WJ3t6uzXM2NiYtC3b18MGDAAIoKvv/4aBw8exOTJk+tqkURkR7744gskJCRg4sSJuPvuu3HkyBHEx8ejf//+DT44AaBOjjyBa78C+N577+Hw4cOoqqpCly5dMH78+AZz/ZCIbHPhwgW8/fbb2Lp1Ky5dugRXV1f0798fUVFRcHR0rO/ybFZn4UlE9Gdm/89CEBHZIYYnEZEChicRkQKGJxGRAoYnEZGC/wdbaj4YdcAOmwAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# graphical illustration of RMSE for main regression\n", + "errors_irm_rmse = np.full((2, irm_rmse.shape[0]), np.nan)\n", + "errors_irm_rmse[0, :] = irm_rmse['main RMSE'] - irm_rmse['main RMSE (sd)']\n", + "errors_irm_rmse[1, :] = irm_rmse['main RMSE'] + irm_rmse['main RMSE (sd)']\n", + "plt.errorbar(x=irm_rmse.index, y=irm_rmse['main RMSE'], fmt='x',\n", + " yerr=errors_irm_rmse, c='darkslategray')" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "9255bc0a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# graphical illustration of log loss for main regression\n", + "errors_irm_logloss = np.full((2, irm_rmse.shape[0]), np.nan)\n", + "errors_irm_logloss[0, :] = irm_rmse['prop log loss'] - irm_rmse['prop log loss (sd)']\n", + "errors_irm_logloss[1, :] = irm_rmse['prop log loss'] + irm_rmse['prop log loss (sd)']\n", + "plt.errorbar(x=irm_rmse.index, y=irm_rmse['prop log loss'], fmt='x',\n", + " yerr=errors_irm_logloss, c='darkslategray')" + ] + }, + { + "cell_type": "markdown", + "id": "27c6157d", + "metadata": {}, + "source": [ + "### Inspection of the benchmark model\n", + "\n", + "It is natural to investigate why the the benchmark model performs so much worse as compared to the ML models. First of all, we can conclude that the predictive performance of the linear and logistic regression for the nuisance functions is considerably worse and more variable than for lasso, random forest and xgboost. Moreover, we can also inspect the propensity score estimates of the logistic regression which appear to be very close to zero and one for many observations.\n", + "\n", + "We first define a helper function that plots the propensity scores for each of the cross-fitting repetitions." + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "78afa7eb", + "metadata": {}, + "outputs": [], + "source": [ + "def rep_propscore_plot(DoubleML):\n", + " \"\"\"\n", + " A function to create histograms as sublots for every repetition's propensity score density \n", + " of a Double Machine Learning model\n", + " \n", + " ...\n", + " \n", + " Parameters\n", + " ----------\n", + " DoubleML : doubleml\n", + " The Double Machine Learning model\n", + " \"\"\"\n", + " \n", + " \n", + " #export nuisance part from the DoubleML model\n", + " m = DoubleML.predictions.get('ml_m')\n", + " \n", + " # dimensions of nuisance array\n", + " h = m.shape[0]\n", + " rep = DoubleML.n_rep\n", + " \n", + " # create histograms as subplots covering the propensity score densities of all repetitions\n", + " fig, ax = plt.subplots(1, rep, figsize=[20,4.8])\n", + " for i in range(rep):\n", + " ax[i].hist(np.reshape(m[:,i], h), bins=25)\n", + " ax[i].set_title('repetition ' + str(i+1))\n", + " ax[i].set_xlabel(\"prop_score\")\n", + " ax[i].set_ylabel(\"density\")\n", + " \n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "53d9d81d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_irm_regression)" + ] + }, + { + "cell_type": "markdown", + "id": "4f8d0f9f", + "metadata": {}, + "source": [ + "Let's compare this to the corresponding plot for the lasso-based model." + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "e67ebd28", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_irm_lasso)" + ] + }, + { + "cell_type": "markdown", + "id": "b282c8d9", + "metadata": {}, + "source": [ + "We observe that the propensity score estimates of the lasso-based model are more centered and only close to zero and one for very few observations." + ] + }, + { + "cell_type": "markdown", + "id": "b29e412d-d86f-46b4-840f-cbbe082faf0b", + "metadata": {}, + "source": [ + "### Conclusion\n", + "\n", + "We can conclude that the interactive regression model (IRM) estimates are close to the true coefficient value, if the nuisance components are estimated with machine learning methods. The performance of Lasso and the tree-based methods random forests and extreme gradient boosting are comparable. All of the ML-based estimators have exhibited a superior performance to the benchmark based on linear and logistic regression, which seems to be rather unstable in the data example considered.\n" + ] + }, + { + "cell_type": "markdown", + "id": "f50297c5", + "metadata": {}, + "source": [ + "## 2. Partially Linear Regression Model (PLR)\n", + "\n", + "The [DoubleML](https://docs.doubleml.org/stable/index.html) package also includes the [Partial Linear Regression (PLR)](https://docs.doubleml.org/stable/guide/models.html#partially-linear-regression-model-plr) model, which assumes the population regression has a linear and additive structure. Although in reality, we never know if this structure really holds for the underlying data generating process, we can apply this model and see how the estimates compare to those from the IRM." + ] + }, + { + "cell_type": "markdown", + "id": "fa24e6e1-b878-401f-b38a-c29cc0620c2c", + "metadata": {}, + "source": [ + "We estimate the function $g_0$ and $m_0$ in the following PLR model:\n", + "\n", + "\\begin{eqnarray}\n", + "& Y = D\\theta_0 + g_0(X) + \\zeta, &\\quad E[\\zeta \\mid D,X]= 0,\\\\\n", + "& D = m_0(X) + V, &\\quad E[V \\mid X] = 0.\n", + "\\end{eqnarray}\n", + "\n", + "To estimate the causal parameter $\\theta_0$, we use double machine learning with 3-fold cross-fitting again. The steps of our analysis are very similar to the IRM cases with the difference being that we use a model class [DoubleMLPLR](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLPLR.html) for estimation." + ] + }, + { + "cell_type": "markdown", + "id": "8e7ad0b5", + "metadata": {}, + "source": [ + "### Assess predictive performance in the PLR" + ] + }, + { + "cell_type": "markdown", + "id": "73c26a84", + "metadata": {}, + "source": [ + "As in the IRM, we want to calculate mean and standard deviation of the RMSE / log loss values across all repetitions to evaluate the prediction performance. Once again, a helper function is used as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "54a843e3", + "metadata": {}, + "outputs": [], + "source": [ + "def pred_acc_plr(DoubleML, prop):\n", + " \"\"\"\n", + " A function to calculate prediction accuracy values for every repetition\n", + " of a Double Machine Learning model using PLR, DoubleMLPLR\n", + " \n", + " ...\n", + " \n", + " Parameters\n", + " ----------\n", + " DoubleML : doubleml.double_ml_plr.DoubleMLPLR\n", + " The PLR Double Machine Learning model\n", + " prop : bool\n", + " Indication if RMSE values have to be computed for main regression or log loss values for propensity score\n", + " \"\"\"\n", + " \n", + " \n", + " # export data, fitted coefficient and predictions of the DoubleML model\n", + " y = DoubleML._dml_data.y\n", + " d = DoubleML._dml_data.d\n", + " theta = DoubleML.coef\n", + " g0 = DoubleML.predictions.get('ml_g')\n", + " m = DoubleML.predictions.get('ml_m')\n", + " \n", + " # dimensions of prediction array\n", + " h = g0.shape[0]\n", + " w = DoubleML.n_rep\n", + " \n", + " # check whether treatment is binary \n", + " if np.isin(d, [0,1]).all() == False:\n", + " raise ValueError(\"Treatment must be a binary variable.\")\n", + " \n", + " # prepare array to store prediction accuracy values\n", + " pred_acc_array = np.zeros((w,))\n", + " \n", + " # check whether to assess main regression or propensity score accuracy: \n", + " if prop == False:\n", + " \n", + " # evaluate main regression accuracy\n", + " # export array with prediction values\n", + " export_pred_array = np.zeros((h, w)) \n", + " for i in range(w):\n", + " for j in range(h):\n", + " export_pred_array[j,i] = theta*d[j] + g0[j,i]\n", + " \n", + " # fill array that contains rmse of each repetition\n", + " for i in range(w):\n", + " pred_acc_array[i] = mean_squared_error(y, export_pred_array[:,i], squared=False)\n", + " \n", + " else:\n", + " \n", + " # evaluate propensity score accuracy\n", + " # fill array that contains log loss of each repetition\n", + " for i in range(w):\n", + " pred_acc_array[i] = log_loss(d, m[:,i], eps=0.025)\n", + " \n", + " return pred_acc_array" + ] + }, + { + "cell_type": "markdown", + "id": "331a36d6", + "metadata": {}, + "source": [ + "### Benchmark: Model based on Linear and Logistic Regression" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "1432e567-d221-490d-9361-39b9072cb6d4", + "metadata": { + "scrolled": true, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.7849990.06712711.6941911.364815e-310.6534320.916565
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.784999 0.067127 11.694191 1.364815e-31 0.653432 0.916565" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Linear and Logistic Regression learners\n", + "linreg = make_pipeline(StandardScaler(), LinearRegression())\n", + "logreg_class = make_pipeline(StandardScaler(), LogisticRegression(penalty=\"none\"))\n", + "\n", + "# Initialize DoubleMLPLR model\n", + "np.random.seed(1234)\n", + "dml_plr_regression = dml.DoubleMLPLR(data_dml,\n", + " ml_g = linreg,\n", + " ml_m = logreg_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_regression.fit(store_predictions=True)\n", + "\n", + "reg_summary = dml_plr_regression.summary\n", + "reg_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "ff708453", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [-0.01500149]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_plr_regression.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "88392566", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_linlog_plr = pred_acc_plr(dml_plr_regression, prop=False)\n", + "rmse_main_linlog_plr_mean = np.mean(rmse_main_linlog_plr)\n", + "rmse_main_linlog_plr_std = np.std(rmse_main_linlog_plr)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_linlog_plr = pred_acc_plr(dml_plr_regression, prop=True)\n", + "logloss_prop_linlog_plr_mean = np.mean(logloss_prop_linlog_plr)\n", + "logloss_prop_linlog_plr_std = np.std(logloss_prop_linlog_plr)" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "08227dfc", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.3418428467276253\n", + "Standard deviation of RMSE is 0.009847706467828324\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_linlog_plr_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_linlog_plr_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "c91ed6e8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 1.0228568161263911\n", + "Standard deviation of log loss is 0.027536454508812133\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_linlog_plr_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_linlog_plr_std)" + ] + }, + { + "cell_type": "markdown", + "id": "4dd8948f", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Lasso" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "id": "0bbbc3ce", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.8047950.07027111.4528072.276523e-300.6670670.942522
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.804795 0.070271 11.452807 2.276523e-30 0.667067 0.942522" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize DoubleMLPLR model\n", + "np.random.seed(1234)\n", + "dml_plr_lasso = dml.DoubleMLPLR(data_dml,\n", + " ml_g = lasso,\n", + " ml_m = lasso_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_lasso.fit(store_predictions=True)\n", + "\n", + "lasso_summary=dml_plr_lasso.summary\n", + "lasso_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "id": "30aef0c8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.00479477]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_plr_lasso.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "id": "96383f94", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_lasso_plr = pred_acc_plr(dml_plr_lasso, prop=False)\n", + "rmse_main_lasso_plr_mean = np.mean(rmse_main_lasso_plr)\n", + "rmse_main_lasso_plr_std = np.std(rmse_main_lasso_plr)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_lasso_plr = pred_acc_plr(dml_plr_lasso, prop=True)\n", + "logloss_prop_lasso_plr_mean = np.mean(logloss_prop_lasso_plr)\n", + "logloss_prop_lasso_plr_std = np.std(logloss_prop_lasso_plr)" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "id": "10a66c25", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.1394799633725696\n", + "Standard deviation of RMSE is 0.003190385536736178\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_lasso_plr_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_lasso_plr_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "id": "afe3b2b9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.6686763881131824\n", + "Standard deviation of log loss 0.003254281706002184\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_lasso_plr_mean)\n", + "print(\"Standard deviation of log loss\", logloss_prop_lasso_plr_std)" + ] + }, + { + "cell_type": "markdown", + "id": "a4ed2694", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Random Forests" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "id": "e5f3ac90", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.7993070.07329710.9050281.090595e-270.6556470.942967
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.799307 0.073297 10.905028 1.090595e-27 0.655647 0.942967" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Random Forest learners\n", + "randomForest = RandomForestRegressor()\n", + "randomForest_class = RandomForestClassifier()\n", + "\n", + "# Initialize DoubleMLPLR model\n", + "np.random.seed(1234)\n", + "dml_plr_forest = dml.DoubleMLPLR(data_dml,\n", + " ml_g = randomForest,\n", + " ml_m = randomForest_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_forest.fit(store_predictions=True)\n", + "\n", + "forest_summary = dml_plr_forest.summary\n", + "forest_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "id": "4c40246d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [-0.00069288]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_plr_forest.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "id": "a977c34b", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_forest_plr = pred_acc_plr(dml_plr_forest, prop=False)\n", + "rmse_main_forest_plr_mean = np.mean(rmse_main_forest_plr)\n", + "rmse_main_forest_plr_std = np.std(rmse_main_forest_plr)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_forest_plr = pred_acc_plr(dml_plr_forest, prop=True)\n", + "logloss_prop_forest_plr_mean = np.mean(logloss_prop_forest_plr)\n", + "logloss_prop_forest_plr_std = np.std(logloss_prop_forest_plr)" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "id": "1f54fed6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.1886867050333019\n", + "Standard deviation of RMSE is 0.006048072563384578\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_forest_plr_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_forest_plr_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "id": "8101acf6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.6836880652313276\n", + "Standard deviation of log loss is 0.005321479254441978\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_forest_plr_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_forest_plr_std)" + ] + }, + { + "cell_type": "markdown", + "id": "6aa9af04", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Extreme Gradient Boosting" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "id": "6fab5d3a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.823840.07167611.4939881.414286e-300.6833580.964321
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.82384 0.071676 11.493988 1.414286e-30 0.683358 0.964321" + ] + }, + "execution_count": 59, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Extreme Gradient Boosting learners\n", + "boost = XGBRegressor(n_jobs = 1, objective = \"reg:squarederror\", \n", + " eta = 0.1, n_estimators = 57, max_depth = 2)\n", + "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", + " objective = \"binary:logistic\",\n", + " eval_metric = \"logloss\",\n", + " eta = 0.1, n_estimators = 10,\n", + " max_depth = 3)\n", + "\n", + "# Initialize DoubleMLPLR model\n", + "np.random.seed(1234)\n", + "dml_plr_boost = dml.DoubleMLPLR(data_dml,\n", + " ml_g = boost,\n", + " ml_m = boost_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_boost.fit(store_predictions=True)\n", + "\n", + "boost_summary = dml_plr_boost.summary\n", + "boost_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "id": "6e3252f8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.02383965]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_plr_boost.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "id": "e90a61cc", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_boost_plr = pred_acc_plr(dml_plr_boost, prop=False)\n", + "rmse_main_boost_plr_mean = np.mean(rmse_main_boost_plr)\n", + "rmse_main_boost_plr_std = np.std(rmse_main_boost_plr)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_boost_plr = pred_acc_plr(dml_plr_boost, prop=True)\n", + "logloss_prop_boost_plr_mean = np.mean(logloss_prop_boost_plr)\n", + "logloss_prop_boost_plr_std = np.std(logloss_prop_boost_plr)" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "id": "72121d00", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.1560362080432272\n", + "Standard deviation of RMSE is 0.0027129250049691073\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_boost_plr_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_boost_plr_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "id": "8513cd4e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.677578683851663\n", + "Standard deviation of log loss is 0.005774390874769318\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_boost_plr_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_boost_plr_std)" + ] + }, + { + "cell_type": "markdown", + "id": "a979a78b", + "metadata": {}, + "source": [ + "#### PLR - Summary of coefficient estimates" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "id": "dba8d33c", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefBias2.5 %97.5 %
regression0.785-0.0150.6530.917
lasso0.8050.0050.6670.943
forest0.799-0.0010.6560.943
xgboost0.8240.0240.6830.964
\n", + "
" + ], + "text/plain": [ + " coef Bias 2.5 % 97.5 %\n", + "regression 0.785 -0.015 0.653 0.917\n", + "lasso 0.805 0.005 0.667 0.943\n", + "forest 0.799 -0.001 0.656 0.943\n", + "xgboost 0.824 0.024 0.683 0.964" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plr_summary = pd.concat((reg_summary, lasso_summary, forest_summary, boost_summary))\n", + "plr_summary.index = ['regression','lasso', 'forest', 'xgboost']\n", + "plr_summary = plr_summary[['coef', '2.5 %', '97.5 %']]\n", + "plr_summary.insert(1, \"Bias\", [plr_summary.loc['regression','coef'] - 0.8, \n", + " plr_summary.loc['lasso','coef'] - 0.8, \n", + " plr_summary.loc['forest','coef'] - 0.8, \n", + " plr_summary.loc['xgboost','coef'] - 0.8])\n", + "plr_summary.round(3) " + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "id": "86fe5d87", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "errors = np.full((2, plr_summary.shape[0]), np.nan)\n", + "errors[0, :] = plr_summary['coef'] - plr_summary['2.5 %']\n", + "errors[1, :] = plr_summary['97.5 %'] - plr_summary['coef']\n", + "plt.errorbar(plr_summary.index, plr_summary.coef, fmt='o', yerr=errors)\n", + "plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", + "\n", + "plt.title('Partially Linear Regression Model (PLR)')\n", + "plt.xlabel('ML method')\n", + "_ = plt.ylabel('Coefficients and 95%-CI')" + ] + }, + { + "cell_type": "markdown", + "id": "19fc42af", + "metadata": {}, + "source": [ + "#### PLR - Summary of prediction accuracy metric's mean values" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "id": "b8937548", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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main RMSEmain RMSE (sd)prop log lossprop log loss (sd)
regression1.3420.0101.0230.028
lasso1.1390.0030.6690.003
forest1.1890.0060.6840.005
xgboost1.1560.0030.6780.006
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" + ], + "text/plain": [ + " main RMSE main RMSE (sd) prop log loss prop log loss (sd)\n", + "regression 1.342 0.010 1.023 0.028\n", + "lasso 1.139 0.003 0.669 0.003\n", + "forest 1.189 0.006 0.684 0.005\n", + "xgboost 1.156 0.003 0.678 0.006" + ] + }, + "execution_count": 66, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plr_rmse_index = ['regression','lasso', 'forest', 'xgboost']\n", + "plr_rmse = pd.DataFrame([[rmse_main_linlog_plr_mean, rmse_main_linlog_plr_std, \n", + " logloss_prop_linlog_plr_mean, logloss_prop_linlog_plr_std],\n", + " [rmse_main_lasso_plr_mean, rmse_main_lasso_plr_std,\n", + " logloss_prop_lasso_plr_mean, logloss_prop_lasso_plr_std],\n", + " [rmse_main_forest_plr_mean, rmse_main_forest_plr_std,\n", + " logloss_prop_forest_plr_mean, logloss_prop_forest_plr_std],\n", + " [rmse_main_boost_plr_mean, rmse_main_boost_plr_std,\n", + " logloss_prop_boost_plr_mean, logloss_prop_boost_plr_std]],\n", + " index=plr_rmse_index,\n", + " columns=['main RMSE', 'main RMSE (sd)',\n", + " 'prop log loss', 'prop log loss (sd)'])\n", + "plr_rmse.round(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "id": "79fe38ed", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# graphical illustration of RMSE for main regression\n", + "errors_plr_rmse = np.full((2, plr_rmse.shape[0]), np.nan)\n", + "errors_plr_rmse[0, :] = plr_rmse['main RMSE'] - plr_rmse['main RMSE (sd)']\n", + "errors_plr_rmse[1, :] = plr_rmse['main RMSE'] + plr_rmse['main RMSE (sd)']\n", + "plt.errorbar(x=plr_rmse.index, y=plr_rmse['main RMSE'], fmt='x',\n", + " yerr=errors_plr_rmse, c='darkslategray')" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "id": "bb40406b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# graphical illustration of log loss for main regression\n", + "errors_plr_logloss = np.full((2, plr_rmse.shape[0]), np.nan)\n", + "errors_plr_logloss[0, :] = plr_rmse['prop log loss'] - plr_rmse['prop log loss (sd)']\n", + "errors_plr_logloss[1, :] = plr_rmse['prop log loss'] + plr_rmse['prop log loss (sd)']\n", + "plt.errorbar(x=plr_rmse.index, y=plr_rmse['prop log loss'], fmt='x',\n", + " yerr=errors_plr_logloss, c='darkslategray')" + ] + }, + { + "cell_type": "markdown", + "id": "27d1d2a9-beed-493d-ae92-8d4e92cde8ae", + "metadata": {}, + "source": [ + "### Summary of IRM and PLR Results" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "id": "1b4ddf50-50de-4bab-a110-767b8d50df21", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefBias2.5 %97.5 %
ModelML
IRMregression1.0580.258-0.1672.282
lasso0.8560.0560.7170.995
forest0.8930.0930.7411.045
xgboost0.791-0.0090.5860.995
PLRregression0.785-0.0150.6530.917
lasso0.8050.0050.6670.943
forest0.799-0.0010.6560.943
xgboost0.8240.0240.6830.964
\n", + "
" + ], + "text/plain": [ + " coef Bias 2.5 % 97.5 %\n", + "Model ML \n", + "IRM regression 1.058 0.258 -0.167 2.282\n", + " lasso 0.856 0.056 0.717 0.995\n", + " forest 0.893 0.093 0.741 1.045\n", + " xgboost 0.791 -0.009 0.586 0.995\n", + "PLR regression 0.785 -0.015 0.653 0.917\n", + " lasso 0.805 0.005 0.667 0.943\n", + " forest 0.799 -0.001 0.656 0.943\n", + " xgboost 0.824 0.024 0.683 0.964" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df_summary = pd.concat((irm_summary,plr_summary)).reset_index().rename(columns={'index': 'ML'})\n", + "df_summary['Model'] = np.concatenate((np.repeat('IRM', 4), np.repeat('PLR', 4)))\n", + "df_summary.set_index(['Model', 'ML']).round(3)" + ] + }, + { + "cell_type": "markdown", + "id": "64aa3065-da5c-49b9-88f2-5c08c1b7e617", + "metadata": {}, + "source": [ + "### Conclusion\n", + "\n", + "As in the IRM model, the ML-based PLR models are associated with a smaller bias as compared to the model that is based on linear and logistic regression. It seems that the estimates obtained from the PLR are slightly closer to the true ATE than those from the IRM analysis. This might suggest, that the parametric assumptions (i.e., an additive and homogeneous causal effect) that are incorporated in the PLR turn out to be **not restrictive** in our example data set. However, if both models are based on appropriate ML learners, the conclusions are very similar. In all cases, the ML-based estimates were very close to the true ATE and we were always able to reject the null hypothesis of a zero effect at all common significance levels. In terms of the A/B testing example, it can be concluded that the new ad increases customers purchases (in $100\\$$) by around 0.8 on average and that this effect is significantly different from zero at the 5% significance level. The results are summarized in the graphic below." + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "id": "c80cadcc", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(8, 9))\n", + "colors = sns.color_palette()\n", + "for ind, model in enumerate(['IRM', 'PLR']):\n", + " sns.set(font_scale=1.15)\n", + " plt.subplot(3, 1, ind+1)\n", + " this_df = df_summary.query('Model == @model')\n", + " errors = np.full((2, this_df.shape[0]), np.nan)\n", + " errors[0, :] = this_df['coef'] - this_df['2.5 %']\n", + " errors[1, :] = this_df['97.5 %'] - this_df['coef']\n", + " plt.errorbar(this_df.ML, this_df.coef, fmt='o', yerr=errors,\n", + " color=colors[ind], ecolor=colors[ind])\n", + " plt.ylim([0.5, 1.2])\n", + " plt.title(model)\n", + " plt.ylabel('Coeff. and 95%-CI')\n", + " plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", + " plt.legend(bbox_to_anchor=(1.04,0.5), loc=\"best\", borderaxespad=0)\n", + "\n", + "_ = plt.xlabel('ML method')" + ] + }, + { + "cell_type": "markdown", + "id": "90109d08", + "metadata": {}, + "source": [ + "## Appendix" + ] + }, + { + "cell_type": "markdown", + "id": "e42903ad", + "metadata": {}, + "source": [ + "### Propensity score estimates" + ] + }, + { + "cell_type": "markdown", + "id": "157d7295", + "metadata": {}, + "source": [ + "For both the IRM and the PLR model, we want to compare the propensity score estimates of all learners. Since repeated sample splitting is used for every learner, we first want to check whether the repetitions provide similare propensity score estimates. If that is the case, it should be legitimate to pick any of the repetitions for the comparision across all learners." + ] + }, + { + "cell_type": "markdown", + "id": "bb614dd1", + "metadata": {}, + "source": [ + "#### IRM - Repetitions of the Linear and Logistic regression model" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "id": "a2a753a7", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_irm_regression)" + ] + }, + { + "cell_type": "markdown", + "id": "d0eca3c9", + "metadata": {}, + "source": [ + "#### IRM - Repetitions of the Lasso model" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "id": "a69be1ca", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_irm_lasso)" + ] + }, + { + "cell_type": "markdown", + "id": "6ae81d8d", + "metadata": {}, + "source": [ + "#### IRM - Repetitions of the Random Forest model" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "id": "2775a78e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "h = dml_irm_regression.predictions.get('ml_m').shape[0]\n", + "fig, ax = plt.subplots(1, 4, figsize=(20,4.8))\n", + "\n", + "#regression histogram\n", + "ax[0].hist(np.reshape(dml_irm_regression.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[0].set_title('regression')\n", + "ax[0].set_xlabel(\"prop_score\")\n", + "ax[0].set_ylabel(\"density\")\n", + "\n", + "#lasso histogram\n", + "ax[1].hist(np.reshape(dml_irm_lasso.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[1].set_title('lasso')\n", + "ax[1].set_xlabel(\"prop_score\")\n", + "ax[1].set_ylabel(\"density\")\n", + "\n", + "#random forest histogram\n", + "ax[2].hist(np.reshape(dml_irm_forest.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[2].set_title('random forest')\n", + "ax[2].set_xlabel(\"prop_score\")\n", + "ax[2].set_ylabel(\"density\")\n", + "\n", + "#boosting histogram\n", + "ax[3].hist(np.reshape(dml_irm_boost.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[3].set_title('xgboost')\n", + "ax[3].set_xlabel(\"prop_score\")\n", + "ax[3].set_ylabel(\"density\")\n", + " \n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "7a9a161d", + "metadata": {}, + "source": [ + "#### PLR - Repetitions of the Linear and Logistic regression model" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "id": "c4da298e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_plr_regression)" + ] + }, + { + "cell_type": "markdown", + "id": "fbbbd43c", + "metadata": {}, + "source": [ + "#### PLR - Repetitions of the Lasso model" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "id": "17b9d772", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_plr_lasso)" + ] + }, + { + "cell_type": "markdown", + "id": "768dabe2", + "metadata": {}, + "source": [ + "#### PLR - Repetitions of the Random Forest model" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "id": "7639ef46", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_plr_forest)" + ] + }, + { + "cell_type": "markdown", + "id": "99539929", + "metadata": {}, + "source": [ + "#### PLR - Repetitions of the Extreme Gradient Boosting model" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "id": "da73a9b4", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_plr_boost)" + ] + }, + { + "cell_type": "markdown", + "id": "70375158", + "metadata": {}, + "source": [ + "#### PLR - Propensity score estimates across learners" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "id": "1aeded78", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "h = dml_plr_regression.predictions.get('ml_m').shape[0]\n", + "fig, ax = plt.subplots(1, 4, figsize=(20,4.8))\n", + "\n", + "#regression histogram\n", + "ax[0].hist(np.reshape(dml_plr_regression.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[0].set_title('regression')\n", + "ax[0].set_xlabel(\"prop_score\")\n", + "ax[0].set_ylabel(\"density\")\n", + "\n", + "#lasso histogram\n", + "ax[1].hist(np.reshape(dml_plr_lasso.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[1].set_title('lasso')\n", + "ax[1].set_xlabel(\"prop_score\")\n", + "ax[1].set_ylabel(\"density\")\n", + "\n", + "#random forest histogram\n", + "ax[2].hist(np.reshape(dml_plr_forest.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[2].set_title('random forest')\n", + "ax[2].set_xlabel(\"prop_score\")\n", + "ax[2].set_ylabel(\"density\")\n", + "\n", + "#boosting histogram\n", + "ax[3].hist(np.reshape(dml_plr_boost.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[3].set_title('xgboost')\n", + "ax[3].set_xlabel(\"prop_score\")\n", + "ax[3].set_ylabel(\"density\")\n", + " \n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "3aa8d603-0df5-48c6-ad62-ac5ffe3e8ada", + "metadata": {}, + "source": [ + "______\n", + "\n", + "**Notes and Acknowledgement**\n", + "\n", + "We would like to thank the organizers of the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge) for setting up this data challenge and making the numerous synthetic data examples publicly available. Although the data examples in the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge) do not explicitly adress A/B testing, we put the data example here in this context to give a tractable example on the use of causal machine learning in practice. The parameters for the random forests and extreme gradient boosting learners have been tuned externally. The corresponding tuning notebook will be uploaded in the examples gallery in the future." + ] + }, + { + "cell_type": "markdown", + "id": "egyptian-platform", + "metadata": {}, + "source": [ + "## References\n", + "\n", + "Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W. and Robins, J. (2018), Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21: C1-C68. doi:10.1111/ectj.12097." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/doc/examples/py_double_ml_abtest_no_split_linreg.ipynb b/doc/examples/py_double_ml_abtest_no_split_linreg.ipynb new file mode 100644 index 00000000..bf2be0c9 --- /dev/null +++ b/doc/examples/py_double_ml_abtest_no_split_linreg.ipynb @@ -0,0 +1,4059 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "consecutive-cabinet", + "metadata": {}, + "source": [ + "# Python: A/B Testing with DoubleML" + ] + }, + { + "cell_type": "markdown", + "id": "opponent-indonesian", + "metadata": {}, + "source": [ + "\"An\n", + "\n", + "Image Source Freepik http://www.freepik.com, Designed by macrovector\n" + ] + }, + { + "cell_type": "markdown", + "id": "c7c96f88", + "metadata": {}, + "source": [ + "In this notebook, we demontrate exemplarily how the [DoubleML](https://docs.doubleml.org/stable/index.html) package can be used to estimate the causal effect of seeing a new ad design on customers' purchases in a webshop. The [DoubleML](https://docs.doubleml.org/stable/index.html) package for Python and R provides an implementation of the double / debiased machine learning (DML) framework of [Chernozhukov et al. (2018)](https://arxiv.org/abs/1608.00060) and can be used to estimate causal effects based on machine learning (ML) methods.\n", + "\n", + "## A/B Testing\n", + "\n", + "A/B testing is a frequently used framework to perform causal inference in practice. For example, a manager of a webshop might want to optimally adapt the webshop design according to users' preferences. For examle, she might want to estimate the effect of a new ad design, which is displayed on the starting page, on a customer's purchases (in $100\\$$). A/B tests refer to an experimental design in which a certain treatment, for example a new ad design (called \"Version $A$\"), is randomly assigned to groups of individuals, like website visitors or app users. If a user is not \"treated\", i.e., he is not exposed to Version $A$, he sees an alternative design \"Version $B$\" like the old design of the ad. The assignment of the treatment might either be unconditionally random, i.e., randomly assigned to all visitors of the online shop or directed towards specific groups of them. In the latter case, the treatment assignment would be conditional on their characteristics, like their shopping history. For example, a discount might only be granted to customers who already made some purchases in the past.\n", + "\n", + "In general, the goal of the A/B test is to assess whether the treatment has an effect on the outcome variable of interest. In our example, the manager wants to evaluate whether the new ad design changed the monetary value of products purchased (in $100\\$$). Alternative settings of A/B tests refer to improvement of a user experience on a website or estimation of price elasticities. Websites and apps are ideal for running A/B tests because they make it very easy to precisely direct the treatment to visitors and users (or to specific subgroups of them) as well as to collect the data required for evaluation of the intervention.\n", + "\n", + "## Scenario\n", + "\n", + "Let's consider the following stylized scenario. The manager of a webshop is performing an A/B test to estimate the effect a new ad design $A$ has on customers' purchases, $Y$, on average. This effect is called the **A**verage **T**reatment **E**ffect (**ATE**). The treatment is assigned randomly conditional on the visitors' characteristics, which we call $V$. Such characteristics could be collected from a customer's shoppers account, for example. These might include the number of previous purchases, time since the last purchase, length of stay on a page as well as whether a customer has a rewards card, among other characteristics.
\n", + "\n", + "In the following, we use a **D**irected **A**cyclical **G**raph (DAG) to illustrate our assumptions on the causal structure of the scenario. As not only the outcome, but also the treatment is dependent on the individuals characteristics, there are arrows going from $V$ to both $A$ and $Y$. In our example, we also assume that the treatment $A$ is a direct cause of the customers' purchases $Y$.\n", + "\n", + "\n", + "![Scenario illustration with a DAG](figures/DAG.svg)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "220997c6", + "metadata": {}, + "source": [ + "Let's assume the conditional randomization has been conducted properly, such that a tidy data set has been collected. Now, a data scientist wants to evaluate whether the new ad design causally affected the sales, by using the [DoubleML](https://docs.doubleml.org/stable/index.html) package.\n", + "\n", + "### Why control for individual characteristics?\n", + "\n", + "Before we start the case study, let us briefly address the question why we need to include individual characteristics in our analysis at all. There are mainly two reasons why we want to control for observable characteristics. First, so-called confounders, i.e., variables that have a causal effect on both the treatment variable and the outcome variable, possibly create a bias in our estimate. In order to uncover the true causal effect of the treatment, it is necessary that our causal framework takes all confounding variables into account. Otherwise, the average causal effect of the treatment on the outcome is not identified. A second reason to include individual characteristics is efficiency. The more variation can be explained within our causal framework, the more precise will be the resulting estimate. In practical terms, greater efficiency leads to tighter confidence intervals and smaller standard errors and p-values. This might help to improve the power of A/B tests even if the treatment variable is unconditionally assigned to individuals.\n", + "\n", + "### Why use machine learning to analyze A/B tests?\n", + "\n", + "ML methods have turned out to be very flexible in terms of modeling complex relationships of explanatory variables and dependent variables and, thus, have exhibited a great predictive performance in many applications. In the double machine learning approach ([Chernozhukov et al. (2018)](https://arxiv.org/abs/1608.00060)), ML methods are used for modelling so-called nuisance functions. In terms of the A/B case study considered here, ML tools can be used to flexibly control for confounding variables. For example, a linear parametric specification as in a standard linear regression model might not be correct and, hence, not sufficient to account for the underlying confounding. Moreover, by using powerful ML techniques, the causal model will likely be able to explain a greater share of the total variation and, hence, lead to more precise estimation." + ] + }, + { + "cell_type": "markdown", + "id": "0ec5b0cf", + "metadata": {}, + "source": [ + "## Data \n", + "\n", + "As an illustrative example we use a data set from the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge). In this challenge, a great number of data sets have been generated in a way that they mimic distributional relationships that are found in many economic real data applications. Although the data have not been generated explicitly to address an A/B testing case study, they are well-suited for demonstration purposes. We will focus on one of the many different data genereting processes (DGP) that we picked at random, in this particualar case a data set called `high42`. An advantage of using the synthetic [ACIC 2019 data](https://sites.google.com/view/acic2019datachallenge/data-challenge) is that we know the true average treatment effect which is 0.8 in our data set.\n", + "\n", + "First we load the data." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "e39d4dd0", + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "\n", + "#fetch_ACIChigh42 needs to be defined\n", + "#df = fetch_ACIChigh42(return_type='DataFrame')\n", + "\n", + "#load code locally\n", + "df = pd.read_csv('data/high42.csv', sep=',', na_values=\".\")\n", + "\n", + "#code can also be loaded using a URL of the data\n", + "#url = 'https://raw.githubusercontent.com/DoubleML/doubleml-hiwi-sandbox/master/case_studies/AB_testing/data/high42.CSV?token=AQWGKQRE57BBRGOCBPSNBJTBD57ZQ'\n", + "#df = pd.read_csv(url)" + ] + }, + { + "cell_type": "markdown", + "id": "11525056-cdec-4916-9cb4-aa4268e99175", + "metadata": {}, + "source": [ + "We see that the data set consists of 1000 observations (= website visitors) and 202 variables. The $Y$ column represents the customers' purchases (in $100\\$$). The treatment variable $A$ is binary with a value 1 indicating that a customer has been exposed to the new ad design (and value 0 otherwise). The remaining 200 columns $V$ represent individual characteristics of the customers." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "10edc74d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(1000, 202)\n" + ] + } + ], + "source": [ + "print(df.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "6760c009", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " Y A V1 V2 V3 V4 V5 V6 V7 V8 ... \\\n", + "0 7.358185 1 10 0 0 7 192.793769 23.676950 8 0.185443 ... \n", + "1 8.333672 1 12 0 1 4 199.653596 19.281270 7 0.514842 ... \n", + "2 7.472758 0 14 1 1 2 194.207792 24.589331 5 0.309199 ... \n", + "3 6.502319 1 0 1 0 9 201.838024 25.513918 4 0.160160 ... \n", + "4 7.043758 1 12 0 0 9 201.360443 31.160641 6 0.291976 ... \n", + "\n", + " V191 V192 V193 V194 V195 V196 V197 V198 V199 \\\n", + "0 1.462837 1 1627.274196 0 0 4.683956 0.565667 0 3 \n", + "1 1.330522 1 1661.484439 1 0 6.766661 -0.395402 0 4 \n", + "2 1.384151 1 1658.939293 0 0 5.647794 1.112766 0 0 \n", + "3 1.220303 1 1650.801625 0 0 5.370363 -0.305842 0 4 \n", + "4 1.170094 1 1676.818876 0 0 3.446532 2.440661 0 1 \n", + "\n", + " V200 \n", + "0 0.024338 \n", + "1 0.056518 \n", + "2 0.013442 \n", + "3 0.034632 \n", + "4 0.017514 \n", + "\n", + "[5 rows x 202 columns]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.head()" + ] + }, + { + "cell_type": "markdown", + "id": "c6e32feb", + "metadata": {}, + "source": [ + "### Descriptive Statistics\n" + ] + }, + { + "cell_type": "markdown", + "id": "horizontal-hanging", + "metadata": {}, + "source": [ + "Once we loaded the data, we find that the outcome variable, $Y$, is continuous with mean around $7.33$. The treatment variable $A$ is binary with a value of $1$ indicating that a visitor was exposed to the new ad design $A$ as opposed to design $B$ (corresponding to a value of $A$ equal to $1$). The control variables $V$ are a collection of mixed data types, including continuous, discrete and binary variables." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "d14f929c-178b-47fc-8293-29a634194f21", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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50%7.3352480.00000010.0000000.0000001.0000007.000000199.87611726.2025826.0000000.282867...1.2937901.000001667.7634800.0000000.0000005.236465-0.0910560.000001.0000000.034009
75%8.2718811.00000012.0000001.0000001.0000008.000000204.39806733.0711898.0000000.374078...1.4768281.000001695.9726311.0000000.0000006.8982400.5946471.000002.0000000.049100
max13.1972601.00000020.0000001.0000001.00000015.000000220.58441095.41002014.0000000.706249...2.4486611.000001825.6970961.0000001.00000038.4279742.8326731.000009.0000000.139716
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" + ], + "text/plain": [ + " Y A V1 V2 V3 \\\n", + "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 \n", + "mean 7.331239 0.443000 9.290000 0.377000 0.616000 \n", + "std 1.379852 0.496989 3.889605 0.484877 0.486601 \n", + "min 3.435052 0.000000 0.000000 0.000000 0.000000 \n", + "25% 6.405583 0.000000 7.000000 0.000000 0.000000 \n", + "50% 7.335248 0.000000 10.000000 0.000000 1.000000 \n", + "75% 8.271881 1.000000 12.000000 1.000000 1.000000 \n", + "max 13.197260 1.000000 20.000000 1.000000 1.000000 \n", + "\n", + " V4 V5 V6 V7 V8 ... \\\n", + "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 ... \n", + "mean 6.477000 200.088758 28.066028 6.031000 0.294206 ... \n", + "std 2.870141 6.105408 9.920941 2.480361 0.119454 ... \n", + "min 0.000000 183.123067 12.020630 0.000000 0.047160 ... \n", + "25% 5.000000 195.941569 21.206230 4.000000 0.204260 ... \n", + "50% 7.000000 199.876117 26.202582 6.000000 0.282867 ... \n", + "75% 8.000000 204.398067 33.071189 8.000000 0.374078 ... \n", + "max 15.000000 220.584410 95.410020 14.000000 0.706249 ... \n", + "\n", + " V191 V192 V193 V194 V195 \\\n", + "count 1000.000000 1000.00000 1000.000000 1000.000000 1000.000000 \n", + "mean 1.318209 0.94200 1667.454561 0.254000 0.174000 \n", + "std 0.270178 0.23386 44.191913 0.435515 0.379299 \n", + "min 0.668093 0.00000 1524.291675 0.000000 0.000000 \n", + "25% 1.119369 1.00000 1637.699514 0.000000 0.000000 \n", + "50% 1.293790 1.00000 1667.763480 0.000000 0.000000 \n", + "75% 1.476828 1.00000 1695.972631 1.000000 0.000000 \n", + "max 2.448661 1.00000 1825.697096 1.000000 1.000000 \n", + "\n", + " V196 V197 V198 V199 V200 \n", + "count 1000.000000 1000.000000 1000.00000 1000.000000 1000.000000 \n", + "mean 5.804205 -0.076921 0.29400 1.629000 0.037936 \n", + "std 2.655835 1.002754 0.45582 1.388988 0.021688 \n", + "min 1.097708 -3.644652 0.00000 0.000000 0.001478 \n", + "25% 4.065465 -0.751355 0.00000 1.000000 0.021711 \n", + "50% 5.236465 -0.091056 0.00000 1.000000 0.034009 \n", + "75% 6.898240 0.594647 1.00000 2.000000 0.049100 \n", + "max 38.427974 2.832673 1.00000 9.000000 0.139716 \n", + "\n", + "[8 rows x 202 columns]" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.describe()" + ] + }, + { + "cell_type": "markdown", + "id": "d7e45649", + "metadata": {}, + "source": [ + "From the explanatory variables $V1$ to $V200$, 107 variables are continuous, while 95 are integers. From the integer-variables 59 are binary variables. " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "bde50bfe", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "float64 107\n", + "int64 95\n", + "dtype: int64\n", + "Number of binary variables: 59\n" + ] + } + ], + "source": [ + "print(df.dtypes.value_counts())\n", + "print(\"Number of binary variables:\", len(df[df.columns[df.isin([0,1]).all()]].columns))" + ] + }, + { + "cell_type": "markdown", + "id": "0ce90b4b", + "metadata": {}, + "source": [ + "Let's continue with some visual inspection." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "b4d2dfb4", + "metadata": {}, + "outputs": [], + "source": [ + "# Define the settings for the graphs first\n", + "import seaborn as sns\n", + "sns.set()\n", + "colors = sns.color_palette()\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "plt.rcParams['figure.figsize'] = 5., 3.75\n", + "sns.set(font_scale=1.5)\n", + "sns.set_style('whitegrid', {'axes.spines.top': False,\n", + " 'axes.spines.bottom': False,\n", + " 'axes.spines.left': False,\n", + " 'axes.spines.right': False})" + ] + }, + { + "cell_type": "markdown", + "id": "11045894", + "metadata": {}, + "source": [ + "The first figure shows that 443 out of the 1000 customers have been exposed to the new ad design." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "2b5037d3", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "df['A'].value_counts().plot(kind='bar', color=colors)\n", + "\n", + "plt.title('Treatment')\n", + "plt.xlabel('A')\n", + "_ = plt.ylabel('count')" + ] + }, + { + "cell_type": "markdown", + "id": "8c2dc825", + "metadata": {}, + "source": [ + "### Unconditional Estimate of ATE" + ] + }, + { + "cell_type": "markdown", + "id": "8da84d00", + "metadata": {}, + "source": [ + "As a first naive estimate, we could calculate the unconditional average treatment effect. In other words, we simply take the difference between $Y$ observed for the customers who have been exposed to the treatment $(A=1)$ and those who haven't been exposed $(A=0)$. As a visualization, we plot the density of the outcome variable conditional on the treatment status to get a first impression on the descriptive relationship of $A$ and $Y$." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "57392f09", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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" + ], + "text/plain": [ + " Y\n", + "A \n", + "0 NaN\n", + "1 1.117603" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df[['A', 'Y']].groupby('A').mean().diff()" + ] + }, + { + "cell_type": "markdown", + "id": "e6f3fa75-a5d4-480c-b627-4b99c6f6afe3", + "metadata": {}, + "source": [ + "The uncoditional effect is around $1.118$. Because we use a simulated data set in this example, we know that the true effect is $0.8$. Therefore the unconditional ATE overestimates the true effect, because it does not account for individual characteristics. In order to get an estimation on the ATE that explicitly takes the confounding variables $V$ into account, we apply the [DoubleML](https://docs.doubleml.org/stable/index.html) package in the next section." + ] + }, + { + "cell_type": "markdown", + "id": "9e21e9bb", + "metadata": {}, + "source": [ + "## Estimate ATE with the `DoubleML` package" + ] + }, + { + "cell_type": "markdown", + "id": "19830a0a", + "metadata": {}, + "source": [ + "Let’s use the package [DoubleML](https://docs.doubleml.org/stable/index.html) to estimate the average treatment effect of the new ad design on the value of customers' purchases. First, the required packages are imported." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "afaf4106", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import doubleml as dml\n", + "\n", + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.linear_model import LogisticRegression\n", + "from sklearn.linear_model import LassoCV, LogisticRegressionCV\n", + "from sklearn.ensemble import RandomForestClassifier, RandomForestRegressor\n", + "from sklearn.preprocessing import StandardScaler\n", + "from sklearn.pipeline import make_pipeline\n", + "from sklearn.metrics import mean_squared_error\n", + "from sklearn.metrics import log_loss\n", + "from xgboost import XGBClassifier, XGBRegressor\n", + "\n", + "import matplotlib.pyplot as plt\n", + "import scipy.stats as stats" + ] + }, + { + "cell_type": "markdown", + "id": "49242003", + "metadata": {}, + "source": [ + "### The Data Backend: `DoubleMLData`" + ] + }, + { + "cell_type": "markdown", + "id": "3653b53a", + "metadata": {}, + "source": [ + "To start our analysis, we initialize the data backend from the previously loaded data set, i.e., we create a new instance of a [DoubleMLData](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLData.html#doubleml.DoubleMLData) object. During initialization, we specify the roles of the variables in the data set, i.e., in our example the outcome variable $Y$ via the parameter `y_col`, the treatment variable $A$ via `d_cols` and the confounding variables $V$ via `x_cols`." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "abdd10b7", + "metadata": {}, + "outputs": [], + "source": [ + "# Specify explanatory variables for data-backend\n", + "features_base = list(df.columns.values)[2:]\n", + "\n", + "# Initialize DoubleMLData (data-backend of DoubleML)\n", + "data_dml = dml.DoubleMLData(df,\n", + " y_col='Y',\n", + " d_cols='A',\n", + " x_cols=features_base)" + ] + }, + { + "cell_type": "markdown", + "id": "5800ca50-c293-4266-8dd7-00fadcea8d51", + "metadata": {}, + "source": [ + "We can print the data-backend to see the variables, which we have assigned as outcome, treatment and controls." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "37b9bd8a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "================== DoubleMLData Object ==================\n", + "\n", + "------------------ Data summary ------------------\n", + "Outcome variable: Y\n", + "Treatment variable(s): ['A']\n", + "Covariates: ['V1', 'V2', 'V3', 'V4', 'V5', 'V6', 'V7', 'V8', 'V9', 'V10', 'V11', 'V12', 'V13', 'V14', 'V15', 'V16', 'V17', 'V18', 'V19', 'V20', 'V21', 'V22', 'V23', 'V24', 'V25', 'V26', 'V27', 'V28', 'V29', 'V30', 'V31', 'V32', 'V33', 'V34', 'V35', 'V36', 'V37', 'V38', 'V39', 'V40', 'V41', 'V42', 'V43', 'V44', 'V45', 'V46', 'V47', 'V48', 'V49', 'V50', 'V51', 'V52', 'V53', 'V54', 'V55', 'V56', 'V57', 'V58', 'V59', 'V60', 'V61', 'V62', 'V63', 'V64', 'V65', 'V66', 'V67', 'V68', 'V69', 'V70', 'V71', 'V72', 'V73', 'V74', 'V75', 'V76', 'V77', 'V78', 'V79', 'V80', 'V81', 'V82', 'V83', 'V84', 'V85', 'V86', 'V87', 'V88', 'V89', 'V90', 'V91', 'V92', 'V93', 'V94', 'V95', 'V96', 'V97', 'V98', 'V99', 'V100', 'V101', 'V102', 'V103', 'V104', 'V105', 'V106', 'V107', 'V108', 'V109', 'V110', 'V111', 'V112', 'V113', 'V114', 'V115', 'V116', 'V117', 'V118', 'V119', 'V120', 'V121', 'V122', 'V123', 'V124', 'V125', 'V126', 'V127', 'V128', 'V129', 'V130', 'V131', 'V132', 'V133', 'V134', 'V135', 'V136', 'V137', 'V138', 'V139', 'V140', 'V141', 'V142', 'V143', 'V144', 'V145', 'V146', 'V147', 'V148', 'V149', 'V150', 'V151', 'V152', 'V153', 'V154', 'V155', 'V156', 'V157', 'V158', 'V159', 'V160', 'V161', 'V162', 'V163', 'V164', 'V165', 'V166', 'V167', 'V168', 'V169', 'V170', 'V171', 'V172', 'V173', 'V174', 'V175', 'V176', 'V177', 'V178', 'V179', 'V180', 'V181', 'V182', 'V183', 'V184', 'V185', 'V186', 'V187', 'V188', 'V189', 'V190', 'V191', 'V192', 'V193', 'V194', 'V195', 'V196', 'V197', 'V198', 'V199', 'V200']\n", + "Instrument variable(s): None\n", + "No. Observations: 1000\n", + "\n", + "------------------ DataFrame info ------------------\n", + "\n", + "RangeIndex: 1000 entries, 0 to 999\n", + "Columns: 202 entries, Y to V200\n", + "dtypes: float64(107), int64(95)\n", + "memory usage: 1.5 MB\n", + "\n" + ] + } + ], + "source": [ + "print(data_dml)" + ] + }, + { + "cell_type": "markdown", + "id": "714346b8-90dd-4f15-b880-d71f4f60b04e", + "metadata": {}, + "source": [ + "## The Inference Problem and Choosing an Appropriate Model\n", + "\n", + "The inference problem is to determine the causal effect of seeing the new ad design $A$ on a customer's purchases $Y$ once we control for individual characteristics $V$. In our example, we are interested in the average treatment effect. Basically, there are two causal models available in [DoubleMLData](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLData.html#doubleml.DoubleMLData) that can be used to estimate the ATE.\n", + "\n", + "The so-called interactive regression model (IRM) called by [DoubleMLIRM](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLIRM.html) is a flexible (nonparametric) model to estimate this causal quantity. The model does not impose functional form restrictions on the underlying regression relationships, for example, linearity or additivity as in a standard linear regression model. This means that the model hosts heterogeneous treatment effects, i.e., account for variation in the effect of the new ad design across customers. Moreover, it is possible to also estimate other causal parameters with the IRM, for example, the average treatment effect on the treated (= those customers who have been exposed to the new ad), which might be of interest too.\n", + "\n", + "The second causal model that can be used here is the partially linear regression model (PLR). The PLR incorporates stronger assumptions, for example, that the treatment effect is additive and constant, i.e., in the model it is assumed that the effect does not very across individuals. We will start with the IRM and include the PLR estimates at the end of the notebook." + ] + }, + { + "cell_type": "markdown", + "id": "9e798e44-8fc8-4c93-9cfb-2d3ad7486dc0", + "metadata": {}, + "source": [ + "## 1. Interactive Regression Model (IRM)\n", + "\n", + "We briefly introduce the [Interactive Regression Model](https://docs.doubleml.org/stable/guide/models.html#interactive-regression-model-irm) (IRM) where the main regression relationship of interest is provided by\n", + "\n", + "$$Y = g_0(D, X) + U, \\quad E(U | X, D) = 0,$$\n", + "\n", + "where the treatment variable is binary, $D \\in \\lbrace 0,1 \\rbrace$. We consider estimation of the average treatment effect (ATE):\n", + "\n", + "$$\\theta_0 = \\mathbb{E}[g_0(1, X) - g_0(0,X)],$$\n", + "\n", + "when treatment effects are fully heterogeneous. In order to be able to use ML methods, the estimation framework generally requires a property called \"double robustness\" or \"Neyman orthogonality\". In the IRM, double robustness can be achieved by including the first-stage estimation\n", + "\n", + "$$D = m_0(X) + V, \\quad E(V | X) = 0,$$\n", + "\n", + "which amounts to estimation of the propensity score, i.e., the probability that a customer is exposed to the treatment provided her observed characteristics. Both predictions are then combined in [the doubly robust score for the average treatment effect](https://docs.doubleml.org/stable/guide/scores.html#interactive-regression-model-irm) which is given by\n", + "\n", + "$$\\psi(W; \\theta, \\eta) := g(1,X) - g(0,X) + \\frac{D (Y - g(1,X))}{m(X)} - \\frac{(1 - D)(Y - g(0,X))}{1 - m(x)} - \\theta.$$" + ] + }, + { + "cell_type": "markdown", + "id": "13a5f6f7-64c5-499b-b68a-16ca98943cd6", + "metadata": {}, + "source": [ + "Because the data set was simulated we are aware of the true ATE, $\\theta_0=0.8$. The interpretation of this is that exposure to the new ad increases sales (in $100\\$$) by around $0.8$ on average. In the following, we try to estimate this causal effect using the [DoubleML](https://docs.doubleml.org/stable/index.html) package and assess whether the estimated effect is significantly different from zero." + ] + }, + { + "cell_type": "markdown", + "id": "69f0731d", + "metadata": {}, + "source": [ + "### Assess predictive performance in the IRM" + ] + }, + { + "cell_type": "markdown", + "id": "6d494c68", + "metadata": {}, + "source": [ + "In the following, we will compare the estimate of the ATE based on different learners. Moreover, we will also have a look how well the learners can predict the nuisance components of the causal model. \n", + "\n", + "To evaluate the predictive performance, we'll first define a helper function that uses a DoubleML model object and returns a summary for a predictive measure. We'll use the root mean squared error (RMSE) for the main regression and the log loss measure $L_{log}$ for the propensity score estimation.\n", + "\n", + "Estimation of the IRM delivers two arrays for the prediction function $g_0(D, X)$: `ml_g0` for $g_0(0, X)$ and `ml_g1` for $g_0(1, X)$. If we want to get the correct prediction for each observation based on the treatment realization, we pick the corresponding value of either `ml_g0` (for $D=0$) or `ml_g1` (for $D=1$). As we apply random sample splitting repeatedly in every model, the RMSE and the log loss can be calculated for each repetition. We are interested in mean and standard deviation across all repetitions." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "aa2a8f81", + "metadata": {}, + "outputs": [], + "source": [ + "def pred_acc_irm(DoubleML, prop):\n", + " \"\"\"\n", + " A function to calculate prediction accuracy values for every repetition\n", + " of a Double Machine Learning model using IRM, DoubleMLIRM\n", + " \n", + " ...\n", + " \n", + " Parameters\n", + " ----------\n", + " DoubleML : doubleml.double_ml_irm.DoubleMLIRM\n", + " The IRM Double Machine Learning model\n", + " prop : bool\n", + " Indication if RMSE values have to be computed for main regression or\n", + " log loss values for propensity score\n", + " \"\"\"\n", + " \n", + " # export data and predictions of the DoubleML model\n", + " y = DoubleML._dml_data.y\n", + " d = DoubleML._dml_data.d\n", + " g0 = DoubleML.predictions.get('ml_g0')\n", + " g1 = DoubleML.predictions.get('ml_g1') \n", + " m = DoubleML.predictions.get('ml_m')\n", + " \n", + " # dimensions of prediction array\n", + " h = g0.shape[0]\n", + " w = DoubleML.n_rep\n", + " \n", + " # check whether treatment is binary \n", + " if np.isin(d, [0,1]).all() == False:\n", + " raise ValueError(\"Treatment must be a binary variable.\")\n", + " \n", + " # prepare array to store prediction accuracy measure values\n", + " pred_acc_array = np.zeros((w,))\n", + " \n", + " # check whether to assess main regression or propensity score accuracy: \n", + " if prop == False:\n", + " \n", + " # evaluate main regression accuracy\n", + " # export an array with correctly picked prediction values \n", + " export_pred_array = np.zeros((h, w)) \n", + " for i in range(w):\n", + " for j in range(h):\n", + " if d[j] == 0:\n", + " export_pred_array[j,i] = g0[j,i]\n", + " else:\n", + " export_pred_array[j,i] = g1[j,i]\n", + " \n", + " # fill array that contains rmse of each repetition\n", + " for i in range(w):\n", + " pred_acc_array[i] = mean_squared_error(y, export_pred_array[:,i], squared=False) \n", + " else:\n", + " \n", + " # evaluate propensity score accuracy\n", + " # fill array that contains log loss of each repetition\n", + " for i in range(w):\n", + " pred_acc_array[i] = log_loss(d, m[:,i], eps=0.025)\n", + " \n", + " return pred_acc_array" + ] + }, + { + "cell_type": "markdown", + "id": "suburban-infrastructure", + "metadata": {}, + "source": [ + "### Benchmark: Model based on Linear and Logistic Regression" + ] + }, + { + "cell_type": "markdown", + "id": "93f3af17-bcf9-429b-af9a-b90ea1153937", + "metadata": {}, + "source": [ + "Let us first start with a benchmark model that is based on linear and logistic regression. Hence, we estimate the functions $g_0(D,X)$ using a linear regression model and $m_0(X)$ by using an (unpenalized) logistic regression. In both cases, we include all available characteristics $V$. Later we will assess whether we can find a \"better\" estimator based on ML methods like lasso, random forests and boosting. Because we have 200 variables and 1000 observations, this is approaching a high dimentional setting, therefore the linear and the logistic regression may not estimate the parameters well." + ] + }, + { + "cell_type": "markdown", + "id": "authorized-school", + "metadata": {}, + "source": [ + "We start by initializing the learners for linear regression and logistic regression. Then, we initialize a causal model object, here of the class [DoubleMLIRM](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLIRM.html). The latter is based on the data-backend we have specified above. To reduce the disproportionate impact of extreme propensity score weights in the interactive model we trim the propensity score from below and above at thresholds of 0.025 and 0.975." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "76037798", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.855559 0.070928 12.062417 1.668137e-33 0.716544 0.994575" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Lasso learners\n", + "lasso = make_pipeline(StandardScaler(), LassoCV(cv=5, max_iter=20000)) \n", + "lasso_class = make_pipeline(StandardScaler(),\n", + " LogisticRegressionCV(cv=5, penalty='l1', solver='liblinear', \n", + " Cs = 4, max_iter=1000)) \n", + "\n", + "# Initialize DoubleMLIRM model\n", + "np.random.seed(1234)\n", + "dml_irm_lasso = dml.DoubleMLIRM(data_dml,\n", + " ml_g = lasso,\n", + " ml_m = lasso_class,\n", + " trimming_threshold = 0.025, \n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_irm_lasso.fit(store_predictions=True)\n", + "\n", + "lasso_summary = dml_irm_lasso.summary\n", + "lasso_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "stock-bookmark", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.05555945]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_irm_lasso.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "85c6e74e", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_lasso_irm = pred_acc_irm(dml_irm_lasso, prop=False)\n", + "rmse_main_lasso_irm_mean = np.mean(rmse_main_lasso_irm)\n", + "rmse_main_lasso_irm_std = np.std(rmse_main_lasso_irm)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_lasso_irm = pred_acc_irm(dml_irm_lasso, prop=True)\n", + "logloss_prop_lasso_irm_mean = np.mean(logloss_prop_lasso_irm)\n", + "logloss_prop_lasso_irm_std = np.std(logloss_prop_lasso_irm)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "c659681b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.1143405452234652\n", + "Standard deviation of RMSE is 0.005869688113839954\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_lasso_irm_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_lasso_irm_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "388cdfcf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.6686766530020503\n", + "Standard deviation of log loss is 0.0032543941531603953\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_lasso_irm_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_lasso_irm_std)" + ] + }, + { + "cell_type": "markdown", + "id": "religious-algebra", + "metadata": {}, + "source": [ + "We see that the lasso-based estimate for the ATE is $0.86$ and, hence, much closer to the true value of $0.8$ than in the benchmark $1.06$. Moreover, we can achieve improvements in terms of estimation precision as can be recognized from the smaller standard error. Also the prediction measures for the nuisance components are much smaller for Lasso than in the linear/logistic benchmark. Using the Lasso learners makes it now possible to conclude that the ATE is significantly different from zero at a significance level of 5%." + ] + }, + { + "cell_type": "markdown", + "id": "33d06b0d", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Random Forest" + ] + }, + { + "cell_type": "markdown", + "id": "4d9d008a-5b6a-4acf-93b9-b26599541653", + "metadata": {}, + "source": [ + "Alternatively, we can repeat this procedure with other machine learning methods, for example a random forest learner as provided by the [RandomForestRegressor](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html) and [RandomForestClassifier](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html) class in [scikit-learn](https://scikit-learn.org)." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "2092891a", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.8931760.07742111.536558.631791e-310.7414331.044919
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.893176 0.077421 11.53655 8.631791e-31 0.741433 1.044919" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Random Forest learners\n", + "randomForest = RandomForestRegressor()\n", + "randomForest_class = RandomForestClassifier()\n", + "\n", + "# Initialize DoubleMLIRM model\n", + "np.random.seed(1234)\n", + "dml_irm_forest = dml.DoubleMLIRM(data_dml,\n", + " ml_g = randomForest,\n", + " ml_m = randomForest_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "# Set nuisance-part specific parameters\n", + "dml_irm_forest.set_ml_nuisance_params('ml_g0', 'A', {\n", + " 'max_features': 200, 'n_estimators': 250})\n", + "dml_irm_forest.set_ml_nuisance_params('ml_g1', 'A', {\n", + " 'max_features': 200, 'n_estimators': 250})\n", + "dml_irm_forest.set_ml_nuisance_params('ml_m', 'A', {\n", + " 'max_features': 200, 'n_estimators': 250})\n", + "\n", + "dml_irm_forest.fit(store_predictions=True) \n", + "\n", + "forest_summary = dml_irm_forest.summary\n", + "forest_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "vital-insight", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.09317591]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_irm_forest.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "14c230b0", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_forest_irm = pred_acc_irm(dml_irm_forest, prop=False)\n", + "rmse_main_forest_irm_mean = np.mean(rmse_main_forest_irm)\n", + "rmse_main_forest_irm_std = np.std(rmse_main_forest_irm)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_forest_irm = pred_acc_irm(dml_irm_forest, prop=True)\n", + "logloss_prop_forest_irm_mean = np.mean(logloss_prop_forest_irm)\n", + "logloss_prop_forest_irm_std = np.std(logloss_prop_forest_irm)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "1d633282", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.1688034544446142\n", + "Standard deviation of RMSE is 0.00826647072034282\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_forest_irm_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_forest_irm_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "16a7a785", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.6823242335385794\n", + "Standard deviation of log loss is 0.0026223238604172463\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_forest_irm_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_forest_irm_std)" + ] + }, + { + "cell_type": "markdown", + "id": "d4b6e16b-6cb9-40d8-a4fa-c438f23b49f3", + "metadata": {}, + "source": [ + "The results are relatively similar to the one obtained by lasso with a bias and standard errors that are slightly greater than before. The predictive accuracy of the random forest learners is also slightly worse than that of Lasso." + ] + }, + { + "cell_type": "markdown", + "id": "9ac68b60", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Extreme Gradient Boosting" + ] + }, + { + "cell_type": "markdown", + "id": "cc71c762-8497-43e5-a151-a5239641d510", + "metadata": {}, + "source": [ + "Next, we estimate the ATE using extreme gradient boosting as provided by [xgboost](https://docs.getml.com/latest/api_reference/predictors.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "90b9ef4e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.7909060.1043067.5825883.387302e-140.5864710.995341
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.790906 0.104306 7.582588 3.387302e-14 0.586471 0.995341" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Extreme Gradient Boosting learners\n", + "boost = XGBRegressor(n_jobs=1, objective = \"reg:squarederror\")\n", + "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", + " objective = \"binary:logistic\", eval_metric = \"logloss\")\n", + "\n", + "# Initialize DoubleMLIRM model\n", + "np.random.seed(1234)\n", + "dml_irm_boost = dml.DoubleMLIRM(data_dml,\n", + " ml_g = boost,\n", + " ml_m = boost_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "# Set nuisance-part specific parameters\n", + "dml_irm_boost.set_ml_nuisance_params('ml_g0', 'A', {\n", + " 'n_estimators': 30, 'eta': 0.2})\n", + "dml_irm_boost.set_ml_nuisance_params('ml_g1', 'A', {\n", + " 'n_estimators': 30, 'eta': 0.2})\n", + "dml_irm_boost.set_ml_nuisance_params('ml_m', 'A', {\n", + " 'n_estimators': 15, 'eta': 0.2})\n", + "\n", + "dml_irm_boost.fit(store_predictions=True)\n", + "\n", + "boost_summary = dml_irm_boost.summary\n", + "boost_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "traditional-ribbon", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [-0.0090944]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_irm_boost.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "efd04e78", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_boost_irm = pred_acc_irm(dml_irm_boost, prop=False)\n", + "rmse_main_boost_irm_mean = np.mean(rmse_main_boost_irm)\n", + "rmse_main_boost_irm_std = np.std(rmse_main_boost_irm)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_boost_irm = pred_acc_irm(dml_irm_boost, prop=True)\n", + "logloss_prop_boost_irm_mean = np.mean(logloss_prop_boost_irm)\n", + "logloss_prop_boost_irm_std = np.std(logloss_prop_boost_irm)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "114aa5cf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.2287566646120192\n", + "Standard deviation of RMSE is 0.010275338353331828\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_boost_irm_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_boost_irm_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "c1ebde27", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.7204831015081563\n", + "Standard deviation of log loss is 0.01297502257820836\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_boost_irm_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_boost_irm_std)" + ] + }, + { + "cell_type": "markdown", + "id": "9ee7f068-1ac4-4d7d-99a7-5c68c91e8b51", + "metadata": {}, + "source": [ + "The estimated coefficient is very close to the true ATE of $0.8$ but has a small negative bias. The interpretation of the results obtained with lasso, random forests and boosting are very similar. In all cases we are able to reject the null hypothesis that the ad has no effect on the sales." + ] + }, + { + "cell_type": "markdown", + "id": "fba54a14-c685-4948-819d-94a99d88e94a", + "metadata": {}, + "source": [ + "#### IRM - Summary of coefficient estimates\n", + "\n", + "We save the estimates, bias and confidence intervals for later peresentation and comparision." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "5e16a294", + "metadata": { + "scrolled": false, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefBias2.5 %97.5 %
regression0.795-0.0050.6250.966
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\n", + "
" + ], + "text/plain": [ + " coef Bias 2.5 % 97.5 %\n", + "regression 0.795 -0.005 0.625 0.966\n", + "lasso 0.856 0.056 0.717 0.995\n", + "forest 0.893 0.093 0.741 1.045\n", + "xgboost 0.791 -0.009 0.586 0.995" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "irm_summary = pd.concat((reg_summary, lasso_summary, forest_summary, boost_summary))\n", + "irm_summary.index = ['regression','lasso', 'forest', 'xgboost']\n", + "irm_summary = irm_summary[['coef', '2.5 %', '97.5 %']]\n", + "irm_summary.insert(1, \"Bias\", [irm_summary.loc['regression','coef'] - 0.8, \n", + " irm_summary.loc['lasso','coef'] - 0.8, \n", + " irm_summary.loc['forest','coef'] - 0.8, \n", + " irm_summary.loc['xgboost','coef'] - 0.8])\n", + "irm_summary.round(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "4b478603", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "errors = np.full((2, irm_summary.shape[0]), np.nan)\n", + "errors[0, :] = irm_summary['coef'] - irm_summary['2.5 %']\n", + "errors[1, :] = irm_summary['97.5 %'] - irm_summary['coef']\n", + "plt.errorbar(irm_summary.index, irm_summary.coef, fmt='o', yerr=errors)\n", + "plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", + "\n", + "plt.title('Interactive Regression Model (IRM)')\n", + "plt.xlabel('ML method')\n", + "_ = plt.ylabel('Coefficients and 95%-CI')" + ] + }, + { + "cell_type": "markdown", + "id": "8c891e02", + "metadata": {}, + "source": [ + "#### IRM - Summary of prediction assessment metric's mean values" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "6790aad8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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main RMSEmain RMSE (sd)prop log lossprop log loss (sd)
regression0.8120.0000.5340.000
lasso1.1140.0060.6690.003
forest1.1690.0080.6820.003
xgboost1.2290.0100.7200.013
\n", + "
" + ], + "text/plain": [ + " main RMSE main RMSE (sd) prop log loss prop log loss (sd)\n", + "regression 0.812 0.000 0.534 0.000\n", + "lasso 1.114 0.006 0.669 0.003\n", + "forest 1.169 0.008 0.682 0.003\n", + "xgboost 1.229 0.010 0.720 0.013" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "irm_rmse_index = ['regression','lasso', 'forest', 'xgboost']\n", + "irm_rmse = pd.DataFrame([[rmse_main_linlog_irm_mean, rmse_main_linlog_irm_std, \n", + " logloss_prop_linlog_irm_mean, logloss_prop_linlog_irm_std],\n", + " [rmse_main_lasso_irm_mean, rmse_main_lasso_irm_std,\n", + " logloss_prop_lasso_irm_mean, logloss_prop_lasso_irm_std],\n", + " [rmse_main_forest_irm_mean, rmse_main_forest_irm_std,\n", + " logloss_prop_forest_irm_mean, logloss_prop_forest_irm_std],\n", + " [rmse_main_boost_irm_mean, rmse_main_boost_irm_std,\n", + " logloss_prop_boost_irm_mean, logloss_prop_boost_irm_std]],\n", + " index=irm_rmse_index,\n", + " columns=['main RMSE', 'main RMSE (sd)',\n", + " 'prop log loss', 'prop log loss (sd)'])\n", + "irm_rmse.round(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "a5be2641", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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idNptbGzqP2oiIiNlUKguW7YMAQEBeP/99wEA3t7euHnzJqKjox8aqqdPn4ZcLoezs7NkgyUiMnY1vv0vKChAfn4+BgwYoNPu5+eHvLw8FBQUVLtebm4u7O3tpRklEVETUWOo5uXlAQC6dOmi025rawsAuHDhgt46165dQ3FxMU6ePAl/f3/I5XL4+fnVOA9LRNTU1fj2v6SkBAAgk8l02s3//35QGo1Gb53c3FwAwKVLlzB37lyYmZkhMTERISEhqKiowJtvvmnQ4HJycnDnzh2D+j44lqysLIPXoUdjTaXFekqvLjV1c3NrqOHUHKpCCACAiYlJte0tWugf7Do6OuKLL76AUqnUhnHv3r1RXFyM6Ohog0NVLpcb1K+KbPNmaDSaBi3YPw1rKi3WU3rGVtMa3/5bWFgA0D8iLS0t1Vn+IGtra/j4+Ogd3fbt2xeFhYVQq9V1HjARkTGrMVSr5lLz8/N12i9evKiz/EFHjx5FQkKCXnt5eTlatWpVbRATETUHNYaqra0tOnTogOTkZJ32Xbt2oXPnznj++ef11jl27BgWLFignVsFgMrKSuzcuROurq4wNTWVYOhERMbHoOtUp02bhtDQUFhaWqJfv374+eefsWPHDnz66acAALVajfz8fHTr1g0ymQwqlQpxcXGYPn06Zs2aBXNzc3z77bc4c+YM4uPjG3SHiIgak0EfU1WpVAgLC8P+/fsxbdo0HDlyBJGRkRg4cCAAID09HcOHD0dOTg4AwNLSEnFxcVAoFAgPD8esWbNQVlaG2NhY9OjRo+H2hoiokRl0pAoAI0aMwIgRI6pdplKpoFKpdNrat2+PZcuW1W90RERNDL+liohIQgxVIiIJMVSJiCTEUCUikhBDlYhIQgxVIiIJMVSJiCTEUCUikhBDlYhIQgxVIiIJMVSJiCTEUCUikhBDlYhIQgxVIiIJMVSJiCTEUCUikhBDlYhIQgxVIiIJMVSJiCTEUCUikhBDlYhIQgxVIiIJMVSJiCTEUCUikhBDlYhIQgaHalJSEl577TUoFAoEBAQgMTHxkf1LS0sRFhYGLy8vuLi4YNKkSfj999/rOVwiIuNmUKju2LEDwcHB8PLywmeffQZ3d3eEhIQgOTn5oesEBQUhOTkZwcHBiIyMRGFhIcaOHYuSkhLJBk9EZGxaGdJp2bJlCAgIwPvvvw8A8Pb2xs2bNxEdHQ1/f3+9/pmZmdizZw/WrFmDPn36AABefvllvPLKK9i4cSPeffddCXeBiMh41HikWlBQgPz8fAwYMECn3c/PD3l5eSgoKNBbJyMjA+bm5vDy8tK2WVtbQ6lUYu/evRIMm4jIONV4pJqXlwcA6NKli067ra0tAODChQvo2LGj3jq2trZo2bKlTnunTp2wY8eOeg2YqCn7askSZGVlNfYwmhVjq2mNoVo1ByqTyXTazc3NAQAajUZvHY1Go9e/ap3q+j9MTk4O7ty5Y3D/qSoVABhVgZs61rRhsJ7Sq01N3dzcGmwcNYaqEAIAYGJiUm17ixb6MwhVy6pTXf+HkcvlBvetkpWV1aAF+ydiTaXFekrPmGpaY8JZWFgA0D8iLS0t1Vn+IJlMpl3+93WqO4IlImouagzVqrnU/Px8nfaLFy/qLP/7OgUFBXpHrBcvXqy2PxFRc1FjqNra2qJDhw5616Tu2rULnTt3xvPPP6+3Tu/evXHr1i0cOHBA26ZWq5GZmYlevXpJMGwiIuNk0HWq06ZNQ2hoKCwtLdGvXz/8/PPP2LFjBz799FMA9wMzPz8f3bp1g0wmg1KphLu7O2bPno3g4GC0bt0aMTExsLCwwMiRIxt0h4iIGpNBoapSqXD37l18/fXXSEhIQMeOHREZGYmBAwcCANLT0xEaGor169fDw8MDALBy5UpEREQgKioKlZWVcHNzw/Lly2Fpadlwe0NE1MhMxKNO1TdBxnQWsLlgTaXFekrPmGrKb6kiIpJQsztSJSJqTDxSJSKSEEOViEhCDFUiIgkxVImIJMRQJSKSEEOViEhCDFUiIgkxVImIJMRQJSKSEEOVqInihyEfL0PrzVCtRkxMDLp3797Yw6gXe3t7fP755409jGajsLAQY8aMgZOTE3r16oXy8vJGHc8PP/yAyMjIRh1DQzK238G0tDSEhIQY1Negr/77p3nrrbfQp0+fxh4GGZG4uDj8+uuvWLp0Kdq2bQszM7NGHc8XX3xhNN/K9E/wzTffoKKiwqC+DNVqtG3bFm3btm3sYZAR+fPPP9GmTRvtdwgTPUy93v77+voiIiICY8aMgaurK8LDw3Hjxg0sWLAAnp6eUCgUGDlypN6tY0tKShAaGgoPDw+4ublh4cKFWLZsGXx9fR+5bQAGbT8jIwPDhg2Di4sLlEolpk6divPnz2uX5+fnY8qUKfDw8ECPHj0wfPhw7NmzR7u8urceiYmJGDJkCJydndGnTx9ERkbq3D57/vz5mDhxIhISEjBgwAA4OjrijTfewL59++pTYsmcOnUK06ZNQ8+ePSGXy9GnTx8sWbJE521sfesGAMeOHcP48eOhVCqhVCoxc+ZMXLp06bHtZ0Pw9fVFQkICrly5Ant7e8TExODq1auYN28evL290aNHD4waNQpHjhzRrnPp0iXY29sjNjYWfn5+8PDwwPbt2wEAp0+fxqRJk+Di4gI3NzfMnDkTV69e1XnMb775Bv7+/nBycoK3tzc+/PBD7c03fX19kZ+fjx9//BH29vZGV9+UlBTY29tj1apV2rZTp07B0dFR+3uckJAAPz8/KBQKDBs2DKmpqbC3t8fhw4d1tpWcnIxXX30VCoUCo0ePxvHjx3WWnz9/HlOnToWnpydcXFzwzjvvIDc3V6dPTc8VACQlJeH111+HQqGAp6cngoODUVhYCAAYM2YMDh48iCNHjlQ7Rj2iHnx8fET37t1FRESE2Lt3rzhy5Ih4/fXXhZeXl/juu+9EWlqamDx5snB0dBTZ2dna9UaPHi3c3d3Fd999J1JTU8WIESOEo6Oj8PHxeei2s7OzxZ07d2rcfn5+vlAoFCIsLEwcPHhQJCcnCz8/P/HKK6+IyspKUVFRIfz9/cXYsWNFenq62L9/v3j33XeFg4ODuHjxohBCiBUrVggHBwftWKKjo4W9vb1YsmSJ2Ldvn/j666+Fs7OzePvtt0VlZaUQQoiQkBDh5uYmAgICRFJSkkhPTxdDhgwRzs7O4tatW/Upc53Y2dmJzz77TAghxNWrV4WLi4uYOHGiSE9PFxkZGSI8PFzY2dmJ1atXCyGkqVtGRoZwcHAQ77zzjkhNTRU//fSTePXVV4WXl5coKip67DWQSk5OjpgyZYrw8vISR48eFVeuXBFeXl5iwIAB4qeffhKpqaliwoQJonv37uLAgQNCCCEKCgqEnZ2dUCgU4ocffhDbt28XRUVFIi8vT7i4uIi33npL7N69W2zbtk34+/sLX19f7etk69atQi6Xi/Xr14vDhw+LjRs3CmdnZzF//nztePr06SMmTZokjh49KsrLyxutNg8zZ84c4eTkJC5evCjKy8vFoEGDRGBgoCgvLxfff/+9sLOzE2FhYWLv3r0iKipKKBQKYWdnJw4dOiSEuP87aGdnJ9zd3cXGjRtFSkqKGDp0qHB2dhbXrl0TQgiRm5srnJ2dxdChQ8XOnTvFzp07hUqlEs7OzuLs2bNCCCEKCwtrfK4yMzOFg4ODiImJEYcPHxaJiYnCy8tLjB49WgghxNmzZ8Wbb74pBg8eLI4ePSpKSkoeue/1DlVfX19tsGzatEnY29uL48ePa/tUVFSIIUOGiHHjxgkhhDhw4ICws7MTaWlp2j6lpaWiZ8+eeqH64LYN3X5SUpKws7MTV69e1fbJzs4Wy5YtEyUlJeLatWvCzs5O/PTTT9rlt27dEh999JE4c+aMEEI3VG/cuCEcHR1FWFiYzr5v27ZNZz9CQkKEnZ2dyM/P1/Y5cuSIsLOzE7t3765FVaXxYKju2bNHjBo1Smg0Gp0+gYGBYtKkSUIIaeqmUqlEYGCgqKio0Pa5fPmycHR0FBEREQ22r4/D+++/r319RkRECCcnJ3HlyhXt8oqKChEYGChUKpUQ4n+hGhISorOd2bNnCy8vL53n4tq1a0KhUIjPP/9cCCHEwoULhZ+fn85rf8uWLWL9+vXan/v376+3bWNy48YN4eXlJd555x3x6aefCrlcLk6dOiWEEKJfv35ixowZOv3/85//VBuqu3bt0vZRq9XC2dlZREVFCSGEmDFjhvD09BSlpaXaPhqNRnh6emq3b8hz9eWXXwoXFxedP07p6ekiJiZG+xy8/fbb2pCtSb3P/r/44oswMTEBABw8eBDPPfccHBwccO/ePdy7dw+VlZXw8fHBL7/8grt37+LQoUMwMzND3759tdt46qmn0K9fv0du29Dt9+jRA2ZmZhg6dCiWLFmCffv24aWXXkJQUBBkMhlsbGzQrVs3LFy4ECEhIdi6dSsqKysRGhqKF198UW8M2dnZuHv3Ll577TWddn9/f5iamuq8FXj22WfRsWNH7c9V87K3b9+uW3El0qdPH2zYsAFPPPEEzp07h9TUVKxatQpqtRp//fUXANS7bmVlZcjJycHAgQPRosX/XlbPP/88Xn75Zb23W01ZZmYm3Nzc0K5dO21bixYtMHDgQOTk5GjfpgOAnZ2dzrqHDh1Cz549YWZmpn0NW1lZQaFQaO8+3LNnT1y4cAFDhgzBypUrceLECQwaNAhjxox5PDsogdatWyMsLAx79+7Fl19+iZkzZ+Kll17CxYsXceXKFfj5+en0r26u2tTUFK+88or2ZysrK7i6umqnADIzM+Hr64unnnpK28fc3By+vr7a15shz5VSqcTt27cxaNAgfPLJJ8jMzETv3r0xffp0nfwxVL1PVD3zzDPa///555+4evUq5HJ5tX1v3LiBGzduwMrKSm+wNjY2j9y2odvv0KEDNmzYgNWrV+P777/H+vXr8fTTT+Pf//43Zs2aBRMTE3z99ddYtWoVdu/ejcTERJiamqJ///4ICwvTuzHhzZs3AdwPzAe1aNEC1tbWOr9ATz75pE6fqn2srKysdryPS2VlJZYtW4b4+HiUlZWhXbt2UCgUMDMz0157V9+63blzB0KIhz6PV65cedy73WBu3ryJzp0767Xb2NhACIHS0lJtW3Wv4a1bt2Lr1q1661dtc+DAgaisrMS3336Lzz//HDExMWjfvj2Cg4Ob1Ikyb29v2NjY4Pr169qDJrVaDQCwtrbW6Vvd68bKykrnD3TVelWhevPmzYe+3qp+Lw15rlxcXLB69WrExsZi3bp1WL16NWxsbDBlypQ6/SGT9Oy/hYUFunbt+tDr56ysrNCmTRuo1WoIIXSCtbi4WJLtA4BCocDKlStx9+5dZGVlYdOmTfjiiy/QvXt3+Pn54bnnnsOHH36I//znP8jNzUVycjLWrFmDZ555BgsXLtTZZlXIFhUVoVOnTtr2yspKqNVq7WMas6oXzKJFi/Dqq6/CwsICADB06FCdfvWp2+zZs2FiYoLr16/rPX5RUVGTqJOhnn766Wr389q1awDuvw6r/v93MpkMffr0wdixY/WWPfHEE9r/BwYGIjAwECUlJdi/fz/WrFmDuXPnwt3dvdogMUbR0dHQaDTo3LkzPvjgA2zcuBHPPfccAP3f96qwfVBJSYleTly/fl37WnrY81BUVITWrVs/ss+DzxVw/w+At7c3bt++jUOHDmH9+vVYvHgxXFxc4OjoWKv9lvTif6VSiStXrqBNmzZwcnLS/ktNTUVcXBxMTU2hVCpx9+5dnbPif/+5PtuPi4uDr68v7t69iyeeeAKenp7473//CwD4448/cPz4cfTq1QvHjx+HiYkJHBwcEBQUBDs7O/zxxx96j9mjRw888cQT2LZtm057cnIy/vrrryZxrWBWVhbs7e2hUqm0gVpYWIgzZ85oj6LrWzdzc3PI5XJs375d58j8jz/+wK+//gpXV9fHv+MNRKlUIisrS+eMfWVlJZKTk+Hk5KQTjn/n7u6O8+fPQy6Xa1+/3bt3x+rVq7F3714AwJw5czB9+nQA9w8kAgICMHXqVNy7dw9FRUUAoHcEZ2yys7Oxbt06zJgxA+Hh4Th+/DjWrVuHdu3aoUOHDkhNTdXpn5KSoreN27dvIzMzU/tzUVERsrKy4OHhAeD+85CWloaysjJtn7KyMqSlpWl/Lw15rpYuXYqhQ4dCCIEnn3wSPj4+2gv9q9Zr2bKlwfsu6TOjUqnw3HPPYfz48diyZQsOHTqEiIgIrFq1Ch07doSJiQk8PDzg4eGB+fPnIyEhAenp6Zg8eTKuX79e4/yFIdvv2bMnioqKMG3aNOzZswf79+9HaGgozMzM4OPjg5deeglPPfUU5s2bh23btuHw4cP49NNPcerUKb15HuD+3NDEiRPx7bff4qOPPkJGRgZiY2OxcOFCuLu7w9vbW8oSNgiFQoGTJ09izZo1OHLkCBISEjBq1CjcvXtXO98rRd2CgoJw7tw5TJkyBWlpaUhKSsK4ceMgk8kwbty4RqyAtMaPHw+ZTIa3334bSUlJSEtLw+TJk3H+/HkEBQU9ct1p06bh3LlzeO+995Camoo9e/ZgypQp+Pnnn7XTWj179sTu3bsRGRmJgwcPYufOnYiOjkaXLl208/5PP/00Tp48iSNHjuhc2mcMysvLERoaCjs7O4wbNw6urq4YNmwYVqxYgby8PMyYMQPbt2/H4sWLkZGRgZiYGGzYsAGA7h8LU1NThISEYPv27UhJScHEiRNhYWGhPcqfNm0aNBoNxo0bh927d2PXrl0YN24cysrKMG3aNACGPVe9evXCb7/9hvnz5yMjIwPp6elYvHgxrKys4O7uDuD+H7cLFy7g4MGD2inBhzLodNZD+Pj4iPfff1+nraioSMyfP1/07NlTODk5iYEDB4q4uDidPmq1WgQHBwtXV1fh5uYmPvzwQzFjxgwRGBj4yG0buv2MjAwxYsQI4erqKnr06CFGjRolfvnlF+3y33//XXvmUC6Xi9dee01s2rRJu/zvl1QJIURcXJzw8/MTcrlc9O3bV0RGRoqysjLt8pCQENG/f3+ddarOACcmJtZUSsk9ePa/vLxchIWFCS8vL6FQKISfn59YsWKFiImJEU5OTtpLROpbt6ptDB8+XDg5OQl3d3cxa9YscenSpce34w3kwbP/QtyvxfTp04Wrq6twdnYWo0eP1p65FuLRz/3x48fFhAkThLOzs3BxcREjR44U+/fv1+mzYcMGMXDgQKFQKIS7u7uYOXOmuHz5snZ5SkqK8PT0FI6OjiIrK6sB9rjuIiMjhYODg85VOjdv3hReXl5i2LBh4t69e2LDhg3C19dXyOVyMWLECLFu3TphZ2cnfvvtNyHE/d9Bb29vkZiYKPr16yecnJzEhAkTRF5ens5jnThxQowfP144OzsLV1dX8e6772qvMqhS03MlxP2reaougXRxcRHvvPOOOH36tHb5sWPHRL9+/YRcLhfbtm175P4/9ltUX758GdnZ2ejfv7/O26ShQ4eibdu2WLly5eMcDhE9ZklJSXBycoKtra22LT4+HosXL8bhw4fx9NNPN+Lo6q9RPqYaEhKCgIAADB48GEII7NixA7/99hvmzJnTGMMhosfoxx9/RExMDGbOnIlnn30WZ8+eRXR0NN54440mH6gA8NiPVIH7H4f87LPPcPr0aVRWVuKll17C1KlTm8T8JBHVT3FxMT7++GPs27cPf/75J9q2bYs33ngDU6ZMgampaWMPr94aJVSJiJor474ug4ioiWGoEhFJiKFKRCQhhioRkYQYqkREEvo/mjYYL385xLkAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# graphical illustration of RMSE for main regression\n", + "errors_irm_rmse = np.full((2, irm_rmse.shape[0]), np.nan)\n", + "errors_irm_rmse[0, :] = irm_rmse['main RMSE'] - irm_rmse['main RMSE (sd)']\n", + "errors_irm_rmse[1, :] = irm_rmse['main RMSE'] + irm_rmse['main RMSE (sd)']\n", + "plt.errorbar(x=irm_rmse.index, y=irm_rmse['main RMSE'], fmt='x',\n", + " yerr=errors_irm_rmse, c='darkslategray')" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "d42b8ca8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "regression 0.812050\n", + "lasso 1.108471\n", + "forest 1.160537\n", + "xgboost 1.218481\n", + "dtype: float64" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "irm_rmse['main RMSE'] - irm_rmse['main RMSE (sd)']" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "9255bc0a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# graphical illustration of log loss for main regression\n", + "errors_irm_logloss = np.full((2, irm_rmse.shape[0]), np.nan)\n", + "errors_irm_logloss[0, :] = irm_rmse['prop log loss'] - irm_rmse['prop log loss (sd)']\n", + "errors_irm_logloss[1, :] = irm_rmse['prop log loss'] + irm_rmse['prop log loss (sd)']\n", + "plt.errorbar(x=irm_rmse.index, y=irm_rmse['prop log loss'], fmt='x',\n", + " yerr=errors_irm_logloss, c='darkslategray')" + ] + }, + { + "cell_type": "markdown", + "id": "27c6157d", + "metadata": {}, + "source": [ + "### Inspection of the benchmark model\n", + "\n", + "It is natural to investigate why the the benchmark model performs so much worse as compared to the ML models. First of all, we can conclude that the predictive performance of the linear and logistic regression for the nuisance functions is considerably worse and more variable than for lasso, random forest and xgboost. Moreover, we can also inspect the propensity score estimates of the logistic regression which appear to be very close to zero and one for many observations.\n", + "\n", + "We first define a helper function that plots the propensity scores for each of the cross-fitting repetitions." + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "78afa7eb", + "metadata": {}, + "outputs": [], + "source": [ + "def rep_propscore_plot(DoubleML):\n", + " \"\"\"\n", + " A function to create histograms as sublots for every repetition's propensity score density \n", + " of a Double Machine Learning model\n", + " \n", + " ...\n", + " \n", + " Parameters\n", + " ----------\n", + " DoubleML : doubleml\n", + " The Double Machine Learning model\n", + " \"\"\"\n", + " \n", + " \n", + " #export nuisance part from the DoubleML model\n", + " m = DoubleML.predictions.get('ml_m')\n", + " \n", + " # dimensions of nuisance array\n", + " h = m.shape[0]\n", + " rep = DoubleML.n_rep\n", + " \n", + " # create histograms as subplots covering the propensity score densities of all repetitions\n", + " fig, ax = plt.subplots(1, rep, figsize=[20,4.8])\n", + " for i in range(rep):\n", + " ax[i].hist(np.reshape(m[:,i], h), bins=25)\n", + " ax[i].set_title('repetition ' + str(i+1))\n", + " ax[i].set_xlabel(\"prop_score\")\n", + " ax[i].set_ylabel(\"density\")\n", + " \n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "53d9d81d", + "metadata": {}, + "outputs": [ + { + "ename": "TypeError", + "evalue": "'AxesSubplot' object is not subscriptable", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mTypeError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_19728/494899183.py\u001b[0m in \u001b[0;36m\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_irm_regression)" + ] + }, + { + "cell_type": "markdown", + "id": "4f8d0f9f", + "metadata": {}, + "source": [ + "Let's compare this to the corresponding plot for the lasso-based model." + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "e67ebd28", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_irm_lasso)" + ] + }, + { + "cell_type": "markdown", + "id": "b282c8d9", + "metadata": {}, + "source": [ + "We observe that the propensity score estimates of the lasso-based model are more centered and only close to zero and one for very few observations." + ] + }, + { + "cell_type": "markdown", + "id": "b29e412d-d86f-46b4-840f-cbbe082faf0b", + "metadata": {}, + "source": [ + "### Conclusion\n", + "\n", + "We can conclude that the interactive regression model (IRM) estimates are close to the true coefficient value, if the nuisance components are estimated with machine learning methods. The performance of Lasso and the tree-based methods random forests and extreme gradient boosting are comparable. All of the ML-based estimators have exhibited a superior performance to the benchmark based on linear and logistic regression, which seems to be rather unstable in the data example considered.\n" + ] + }, + { + "cell_type": "markdown", + "id": "f50297c5", + "metadata": {}, + "source": [ + "## 2. Partially Linear Regression Model (PLR)\n", + "\n", + "The [DoubleML](https://docs.doubleml.org/stable/index.html) package also includes the [Partial Linear Regression (PLR)](https://docs.doubleml.org/stable/guide/models.html#partially-linear-regression-model-plr) model, which assumes the population regression has a linear and additive structure. Although in reality, we never know if this structure really holds for the underlying data generating process, we can apply this model and see how the estimates compare to those from the IRM." + ] + }, + { + "cell_type": "markdown", + "id": "fa24e6e1-b878-401f-b38a-c29cc0620c2c", + "metadata": {}, + "source": [ + "We estimate the function $g_0$ and $m_0$ in the following PLR model:\n", + "\n", + "\\begin{eqnarray}\n", + "& Y = D\\theta_0 + g_0(X) + \\zeta, &\\quad E[\\zeta \\mid D,X]= 0,\\\\\n", + "& D = m_0(X) + V, &\\quad E[V \\mid X] = 0.\n", + "\\end{eqnarray}\n", + "\n", + "To estimate the causal parameter $\\theta_0$, we use double machine learning with 3-fold cross-fitting again. The steps of our analysis are very similar to the IRM cases with the difference being that we use a model class [DoubleMLPLR](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLPLR.html) for estimation." + ] + }, + { + "cell_type": "markdown", + "id": "8e7ad0b5", + "metadata": {}, + "source": [ + "### Assess predictive performance in the PLR" + ] + }, + { + "cell_type": "markdown", + "id": "73c26a84", + "metadata": {}, + "source": [ + "As in the IRM, we want to calculate mean and standard deviation of the RMSE / log loss values across all repetitions to evaluate the prediction performance. Once again, a helper function is used as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "54a843e3", + "metadata": {}, + "outputs": [], + "source": [ + "def pred_acc_plr(DoubleML, prop):\n", + " \"\"\"\n", + " A function to calculate prediction accuracy values for every repetition\n", + " of a Double Machine Learning model using PLR, DoubleMLPLR\n", + " \n", + " ...\n", + " \n", + " Parameters\n", + " ----------\n", + " DoubleML : doubleml.double_ml_plr.DoubleMLPLR\n", + " The PLR Double Machine Learning model\n", + " prop : bool\n", + " Indication if RMSE values have to be computed for main regression or log loss values for propensity score\n", + " \"\"\"\n", + " \n", + " \n", + " # export data, fitted coefficient and predictions of the DoubleML model\n", + " y = DoubleML._dml_data.y\n", + " d = DoubleML._dml_data.d\n", + " theta = DoubleML.coef\n", + " g0 = DoubleML.predictions.get('ml_g')\n", + " m = DoubleML.predictions.get('ml_m')\n", + " \n", + " # dimensions of prediction array\n", + " h = g0.shape[0]\n", + " w = DoubleML.n_rep\n", + " \n", + " # check whether treatment is binary \n", + " if np.isin(d, [0,1]).all() == False:\n", + " raise ValueError(\"Treatment must be a binary variable.\")\n", + " \n", + " # prepare array to store prediction accuracy values\n", + " pred_acc_array = np.zeros((w,))\n", + " \n", + " # check whether to assess main regression or propensity score accuracy: \n", + " if prop == False:\n", + " \n", + " # evaluate main regression accuracy\n", + " # export array with prediction values\n", + " export_pred_array = np.zeros((h, w)) \n", + " for i in range(w):\n", + " for j in range(h):\n", + " export_pred_array[j,i] = theta*d[j] + g0[j,i]\n", + " \n", + " # fill array that contains rmse of each repetition\n", + " for i in range(w):\n", + " pred_acc_array[i] = mean_squared_error(y, export_pred_array[:,i], squared=False)\n", + " \n", + " else:\n", + " \n", + " # evaluate propensity score accuracy\n", + " # fill array that contains log loss of each repetition\n", + " for i in range(w):\n", + " pred_acc_array[i] = log_loss(d, m[:,i], eps=0.025)\n", + " \n", + " return pred_acc_array" + ] + }, + { + "cell_type": "markdown", + "id": "331a36d6", + "metadata": {}, + "source": [ + "### Benchmark: Model based on Linear and Logistic Regression" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "1432e567-d221-490d-9361-39b9072cb6d4", + "metadata": { + "scrolled": true, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.7849990.06712711.6941911.364815e-310.6534320.916565
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.784999 0.067127 11.694191 1.364815e-31 0.653432 0.916565" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Linear and Logistic Regression learners\n", + "linreg = make_pipeline(StandardScaler(), LinearRegression())\n", + "logreg_class = make_pipeline(StandardScaler(), LogisticRegression(penalty=\"none\"))\n", + "\n", + "# Initialize DoubleMLPLR model\n", + "np.random.seed(1234)\n", + "dml_plr_regression = dml.DoubleMLPLR(data_dml,\n", + " ml_g = linreg,\n", + " ml_m = logreg_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_regression.fit(store_predictions=True)\n", + "\n", + "reg_summary = dml_plr_regression.summary\n", + "reg_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "ff708453", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [-0.01500149]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_plr_regression.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "88392566", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_linlog_plr = pred_acc_plr(dml_plr_regression, prop=False)\n", + "rmse_main_linlog_plr_mean = np.mean(rmse_main_linlog_plr)\n", + "rmse_main_linlog_plr_std = np.std(rmse_main_linlog_plr)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_linlog_plr = pred_acc_plr(dml_plr_regression, prop=True)\n", + "logloss_prop_linlog_plr_mean = np.mean(logloss_prop_linlog_plr)\n", + "logloss_prop_linlog_plr_std = np.std(logloss_prop_linlog_plr)" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "08227dfc", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.3418428467276253\n", + "Standard deviation of RMSE is 0.009847706467828324\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_linlog_plr_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_linlog_plr_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "c91ed6e8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 1.0228568161263911\n", + "Standard deviation of log loss is 0.027536454508812133\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_linlog_plr_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_linlog_plr_std)" + ] + }, + { + "cell_type": "markdown", + "id": "4dd8948f", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Lasso" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "id": "0bbbc3ce", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.8047950.07027111.4528072.276523e-300.6670670.942522
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.804795 0.070271 11.452807 2.276523e-30 0.667067 0.942522" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize DoubleMLPLR model\n", + "np.random.seed(1234)\n", + "dml_plr_lasso = dml.DoubleMLPLR(data_dml,\n", + " ml_g = lasso,\n", + " ml_m = lasso_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_lasso.fit(store_predictions=True)\n", + "\n", + "lasso_summary=dml_plr_lasso.summary\n", + "lasso_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "id": "30aef0c8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.00479477]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_plr_lasso.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "id": "96383f94", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_lasso_plr = pred_acc_plr(dml_plr_lasso, prop=False)\n", + "rmse_main_lasso_plr_mean = np.mean(rmse_main_lasso_plr)\n", + "rmse_main_lasso_plr_std = np.std(rmse_main_lasso_plr)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_lasso_plr = pred_acc_plr(dml_plr_lasso, prop=True)\n", + "logloss_prop_lasso_plr_mean = np.mean(logloss_prop_lasso_plr)\n", + "logloss_prop_lasso_plr_std = np.std(logloss_prop_lasso_plr)" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "id": "10a66c25", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.1394799633725696\n", + "Standard deviation of RMSE is 0.003190385536736178\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_lasso_plr_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_lasso_plr_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "id": "afe3b2b9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.6686763881131824\n", + "Standard deviation of log loss 0.003254281706002184\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_lasso_plr_mean)\n", + "print(\"Standard deviation of log loss\", logloss_prop_lasso_plr_std)" + ] + }, + { + "cell_type": "markdown", + "id": "a4ed2694", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Random Forests" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "id": "e5f3ac90", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.7993070.07329710.9050281.090595e-270.6556470.942967
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.799307 0.073297 10.905028 1.090595e-27 0.655647 0.942967" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Random Forest learners\n", + "randomForest = RandomForestRegressor()\n", + "randomForest_class = RandomForestClassifier()\n", + "\n", + "# Initialize DoubleMLPLR model\n", + "np.random.seed(1234)\n", + "dml_plr_forest = dml.DoubleMLPLR(data_dml,\n", + " ml_g = randomForest,\n", + " ml_m = randomForest_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_forest.fit(store_predictions=True)\n", + "\n", + "forest_summary = dml_plr_forest.summary\n", + "forest_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "id": "4c40246d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [-0.00069288]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_plr_forest.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "id": "a977c34b", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_forest_plr = pred_acc_plr(dml_plr_forest, prop=False)\n", + "rmse_main_forest_plr_mean = np.mean(rmse_main_forest_plr)\n", + "rmse_main_forest_plr_std = np.std(rmse_main_forest_plr)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_forest_plr = pred_acc_plr(dml_plr_forest, prop=True)\n", + "logloss_prop_forest_plr_mean = np.mean(logloss_prop_forest_plr)\n", + "logloss_prop_forest_plr_std = np.std(logloss_prop_forest_plr)" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "id": "1f54fed6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.1886867050333019\n", + "Standard deviation of RMSE is 0.006048072563384578\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_forest_plr_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_forest_plr_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "id": "8101acf6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.6836880652313276\n", + "Standard deviation of log loss is 0.005321479254441978\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_forest_plr_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_forest_plr_std)" + ] + }, + { + "cell_type": "markdown", + "id": "6aa9af04", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Extreme Gradient Boosting" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "id": "6fab5d3a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.823840.07167611.4939881.414286e-300.6833580.964321
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.82384 0.071676 11.493988 1.414286e-30 0.683358 0.964321" + ] + }, + "execution_count": 59, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Extreme Gradient Boosting learners\n", + "boost = XGBRegressor(n_jobs = 1, objective = \"reg:squarederror\", \n", + " eta = 0.1, n_estimators = 57, max_depth = 2)\n", + "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", + " objective = \"binary:logistic\",\n", + " eval_metric = \"logloss\",\n", + " eta = 0.1, n_estimators = 10,\n", + " max_depth = 3)\n", + "\n", + "# Initialize DoubleMLPLR model\n", + "np.random.seed(1234)\n", + "dml_plr_boost = dml.DoubleMLPLR(data_dml,\n", + " ml_g = boost,\n", + " ml_m = boost_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_boost.fit(store_predictions=True)\n", + "\n", + "boost_summary = dml_plr_boost.summary\n", + "boost_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "id": "6e3252f8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.02383965]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_plr_boost.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "id": "e90a61cc", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_boost_plr = pred_acc_plr(dml_plr_boost, prop=False)\n", + "rmse_main_boost_plr_mean = np.mean(rmse_main_boost_plr)\n", + "rmse_main_boost_plr_std = np.std(rmse_main_boost_plr)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_boost_plr = pred_acc_plr(dml_plr_boost, prop=True)\n", + "logloss_prop_boost_plr_mean = np.mean(logloss_prop_boost_plr)\n", + "logloss_prop_boost_plr_std = np.std(logloss_prop_boost_plr)" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "id": "72121d00", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.1560362080432272\n", + "Standard deviation of RMSE is 0.0027129250049691073\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_boost_plr_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_boost_plr_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "id": "8513cd4e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.677578683851663\n", + "Standard deviation of log loss is 0.005774390874769318\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_boost_plr_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_boost_plr_std)" + ] + }, + { + "cell_type": "markdown", + "id": "a979a78b", + "metadata": {}, + "source": [ + "#### PLR - Summary of coefficient estimates" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "id": "dba8d33c", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefBias2.5 %97.5 %
regression0.785-0.0150.6530.917
lasso0.8050.0050.6670.943
forest0.799-0.0010.6560.943
xgboost0.8240.0240.6830.964
\n", + "
" + ], + "text/plain": [ + " coef Bias 2.5 % 97.5 %\n", + "regression 0.785 -0.015 0.653 0.917\n", + "lasso 0.805 0.005 0.667 0.943\n", + "forest 0.799 -0.001 0.656 0.943\n", + "xgboost 0.824 0.024 0.683 0.964" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plr_summary = pd.concat((reg_summary, lasso_summary, forest_summary, boost_summary))\n", + "plr_summary.index = ['regression','lasso', 'forest', 'xgboost']\n", + "plr_summary = plr_summary[['coef', '2.5 %', '97.5 %']]\n", + "plr_summary.insert(1, \"Bias\", [plr_summary.loc['regression','coef'] - 0.8, \n", + " plr_summary.loc['lasso','coef'] - 0.8, \n", + " plr_summary.loc['forest','coef'] - 0.8, \n", + " plr_summary.loc['xgboost','coef'] - 0.8])\n", + "plr_summary.round(3) " + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "id": "86fe5d87", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "errors = np.full((2, plr_summary.shape[0]), np.nan)\n", + "errors[0, :] = plr_summary['coef'] - plr_summary['2.5 %']\n", + "errors[1, :] = plr_summary['97.5 %'] - plr_summary['coef']\n", + "plt.errorbar(plr_summary.index, plr_summary.coef, fmt='o', yerr=errors)\n", + "plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", + "\n", + "plt.title('Partially Linear Regression Model (PLR)')\n", + "plt.xlabel('ML method')\n", + "_ = plt.ylabel('Coefficients and 95%-CI')" + ] + }, + { + "cell_type": "markdown", + "id": "19fc42af", + "metadata": {}, + "source": [ + "#### PLR - Summary of prediction accuracy metric's mean values" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "id": "b8937548", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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main RMSEmain RMSE (sd)prop log lossprop log loss (sd)
regression1.3420.0101.0230.028
lasso1.1390.0030.6690.003
forest1.1890.0060.6840.005
xgboost1.1560.0030.6780.006
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" + ], + "text/plain": [ + " main RMSE main RMSE (sd) prop log loss prop log loss (sd)\n", + "regression 1.342 0.010 1.023 0.028\n", + "lasso 1.139 0.003 0.669 0.003\n", + "forest 1.189 0.006 0.684 0.005\n", + "xgboost 1.156 0.003 0.678 0.006" + ] + }, + "execution_count": 66, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plr_rmse_index = ['regression','lasso', 'forest', 'xgboost']\n", + "plr_rmse = pd.DataFrame([[rmse_main_linlog_plr_mean, rmse_main_linlog_plr_std, \n", + " logloss_prop_linlog_plr_mean, logloss_prop_linlog_plr_std],\n", + " [rmse_main_lasso_plr_mean, rmse_main_lasso_plr_std,\n", + " logloss_prop_lasso_plr_mean, logloss_prop_lasso_plr_std],\n", + " [rmse_main_forest_plr_mean, rmse_main_forest_plr_std,\n", + " logloss_prop_forest_plr_mean, logloss_prop_forest_plr_std],\n", + " [rmse_main_boost_plr_mean, rmse_main_boost_plr_std,\n", + " logloss_prop_boost_plr_mean, logloss_prop_boost_plr_std]],\n", + " index=plr_rmse_index,\n", + " columns=['main RMSE', 'main RMSE (sd)',\n", + " 'prop log loss', 'prop log loss (sd)'])\n", + "plr_rmse.round(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "id": "79fe38ed", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# graphical illustration of RMSE for main regression\n", + "errors_plr_rmse = np.full((2, plr_rmse.shape[0]), np.nan)\n", + "errors_plr_rmse[0, :] = plr_rmse['main RMSE'] - plr_rmse['main RMSE (sd)']\n", + "errors_plr_rmse[1, :] = plr_rmse['main RMSE'] + plr_rmse['main RMSE (sd)']\n", + "plt.errorbar(x=plr_rmse.index, y=plr_rmse['main RMSE'], fmt='x',\n", + " yerr=errors_plr_rmse, c='darkslategray')" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "id": "bb40406b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# graphical illustration of log loss for main regression\n", + "errors_plr_logloss = np.full((2, plr_rmse.shape[0]), np.nan)\n", + "errors_plr_logloss[0, :] = plr_rmse['prop log loss'] - plr_rmse['prop log loss (sd)']\n", + "errors_plr_logloss[1, :] = plr_rmse['prop log loss'] + plr_rmse['prop log loss (sd)']\n", + "plt.errorbar(x=plr_rmse.index, y=plr_rmse['prop log loss'], fmt='x',\n", + " yerr=errors_plr_logloss, c='darkslategray')" + ] + }, + { + "cell_type": "markdown", + "id": "27d1d2a9-beed-493d-ae92-8d4e92cde8ae", + "metadata": {}, + "source": [ + "### Summary of IRM and PLR Results" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "id": "1b4ddf50-50de-4bab-a110-767b8d50df21", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefBias2.5 %97.5 %
ModelML
IRMregression1.0580.258-0.1672.282
lasso0.8560.0560.7170.995
forest0.8930.0930.7411.045
xgboost0.791-0.0090.5860.995
PLRregression0.785-0.0150.6530.917
lasso0.8050.0050.6670.943
forest0.799-0.0010.6560.943
xgboost0.8240.0240.6830.964
\n", + "
" + ], + "text/plain": [ + " coef Bias 2.5 % 97.5 %\n", + "Model ML \n", + "IRM regression 1.058 0.258 -0.167 2.282\n", + " lasso 0.856 0.056 0.717 0.995\n", + " forest 0.893 0.093 0.741 1.045\n", + " xgboost 0.791 -0.009 0.586 0.995\n", + "PLR regression 0.785 -0.015 0.653 0.917\n", + " lasso 0.805 0.005 0.667 0.943\n", + " forest 0.799 -0.001 0.656 0.943\n", + " xgboost 0.824 0.024 0.683 0.964" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df_summary = pd.concat((irm_summary,plr_summary)).reset_index().rename(columns={'index': 'ML'})\n", + "df_summary['Model'] = np.concatenate((np.repeat('IRM', 4), np.repeat('PLR', 4)))\n", + "df_summary.set_index(['Model', 'ML']).round(3)" + ] + }, + { + "cell_type": "markdown", + "id": "64aa3065-da5c-49b9-88f2-5c08c1b7e617", + "metadata": {}, + "source": [ + "### Conclusion\n", + "\n", + "As in the IRM model, the ML-based PLR models are associated with a smaller bias as compared to the model that is based on linear and logistic regression. It seems that the estimates obtained from the PLR are slightly closer to the true ATE than those from the IRM analysis. This might suggest, that the parametric assumptions (i.e., an additive and homogeneous causal effect) that are incorporated in the PLR turn out to be **not restrictive** in our example data set. However, if both models are based on appropriate ML learners, the conclusions are very similar. In all cases, the ML-based estimates were very close to the true ATE and we were always able to reject the null hypothesis of a zero effect at all common significance levels. In terms of the A/B testing example, it can be concluded that the new ad increases customers purchases (in $100\\$$) by around 0.8 on average and that this effect is significantly different from zero at the 5% significance level. The results are summarized in the graphic below." + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "id": "c80cadcc", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(8, 9))\n", + "colors = sns.color_palette()\n", + "for ind, model in enumerate(['IRM', 'PLR']):\n", + " sns.set(font_scale=1.15)\n", + " plt.subplot(3, 1, ind+1)\n", + " this_df = df_summary.query('Model == @model')\n", + " errors = np.full((2, this_df.shape[0]), np.nan)\n", + " errors[0, :] = this_df['coef'] - this_df['2.5 %']\n", + " errors[1, :] = this_df['97.5 %'] - this_df['coef']\n", + " plt.errorbar(this_df.ML, this_df.coef, fmt='o', yerr=errors,\n", + " color=colors[ind], ecolor=colors[ind])\n", + " plt.ylim([0.5, 1.2])\n", + " plt.title(model)\n", + " plt.ylabel('Coeff. and 95%-CI')\n", + " plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", + " plt.legend(bbox_to_anchor=(1.04,0.5), loc=\"best\", borderaxespad=0)\n", + "\n", + "_ = plt.xlabel('ML method')" + ] + }, + { + "cell_type": "markdown", + "id": "90109d08", + "metadata": {}, + "source": [ + "## Appendix" + ] + }, + { + "cell_type": "markdown", + "id": "e42903ad", + "metadata": {}, + "source": [ + "### Propensity score estimates" + ] + }, + { + "cell_type": "markdown", + "id": "157d7295", + "metadata": {}, + "source": [ + "For both the IRM and the PLR model, we want to compare the propensity score estimates of all learners. Since repeated sample splitting is used for every learner, we first want to check whether the repetitions provide similare propensity score estimates. If that is the case, it should be legitimate to pick any of the repetitions for the comparision across all learners." + ] + }, + { + "cell_type": "markdown", + "id": "bb614dd1", + "metadata": {}, + "source": [ + "#### IRM - Repetitions of the Linear and Logistic regression model" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "id": "a2a753a7", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_irm_regression)" + ] + }, + { + "cell_type": "markdown", + "id": "d0eca3c9", + "metadata": {}, + "source": [ + "#### IRM - Repetitions of the Lasso model" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "id": "a69be1ca", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_irm_lasso)" + ] + }, + { + "cell_type": "markdown", + "id": "6ae81d8d", + "metadata": {}, + "source": [ + "#### IRM - Repetitions of the Random Forest model" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "id": "2775a78e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "h = dml_irm_regression.predictions.get('ml_m').shape[0]\n", + "fig, ax = plt.subplots(1, 4, figsize=(20,4.8))\n", + "\n", + "#regression histogram\n", + "ax[0].hist(np.reshape(dml_irm_regression.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[0].set_title('regression')\n", + "ax[0].set_xlabel(\"prop_score\")\n", + "ax[0].set_ylabel(\"density\")\n", + "\n", + "#lasso histogram\n", + "ax[1].hist(np.reshape(dml_irm_lasso.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[1].set_title('lasso')\n", + "ax[1].set_xlabel(\"prop_score\")\n", + "ax[1].set_ylabel(\"density\")\n", + "\n", + "#random forest histogram\n", + "ax[2].hist(np.reshape(dml_irm_forest.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[2].set_title('random forest')\n", + "ax[2].set_xlabel(\"prop_score\")\n", + "ax[2].set_ylabel(\"density\")\n", + "\n", + "#boosting histogram\n", + "ax[3].hist(np.reshape(dml_irm_boost.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[3].set_title('xgboost')\n", + "ax[3].set_xlabel(\"prop_score\")\n", + "ax[3].set_ylabel(\"density\")\n", + " \n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "7a9a161d", + "metadata": {}, + "source": [ + "#### PLR - Repetitions of the Linear and Logistic regression model" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "id": "c4da298e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_plr_regression)" + ] + }, + { + "cell_type": "markdown", + "id": "fbbbd43c", + "metadata": {}, + "source": [ + "#### PLR - Repetitions of the Lasso model" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "id": "17b9d772", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_plr_lasso)" + ] + }, + { + "cell_type": "markdown", + "id": "768dabe2", + "metadata": {}, + "source": [ + "#### PLR - Repetitions of the Random Forest model" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "id": "7639ef46", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_plr_forest)" + ] + }, + { + "cell_type": "markdown", + "id": "99539929", + "metadata": {}, + "source": [ + "#### PLR - Repetitions of the Extreme Gradient Boosting model" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "id": "da73a9b4", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_plr_boost)" + ] + }, + { + "cell_type": "markdown", + "id": "70375158", + "metadata": {}, + "source": [ + "#### PLR - Propensity score estimates across learners" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "id": "1aeded78", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "h = dml_plr_regression.predictions.get('ml_m').shape[0]\n", + "fig, ax = plt.subplots(1, 4, figsize=(20,4.8))\n", + "\n", + "#regression histogram\n", + "ax[0].hist(np.reshape(dml_plr_regression.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[0].set_title('regression')\n", + "ax[0].set_xlabel(\"prop_score\")\n", + "ax[0].set_ylabel(\"density\")\n", + "\n", + "#lasso histogram\n", + "ax[1].hist(np.reshape(dml_plr_lasso.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[1].set_title('lasso')\n", + "ax[1].set_xlabel(\"prop_score\")\n", + "ax[1].set_ylabel(\"density\")\n", + "\n", + "#random forest histogram\n", + "ax[2].hist(np.reshape(dml_plr_forest.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[2].set_title('random forest')\n", + "ax[2].set_xlabel(\"prop_score\")\n", + "ax[2].set_ylabel(\"density\")\n", + "\n", + "#boosting histogram\n", + "ax[3].hist(np.reshape(dml_plr_boost.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[3].set_title('xgboost')\n", + "ax[3].set_xlabel(\"prop_score\")\n", + "ax[3].set_ylabel(\"density\")\n", + " \n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "3aa8d603-0df5-48c6-ad62-ac5ffe3e8ada", + "metadata": {}, + "source": [ + "______\n", + "\n", + "**Notes and Acknowledgement**\n", + "\n", + "We would like to thank the organizers of the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge) for setting up this data challenge and making the numerous synthetic data examples publicly available. Although the data examples in the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge) do not explicitly adress A/B testing, we put the data example here in this context to give a tractable example on the use of causal machine learning in practice. The parameters for the random forests and extreme gradient boosting learners have been tuned externally. The corresponding tuning notebook will be uploaded in the examples gallery in the future." + ] + }, + { + "cell_type": "markdown", + "id": "egyptian-platform", + "metadata": {}, + "source": [ + "## References\n", + "\n", + "Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W. and Robins, J. (2018), Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21: C1-C68. doi:10.1111/ectj.12097." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/doc/examples/py_double_ml_abtest_tuning.ipynb b/doc/examples/py_double_ml_abtest_tuning.ipynb new file mode 100644 index 00000000..332ba090 --- /dev/null +++ b/doc/examples/py_double_ml_abtest_tuning.ipynb @@ -0,0 +1,1931 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "copyrighted-berry", + "metadata": { + "papermill": { + "duration": 0.02998, + "end_time": "2021-05-26T10:02:06.433929", + "exception": false, + "start_time": "2021-05-26T10:02:06.403949", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Tuning Parameters for Python A/B Testing with DoubleML" + ] + }, + { + "cell_type": "markdown", + "id": "exciting-march", + "metadata": { + "papermill": { + "duration": 0.028056, + "end_time": "2021-05-26T10:02:06.564012", + "exception": false, + "start_time": "2021-05-26T10:02:06.535956", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "Here, we illustrate how to tune the parameters of lasso, random forest and gradient boosting. The results are the same as in the A/B Test Main notebook [TODO: Insert link]. The baseline learner linear regression requires no tuning and is therefore not included in this notebook.\n", + "\n", + "Tuning in [DoubleML](https://docs.doubleml.org/stable/index.html) builds upon the functionalities of the Python package scikit learn. The hyperparameter-tuning is performed using either an exhaustive search over specified parameter values implemented in [sklearn.model_selection.GridSearchCV](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.RandomizedSearchCV.html) or via a randomized search implemented in [sklearn.model_selection.RandomizedSearchCV](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html).\n", + "\n", + "We will perform parameter tuning in the A/B Case Study example based on the models:\n", + "\n", + "* Partially linear regression (PLR)\n", + "* Interactive regression model (IRM)\n", + "\n", + "for\n", + "* logistic regression ([LogisticRegressionCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegressionCV.html)),\n", + "* lasso ([LassoCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html)),\n", + "* random forests ([RandomForestRegressor](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html)),\n", + "* extreme gradient boosting ([XGBRegressor/XGBClassifier](https://xgboost.readthedocs.io/en/latest/python/python_api.html)). " + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "grave-marking", + "metadata": { + "papermill": { + "duration": 0.546507, + "end_time": "2021-05-26T10:02:07.138982", + "exception": false, + "start_time": "2021-05-26T10:02:06.592475", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "import pandas as pd\n", + "df = pd.read_csv('data/high42.csv', sep=',', na_values=\".\")\n", + "\n", + "#code can also be loaded using a URL of the data\n", + "#url = 'https://raw.githubusercontent.com/DoubleML/doubleml-hiwi-sandbox/master/case_studies/AB_testing/data/high42.CSV?token=AQWGKQUK2PJ4ANBW5GFDG2LAY5ZN4'\n", + "#df = pd.read_csv(url)" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "linear-period", + "metadata": { + "papermill": { + "duration": 7.12797, + "end_time": "2021-05-26T10:02:14.295968", + "exception": false, + "start_time": "2021-05-26T10:02:07.167998", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "#pip install -U DoubleML" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "sonic-disclaimer", + "metadata": { + "papermill": { + "duration": 1.50983, + "end_time": "2021-05-26T10:02:15.836637", + "exception": false, + "start_time": "2021-05-26T10:02:14.326807", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import doubleml as dml\n", + "\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "\n", + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.linear_model import LogisticRegression\n", + "\n", + "from sklearn.linear_model import LassoCV, LogisticRegressionCV\n", + "from sklearn.ensemble import RandomForestClassifier, RandomForestRegressor\n", + "from sklearn.preprocessing import StandardScaler\n", + "from sklearn.pipeline import make_pipeline\n", + "\n", + "from xgboost import XGBClassifier, XGBRegressor\n", + "\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "9ad48b2f-db15-4002-ade7-4fbd5d3666d0", + "metadata": {}, + "source": [ + "### The Data Backend: `DoubleMLData`" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "economic-chicken", + "metadata": { + "papermill": { + "duration": 0.066803, + "end_time": "2021-05-26T10:02:15.993192", + "exception": false, + "start_time": "2021-05-26T10:02:15.926389", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# Set up basic model: Specify variables for data-backend\n", + "features_base = list(df.columns.values)[2:]\n", + "\n", + "# Initialize DoubleMLData (data-backend of DoubleML)\n", + "data_dml_base = dml.DoubleMLData(df,\n", + " y_col='Y',\n", + " d_cols='A',\n", + " x_cols=features_base)\n", + "\n", + "#print(data_dml_base)" + ] + }, + { + "cell_type": "markdown", + "id": "960d19cb-1db9-4a68-9be1-9b8194f1bbb9", + "metadata": {}, + "source": [ + "## 1. Tuning: Interactive Regression Model (IRM)\n", + "### Lasso\n", + "\n", + "We start our tuning exercise with the interactive regression model with the nuisance parts being estimated by lasso. In a first step we set up our learners based on the [sklearn.linear_model](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.linear_model) package. Here, we don't have to specify parameters. In a second step we initalize our model object, here we use the class [DoubleMLIRM](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLIRM.html). We specify the linear model [LassoCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html#sklearn.linear_model.LassoCV) in a pipeline with a standard scaler applied. \n", + "\n", + "For the lasso regression we set 5 folds of cross validation and the maximum number of iterations to 10000. [LogisticRegressionCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegressionCV.html) with L1 penalty is a lassso classifier. A liblinear `solver` is chosen, which is specifically good for small datasets. A grid of `Cs`, which control the strength of regularization, is created that ranges from 0 to 1. The best `C` is selected by the cross-validation, defined by the `cv` parameter. Note that if we don't specify any parameters for the learners, default values are used.\n", + "\n", + "Using the assigned learners, we initialize the `DoubleMLIRM` model." + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "c383b584-7011-4469-87fa-3eb2fd742850", + "metadata": { + "papermill": { + "duration": 8.853437, + "end_time": "2021-05-26T10:04:04.449701", + "exception": false, + "start_time": "2021-05-26T10:03:55.596264", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# Lasso\n", + "Cs = 0.0001*np.logspace(0, 4, 10) \n", + "lasso = make_pipeline(StandardScaler(), LassoCV(cv=5, max_iter=10000)) \n", + "\n", + "lasso_class = make_pipeline(StandardScaler(), LogisticRegressionCV(cv=5, penalty='l1', solver='liblinear', \n", + " Cs = Cs, max_iter=1000)) \n", + "\n", + "\n", + "# Initialize DoubleMLIRM model\n", + "np.random.seed(123)\n", + "\n", + "dml_irm_lasso = dml.DoubleMLIRM(data_dml_base,\n", + " ml_g = lasso,\n", + " ml_m = lasso_class,\n", + " trimming_threshold = 0.025, \n", + " n_folds = 3)" + ] + }, + { + "cell_type": "markdown", + "id": "21b99548-3e20-47fb-98f5-4edf174a64f3", + "metadata": { + "papermill": { + "duration": 0.031063, + "end_time": "2021-05-26T10:02:16.524653", + "exception": false, + "start_time": "2021-05-26T10:02:16.493590", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "When one doesn't know, which hyperparameters to set when assigning the learner, trying different parameters or tuning is necessery.\n", + "\n", + "### 1. Parameters to Tune\n", + "\n", + "All parameters of a learner can be accessed via a the field [.get_params()](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLPLR.html#doubleml.DoubleMLPLR.get_params). For example in the case of the [LassoCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html#sklearn.linear_model.LassoCV) the parameters that can tuned are:" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "bd39548f-3c2a-4763-bad7-f6096ddbc7e0", + "metadata": { + "papermill": { + "duration": 0.041091, + "end_time": "2021-05-26T10:02:16.597951", + "exception": false, + "start_time": "2021-05-26T10:02:16.556860", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "dict_keys(['memory', 'steps', 'verbose', 'standardscaler', 'lassocv', 'standardscaler__copy', 'standardscaler__with_mean', 'standardscaler__with_std', 'lassocv__alphas', 'lassocv__copy_X', 'lassocv__cv', 'lassocv__eps', 'lassocv__fit_intercept', 'lassocv__max_iter', 'lassocv__n_alphas', 'lassocv__n_jobs', 'lassocv__normalize', 'lassocv__positive', 'lassocv__precompute', 'lassocv__random_state', 'lassocv__selection', 'lassocv__tol', 'lassocv__verbose'])\n" + ] + } + ], + "source": [ + "print(lasso.get_params().keys())" + ] + }, + { + "cell_type": "markdown", + "id": "5fa3a099-fe24-487b-bfaf-0385439d6214", + "metadata": { + "papermill": { + "duration": 0.03054, + "end_time": "2021-05-26T10:02:16.659995", + "exception": false, + "start_time": "2021-05-26T10:02:16.629455", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### 2. Tuning Space" + ] + }, + { + "cell_type": "markdown", + "id": "0e583d7d-3683-47f0-9e78-23bb56956eb5", + "metadata": { + "papermill": { + "duration": 0.030255, + "end_time": "2021-05-26T10:02:16.721040", + "exception": false, + "start_time": "2021-05-26T10:02:16.690785", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "Now, we have to specify at least\n", + "\n", + "1. which parameters we would like to tune\n", + "2. the tuning space, i.e., a grid of values for these parameters, \n", + "\n", + "To specify the exact tuning set up in our example, we have to create objects that address points 1. and 2. These are then passed as arguments to the method [tune()](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLPLR.html#doubleml.DoubleMLPLR.tune). To pass the tuning space to the model object, we collect the tuning spaces for all nuisance parts in a named list. The names of the arguments must match the names of the nuisance components. Since tuning takes time the `tune()` method has been commented out. If you uncomment it, it will yield a `C` of $4$ to be the best regularization parameter. A random state of $0$ is assigned for replication." + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "19f95dae-0623-41eb-8787-ce0c532526e5", + "metadata": { + "papermill": { + "duration": 8.853437, + "end_time": "2021-05-26T10:04:04.449701", + "exception": false, + "start_time": "2021-05-26T10:03:55.596264", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "tuning_space_ml_g = {} #no tuning here (empty grid)\n", + "tuning_space_ml_m = {\n", + " 'logisticregressioncv__Cs' : np.logspace(0.001, 1, 20, dtype =int),\n", + " 'logisticregressioncv__random_state' : [0]\n", + " }\n", + "\n", + "tuning_spaces = ({\"ml_g\" : tuning_space_ml_g, \n", + " \"ml_m\" : tuning_space_ml_m})\n", + "\n", + "#to tune lasso, uncomment next two lines\n", + "#dml_irm_lasso.tune(tuning_spaces, search_mode = 'randomized_search', tune_on_folds = True,\n", + "# n_folds_tune=3, n_iter_randomized_search = 50, set_as_params = True, n_jobs_cv = -1)" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "dff114cc-6bbd-4ee4-9f9a-88c8f77cd36f", + "metadata": { + "papermill": { + "duration": 8.853437, + "end_time": "2021-05-26T10:04:04.449701", + "exception": false, + "start_time": "2021-05-26T10:03:55.596264", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'A': [None]}\n", + "{'A': [None]}\n", + "{'A': [None]}\n" + ] + } + ], + "source": [ + "print(dml_irm_lasso.get_params('ml_g0'))\n", + "print(dml_irm_lasso.get_params('ml_g1'))\n", + "print(dml_irm_lasso.get_params('ml_m'))" + ] + }, + { + "cell_type": "markdown", + "id": "56e8c8fb-dc94-413c-bc43-7f016cf10e28", + "metadata": {}, + "source": [ + "Next, the best paramter of C is assigned using [.set_ml_nuisance_params](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLPLR.html#doubleml.DoubleMLPLR.set_ml_nuisance_params) method and the model is fit. If you notice only the parameter `C=4` is set for the nuisance fuctnion `ml_m`, while the parameters of the other functions (`mlg0` and `ml_g1`) are left to their defaults. The result of the estimate is the same as in the main notebook." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "9681a76b-1e3a-42ee-9b0e-f9e87762589e", + "metadata": { + "papermill": { + "duration": 8.853437, + "end_time": "2021-05-26T10:04:04.449701", + "exception": false, + "start_time": "2021-05-26T10:03:55.596264", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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To reduce the disproportionate impact of extreme propensity score weights in the interactive model, we trim the propensity scores, which are close to the bounds. The trimming threshold for the propensitiy scores is set to $0.025$ meaning that propensity score below $2.5%$ or abobe $97.5%$ are removed. This will remove some of the variance in the model, but will add bias back.\n", + "\n", + "A random forest regression and classifier are called." + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "id": "downtown-investor", + "metadata": { + "papermill": { + "duration": 0.041146, + "end_time": "2021-05-26T10:04:04.636144", + "exception": false, + "start_time": "2021-05-26T10:04:04.594998", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# Random Forest\n", + "randomForest = RandomForestRegressor()\n", + "randomForest_class = RandomForestClassifier()\n", + "\n", + "np.random.seed(123)\n", + "dml_irm_forest = dml.DoubleMLIRM(data_dml_base,\n", + " ml_g = randomForest,\n", + " ml_m = randomForest_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3)" + ] + }, + { + "cell_type": "markdown", + "id": "9921bb70-a994-4358-9114-c554f736b69c", + "metadata": {}, + "source": [ + "A tuning grid of parameters is created for the two learners. Uncommenting the [`.tune`](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLIRM.html?highlight=tune#doubleml.DoubleMLIRM.tune) method will begin the tuning, which can take more than an hour." + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "id": "automated-watershed", + "metadata": { + "papermill": { + "duration": 152.721269, + "end_time": "2021-05-26T10:06:37.391258", + "exception": false, + "start_time": "2021-05-26T10:04:04.669989", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "dict" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#RF Tuning \n", + "\n", + "tuning_space_ml_g = {\n", + " 'max_depth': [8, 10, 12, 15],\n", + "'max_features': ['auto', 'sqrt'],\n", + " 'min_samples_leaf': [1, 2, 4, 5],\n", + " 'min_samples_split': [4, 5, 6, 10],\n", + " 'n_estimators': [100, 200, 300, ]}\n", + "\n", + "tuning_space_ml_m = {\n", + " 'max_depth': [3, 5, 6, 7, 10],\n", + "'max_features': ['auto', 'sqrt'],\n", + " 'min_samples_leaf': [5, 6, 7, 8],\n", + " 'min_samples_split': [2, 3, 5],\n", + " 'n_estimators': [100, 200]}\n", + "\n", + "tuning_spaces = ({\"ml_g\" : tuning_space_ml_g, \n", + " \"ml_m\" : tuning_space_ml_m})\n", + "\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")\n", + "\n", + "type(tuning_spaces)\n", + "#dml_irm_forest.tune(tuning_spaces, search_mode = 'randomized_search', tune_on_folds = True,\n", + "# n_folds_tune=3, n_iter_randomized_search = 50, set_as_params = True, return_tune_res = True, n_jobs_cv = -1)" + ] + }, + { + "cell_type": "markdown", + "id": "05feed3c-abdd-4b19-9ac0-41d9e3b4a56c", + "metadata": {}, + "source": [ + "Using the [.get_params](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLIRM.html?highlight=get_params#doubleml.DoubleMLIRM.get_params) method the tuned parameters are printed, which are then hardcoded into [.set_ml_nuisance_params](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLPLR.html#doubleml.DoubleMLPLR.set_ml_nuisance_params) method. This way one does not have to wait for the tuning every time." + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "id": "convinced-effect", + "metadata": { + "papermill": { + "duration": 0.042846, + "end_time": "2021-05-26T10:06:37.468481", + "exception": false, + "start_time": "2021-05-26T10:06:37.425635", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'A': [None]}\n", + "{'A': [None]}\n", + "{'A': [None]}\n" + ] + } + ], + "source": [ + "print(dml_irm_forest.get_params('ml_g0'))\n", + "print(dml_irm_forest.get_params('ml_g1'))\n", + "print(dml_irm_forest.get_params('ml_m'))" + ] + }, + { + "cell_type": "markdown", + "id": "b5d0d2e7-d4be-47e7-925c-ea1b6893d269", + "metadata": {}, + "source": [ + "The results are the same as those in the main notebook." + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "id": "every-stack", + "metadata": { + "papermill": { + "duration": 13.713732, + "end_time": "2021-05-26T10:06:51.217700", + "exception": false, + "start_time": "2021-05-26T10:06:37.503968", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.86203 0.08229 10.475455 1.119983e-25 0.700743 1.023316" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#Set nuisance-part specific parameters\n", + "dml_irm_forest.set_ml_nuisance_params('ml_g0', 'A', {\n", + " 'max_features': 200, 'n_estimators': 250})\n", + "dml_irm_forest.set_ml_nuisance_params('ml_g1', 'A', {\n", + " 'max_features': 200, 'n_estimators': 250})\n", + "dml_irm_forest.set_ml_nuisance_params('ml_m', 'A', {\n", + " 'max_features': 200, 'n_estimators': 250})\n", + "\n", + "dml_irm_forest.fit(store_predictions=True) \n", + "forest_summary = dml_irm_forest.summary\n", + "\n", + "forest_summary" + ] + }, + { + "cell_type": "markdown", + "id": "preliminary-ladder", + "metadata": { + "papermill": { + "duration": 0.035057, + "end_time": "2021-05-26T10:06:51.519120", + "exception": false, + "start_time": "2021-05-26T10:06:51.484063", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Boosted Trees\n", + "\n", + "First we specify the learning task and the corresponding learning objective. The first nuiscance function is estimated using the `XGBRegressor` with objective option reg:squarederror, is a regression with squared loss. The default evaluation metric is the rmse. The second nuisance function is estimated by classification, hence the objective is binary:lorgistic with an evaluation metric logloss. Eta, which ranges $[0,1]$ is the step size shrinkage is used during update to prevent overfitting. Because our outpuv value is already numeric we set the label encoder to false. For further information see the documentation of [XGBoost](https://xgboost.readthedocs.io/en/latest/parameter.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "id": "touched-duration", + "metadata": { + "papermill": { + "duration": 0.044223, + "end_time": "2021-05-26T10:06:51.598881", + "exception": false, + "start_time": "2021-05-26T10:06:51.554658", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "boost = XGBRegressor(n_jobs=1, objective = \"reg:squarederror\")\n", + "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", + " objective = \"binary:logistic\", eval_metric = \"logloss\")\n", + "\n", + "np.random.seed(123)\n", + "dml_irm_boost = dml.DoubleMLIRM(data_dml_base,\n", + " ml_g = boost,\n", + " ml_m = boost_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3)" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "id": "domestic-belfast", + "metadata": { + "papermill": { + "duration": 0.042653, + "end_time": "2021-05-26T10:06:51.678474", + "exception": false, + "start_time": "2021-05-26T10:06:51.635821", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['ml_g0', 'ml_g1', 'ml_m']\n" + ] + } + ], + "source": [ + "print(dml_irm_boost.params_names)\n" + ] + }, + { + "cell_type": "markdown", + "id": "054d8a6d-e58f-444e-a2ce-b6de8590d123", + "metadata": {}, + "source": [ + "### Grid Search" + ] + }, + { + "cell_type": "markdown", + "id": "4dcdf726-db3a-4975-b452-5d383ce80582", + "metadata": {}, + "source": [ + "Similarly to the lasso and random forest the tuning for gradient boosting is done. Due to the smaller parameter grid, it only takes about 2 minutes to tune. The hardcoded parameters can be verified by uncommenting the `.tune` method and letting it run." + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "id": "50cebc31-f53b-45ea-90c3-184c002dfe31", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "dict" + ] + }, + "execution_count": 55, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#parameter space wide\n", + "\n", + "tuning_space_ml_g = {'n_estimators': [5,8,15,25,30, 40, 50], 'eta': [0.01,0.1,0.2,0,5]}\n", + "\n", + "tuning_space_ml_m = {'n_estimators': [5,8,15,25,30, 40, 50], 'eta': [0.01,0.1,0.2,0,5]}\n", + "\n", + "tuning_spaces = ({\"ml_g\" : tuning_space_ml_g, \n", + " \"ml_m\" : tuning_space_ml_m})\n", + "\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")\n", + "\n", + "type(tuning_spaces)\n", + "#dml_irm_boost.tune(tuning_spaces, search_mode = 'randomized_search', tune_on_folds = True,\n", + "# n_folds_tune=5, set_as_params = True, return_tune_res = False)" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "id": "2d9368b4-af15-4921-82ac-321ea78f56f7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'A': [None]}\n", + "{'A': [None]}\n", + "{'A': [None]}\n" + ] + } + ], + "source": [ + "print(dml_irm_boost.get_params('ml_g0'))\n", + "print(dml_irm_boost.get_params('ml_g1'))\n", + "print(dml_irm_boost.get_params('ml_m'))" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "id": "03b67303-08ee-458b-86dc-03b96664bee9", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#Set nuisance-part specific parameters\n", + "dml_irm_boost.set_ml_nuisance_params('ml_g0', 'A', {\n", + " 'n_estimators': 30, 'eta': 0.2})\n", + "dml_irm_boost.set_ml_nuisance_params('ml_g1', 'A', {\n", + " 'n_estimators': 30, 'eta': 0.2})\n", + "dml_irm_boost.set_ml_nuisance_params('ml_m', 'A', {\n", + " 'n_estimators': 15, 'eta': 0.2})" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "id": "published-haiti", + "metadata": { + "papermill": { + "duration": 1.624245, + "end_time": "2021-05-26T10:06:57.845803", + "exception": false, + "start_time": "2021-05-26T10:06:56.221558", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.739225 0.092511 7.990648 1.342310e-15 0.557906 0.920544" + ] + }, + "execution_count": 58, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dml_irm_boost.fit(store_predictions=True)\n", + "boost_summary = dml_irm_boost.summary\n", + "\n", + "boost_summary" + ] + }, + { + "cell_type": "markdown", + "id": "29edef0d-7e46-4004-8dab-ebebd92d0c6b", + "metadata": {}, + "source": [ + "### Summary Results\n", + "We define a small function which calculates the bias from the true parameter $0.8$." + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "id": "e3486038-6b28-4278-a661-072a528a1602", + "metadata": {}, + "outputs": [], + "source": [ + "def bias(x):\n", + " x=x - 0.8\n", + " x=round(abs(x),3)\n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "id": "touched-bristol", + "metadata": { + "papermill": { + "duration": 0.054738, + "end_time": "2021-05-26T10:06:57.937711", + "exception": false, + "start_time": "2021-05-26T10:06:57.882973", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefBias2.5 %97.5 %
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" + ], + "text/plain": [ + " coef Bias 2.5 % 97.5 %\n", + "lasso 0.834 0.034 0.696 0.972\n", + "forest 0.862 0.062 0.701 1.023\n", + "xgboost 0.739 0.061 0.558 0.921" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "irm_summary = pd.concat((lasso_summary, forest_summary, boost_summary))\n", + "irm_summary.index = ['lasso', 'forest', 'xgboost']\n", + "\n", + "irm_summary.insert(1, \"Bias\", [bias(irm_summary.loc['lasso','coef']), \n", + " bias(irm_summary.loc['forest','coef']), \n", + " bias(irm_summary.loc['xgboost','coef'])])\n", + "\n", + "irm_summary[['coef', 'Bias', '2.5 %', '97.5 %']].round(3)" + ] + }, + { + "cell_type": "markdown", + "id": "fc7c0d5e-e824-48c1-8427-60416601e330", + "metadata": { + "papermill": { + "duration": 0.030715, + "end_time": "2021-05-26T10:02:16.264183", + "exception": false, + "start_time": "2021-05-26T10:02:16.233468", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## 2. Tuning: Partial Linear Regression Model\n", + "\n", + "### Lasso\n", + "\n", + "The lasso tuning from above problem works quite well, therefore it was unchanged." + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "id": "524baf7e-978d-452e-b38f-1e91c6004f74", + "metadata": { + "papermill": { + "duration": 0.044535, + "end_time": "2021-05-26T10:02:16.462934", + "exception": false, + "start_time": "2021-05-26T10:02:16.418399", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 61, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#PLR\n", + "from sklearn.linear_model import Lasso\n", + "\n", + "#is pipeline bc. there is scaling applied before\n", + "lasso = make_pipeline(StandardScaler(), LassoCV(cv=5, max_iter=10000)) #lasso is only for regression (not for classification)\n", + "\n", + "lasso_class = make_pipeline(StandardScaler(),\n", + " LogisticRegressionCV(cv=5, penalty='l1', solver='liblinear', #logistic reg with l1 penalty is a lassso classifier\n", + " max_iter=1000)) #liblinear solver for small datasets\n", + "\n", + "np.random.seed(123)\n", + "# Initialize DoubleMLPLR model\n", + "dml_plr_lasso = dml.DoubleMLPLR(data_dml_base,\n", + " ml_g = lasso,\n", + " ml_m = lasso_class,\n", + " n_folds = 3)\n", + "\n", + "dml_plr_lasso" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "id": "5bda9cf2-d2dc-4e9a-a29c-51fec8ada893", + "metadata": { + "papermill": { + "duration": 48.914961, + "end_time": "2021-05-26T10:03:05.666964", + "exception": false, + "start_time": "2021-05-26T10:02:16.752003", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.784574 0.070414 11.14235 7.803312e-29 0.646566 0.922582" + ] + }, + "execution_count": 63, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dml_plr_lasso.fit(store_predictions=True)\n", + "lasso_summary = dml_plr_lasso.summary\n", + "\n", + "lasso_summary" + ] + }, + { + "cell_type": "markdown", + "id": "c6fef8ee-7283-4ec4-9f75-228c512e713e", + "metadata": { + "papermill": { + "duration": 0.04306, + "end_time": "2021-05-26T10:03:09.220743", + "exception": false, + "start_time": "2021-05-26T10:03:09.177683", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "The coefficient estimated with lasso is the same as in the main notebook [TODO:insert link of main notebook]." + ] + }, + { + "cell_type": "markdown", + "id": "ff1daf63-a0b5-4b25-8401-4240c92b82cf", + "metadata": { + "papermill": { + "duration": 0.032194, + "end_time": "2021-05-26T10:03:09.284890", + "exception": false, + "start_time": "2021-05-26T10:03:09.252696", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Random Forest" + ] + }, + { + "cell_type": "markdown", + "id": "5884e36c-3e4d-4cfd-8011-96b3b02612db", + "metadata": {}, + "source": [ + "In this case we use the random forest defaults which perform quite well. Therefore no tuning grid is provided." + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "id": "95c1f2ae-e9dd-4bf4-b1cc-b163b0f1e761", + "metadata": { + "papermill": { + "duration": 0.040901, + "end_time": "2021-05-26T10:03:09.357683", + "exception": false, + "start_time": "2021-05-26T10:03:09.316782", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "randomForest = RandomForestRegressor()\n", + "randomForest_class = RandomForestClassifier()\n", + "\n", + "np.random.seed(123)\n", + "dml_plr_forest = dml.DoubleMLPLR(data_dml_base,\n", + " ml_g = randomForest,\n", + " ml_m = randomForest_class,\n", + " n_folds = 3,\n", + " n_rep=3)" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "id": "82241056-5645-409e-961d-6450cc34e8fe", + "metadata": { + "papermill": { + "duration": 43.429064, + "end_time": "2021-05-26T10:03:53.091617", + "exception": false, + "start_time": "2021-05-26T10:03:09.662553", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.823899 0.073474 11.213529 3.499555e-29 0.679893 0.967904" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dml_plr_forest.fit(store_predictions=True)\n", + "forest_summary = dml_plr_forest.summary\n", + "\n", + "forest_summary" + ] + }, + { + "cell_type": "markdown", + "id": "f5dcd940-e798-4e5f-b867-b33f921b1809", + "metadata": { + "papermill": { + "duration": 0.031748, + "end_time": "2021-05-26T10:03:53.155272", + "exception": false, + "start_time": "2021-05-26T10:03:53.123524", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Bosting\n", + "\n", + "Hyperparameters are pre-set for the boosting learners. The squared error objective is appropriate for a regression learner and the binary:logistic with a log loss evaluation metric for a classifier." + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "id": "a0504319-cee1-42c3-8a44-c7a5f417d9de", + "metadata": { + "papermill": { + "duration": 0.039558, + "end_time": "2021-05-26T10:03:53.369239", + "exception": false, + "start_time": "2021-05-26T10:03:53.329681", + "status": "completed" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "boost = XGBRegressor(n_jobs=1, objective = \"reg:squarederror\",\n", + " eta=0.1)\n", + "\n", + "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", + " objective = \"binary:logistic\", eval_metric = \"logloss\",\n", + " eta=0.1)\n", + "\n", + "# Boosted Trees\n", + "\n", + "np.random.seed(123)\n", + "dml_plr_boost = dml.DoubleMLPLR(data_dml_base,\n", + " ml_g = boost,\n", + " ml_m = boost_class,\n", + " n_folds = 3)" + ] + }, + { + "cell_type": "markdown", + "id": "f49b5655-7425-46b9-b3c2-7eda01c0e86f", + "metadata": { + "papermill": { + "duration": 0.032229, + "end_time": "2021-05-26T10:03:53.505178", + "exception": false, + "start_time": "2021-05-26T10:03:53.472949", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "Bosting is not very good without tuning, therefore a grid of parameters is provided below. It was found using a randomized search, that `n_estimators` in range $55$ and $65$ provide good results. Therfore in the gird search below this range for `n_estimators` is used. Similarly for the $ml_m$ it was found that `n_estimators` between $1$ and $10$ perform well. This refined our search to a smaller range of hyperparameters. To tune, uncomment `dml_plr_boost.tune`." + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "id": "0e0fbdf2-230c-4b61-ba88-faa1a2ca1fba", + "metadata": { + "papermill": { + "duration": 0.041937, + "end_time": "2021-05-26T10:03:53.579534", + "exception": false, + "start_time": "2021-05-26T10:03:53.537597", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['ml_g', 'ml_m']\n", + "{'A': [None]}\n", + "{'A': [None]}\n" + ] + } + ], + "source": [ + "#tuning further parameters\n", + "\n", + "tuning_space_ml_g = {'n_estimators': np.linspace(55, 65, 5, dtype = int), 'max_depth': [2,3,4,6]}\n", + "\n", + "tuning_space_ml_m = {'n_estimators': np.linspace(1, 10, 5, dtype = int), 'max_depth': [2,3,4,6]}\n", + "\n", + "tuning_spaces = ({\"ml_g\" : tuning_space_ml_g, \n", + " \"ml_m\" : tuning_space_ml_m})\n", + "\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")\n", + "\n", + "type(tuning_spaces)\n", + "#dml_plr_boost.tune(tuning_spaces, search_mode = 'randomized_search')\n", + "\n", + "print(dml_plr_boost.params_names)\n", + "print(dml_plr_boost.get_params('ml_g'))\n", + "print(dml_plr_boost.get_params('ml_m'))" + ] + }, + { + "cell_type": "markdown", + "id": "aab368e4-f997-4764-9d12-c3a1eaf1de04", + "metadata": { + "papermill": { + "duration": 0.03227, + "end_time": "2021-05-26T10:03:53.644151", + "exception": false, + "start_time": "2021-05-26T10:03:53.611881", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "The results of the tuning will show that the best hyperparameters for $ml_g$ are `n_estimators: 57, max_depth: 2` and the best hyperparameters for $ml_m$ are `n_estimators: 10, max_depth: 3`. These parameters are hardcoded using the [`.set_ml_nuisance_params`](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLPLR.html#doubleml.DoubleMLPLR.set_ml_nuisance_params) method. " + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "id": "140830c6-2e1a-4ed5-b008-a9f2d00f4dfa", + "metadata": { + "papermill": { + "duration": 0.039799, + "end_time": "2021-05-26T10:03:53.716377", + "exception": false, + "start_time": "2021-05-26T10:03:53.676578", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dml_plr_boost.set_ml_nuisance_params('ml_g', 'A', { \n", + " 'n_estimators': 57, 'max_depth': 2})\n", + "dml_plr_boost.set_ml_nuisance_params('ml_m', 'A', { \n", + " 'n_estimators': 10, 'max_depth': 3}) " + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "id": "3972a161-0583-4b9c-b7cb-3a34129c7394", + "metadata": { + "papermill": { + "duration": 1.529645, + "end_time": "2021-05-26T10:03:55.279584", + "exception": false, + "start_time": "2021-05-26T10:03:53.749939", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefBias2.5 %97.5 %
lasso0.7850.0150.6470.923
forest0.8240.0240.6800.968
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" + ], + "text/plain": [ + " coef Bias 2.5 % 97.5 %\n", + "lasso 0.785 0.015 0.647 0.923\n", + "forest 0.824 0.024 0.680 0.968\n", + "xgboost 0.815 0.015 0.675 0.954" + ] + }, + "execution_count": 70, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plr_summary = pd.concat((lasso_summary, forest_summary, boost_summary))\n", + "plr_summary.index = ['lasso', 'forest', 'xgboost']\n", + "\n", + "plr_summary.insert(1, \"Bias\", [bias(plr_summary.loc['lasso','coef']), \n", + " bias(plr_summary.loc['forest','coef']), \n", + " bias(plr_summary.loc['xgboost','coef'])])\n", + "\n", + "plr_summary[['coef', 'Bias', '2.5 %', '97.5 %']].round(3)" + ] + }, + { + "cell_type": "markdown", + "id": "agricultural-holder", + "metadata": { + "papermill": { + "duration": 0.038336, + "end_time": "2021-05-26T10:06:58.015999", + "exception": false, + "start_time": "2021-05-26T10:06:57.977663", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Summary Results All Models\n", + "Regression results are left out because there is no tuning required." + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "id": "pediatric-subdivision", + "metadata": { + "papermill": { + "duration": 0.065362, + "end_time": "2021-05-26T10:06:58.120049", + "exception": false, + "start_time": "2021-05-26T10:06:58.054687", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " coef Bias 2.5 % 97.5 %\n", + "Model ML \n", + "IRM Tune lasso 0.834 0.034 0.696 0.972\n", + " forest 0.862 0.062 0.701 1.023\n", + " xgboost 0.739 0.061 0.558 0.921\n", + "PLR Tune lasso 0.785 0.015 0.647 0.923\n", + " forest 0.824 0.024 0.680 0.968\n", + " xgboost 0.815 0.015 0.675 0.954" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df_summary = pd.concat((irm_summary, plr_summary)).reset_index().rename(columns={'index': 'ML'})\n", + "df_summary['Model'] = np.concatenate((np.repeat('IRM Tune', 3), np.repeat('PLR Tune', 3)))\n", + "df_summary\n", + "\n", + "df_summary=df_summary[['ML', 'Model','coef', 'Bias', '2.5 %', '97.5 %']]\n", + "df_summary\n", + "df_summary.set_index(['Model', 'ML']).round(3)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.12" + }, + "papermill": { + "default_parameters": {}, + "duration": 299.684742, + "end_time": "2021-05-26T10:06:59.042230", + "environment_variables": {}, + "exception": null, + "input_path": "__notebook__.ipynb", + "output_path": "__notebook__.ipynb", + "parameters": {}, + "start_time": "2021-05-26T10:01:59.357488", + "version": "2.3.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 8cd7164012dd3e74ade1b1c5ead138c2b8ece976 Mon Sep 17 00:00:00 2001 From: JoshuaFalke <61840730+JoshuaFalke@users.noreply.github.com> Date: Fri, 20 May 2022 23:12:38 +0200 Subject: [PATCH 03/20] Add files via upload --- doc/examples/data/DGPs_and_Data.ipynb | 247 +++ doc/examples/data/DGPs_preprocessed.csv | 1601 ++++++++++++++++++ doc/examples/data/high1.CSV | 1001 ++++++++++++ doc/examples/data/high2.CSV | 2001 ++++++++++++++++++++++ doc/examples/data/high3.CSV | 1001 ++++++++++++ doc/examples/data/high42.CSV | 2002 +++++++++++------------ 6 files changed, 6852 insertions(+), 1001 deletions(-) create mode 100644 doc/examples/data/DGPs_and_Data.ipynb create mode 100644 doc/examples/data/DGPs_preprocessed.csv create mode 100644 doc/examples/data/high1.CSV create mode 100644 doc/examples/data/high2.CSV create mode 100644 doc/examples/data/high3.CSV diff --git a/doc/examples/data/DGPs_and_Data.ipynb b/doc/examples/data/DGPs_and_Data.ipynb new file mode 100644 index 00000000..1718bcbc --- /dev/null +++ b/doc/examples/data/DGPs_and_Data.ipynb @@ -0,0 +1,247 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "lasting-skirt", + "metadata": {}, + "source": [ + "# Description of Data Files" + ] + }, + { + "cell_type": "markdown", + "id": "operating-positive", + "metadata": {}, + "source": [ + "## DGPs, true ATE etc.\n", + "\n", + "\n", + "Load the prepocessed data frame which connects the DGP to the settings (different names and details like this) and the true average treatment effects. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "attached-sculpture", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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RenamedOriginalScenarioDS#Random seedfilenameDGPidtrueATE
0high1CHDScenario3DS86NaN30.337781high13-0.80000
1high10CHDScenario15DS13NaN150.218848high1015-0.16058
2high100CHDScenario3DS72NaN30.130252high1003-0.80000
3high1000CHDScenario1DS5050.010.425784high100010.20000
4high1001CHDScenario15DS20NaN150.307721high100115-0.16058
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" + ], + "text/plain": [ + " Renamed Original Scenario DS# Random seed filename DGPid \\\n", + "0 high1 CHDScenario3DS86 NaN 3 0.337781 high1 3 \n", + "1 high10 CHDScenario15DS13 NaN 15 0.218848 high10 15 \n", + "2 high100 CHDScenario3DS72 NaN 3 0.130252 high100 3 \n", + "3 high1000 CHDScenario1DS50 50.0 1 0.425784 high1000 1 \n", + "4 high1001 CHDScenario15DS20 NaN 15 0.307721 high1001 15 \n", + "\n", + " trueATE \n", + "0 -0.80000 \n", + "1 -0.16058 \n", + "2 -0.80000 \n", + "3 0.20000 \n", + "4 -0.16058 " + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas as pd\n", + "\n", + "dgps = pd.read_csv('DGPs_preprocessed.csv', sep=',', na_values=\".\")\n", + "dgps.head()" + ] + }, + { + "cell_type": "markdown", + "id": "distributed-testing", + "metadata": {}, + "source": [ + "Select the DGP with ID `42` - that's the one we use in the case study. " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "labeled-raising", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " Renamed Original Scenario DS# Random seed filename DGPid \\\n", + "957 high42 CHDScenario2DS24 124.0 2 0.752854 high42 2 \n", + "\n", + " trueATE \n", + "957 0.8 " + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dgps.loc[dgps.Renamed == 'high42']" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/doc/examples/data/DGPs_preprocessed.csv b/doc/examples/data/DGPs_preprocessed.csv new file mode 100644 index 00000000..cad39317 --- /dev/null +++ b/doc/examples/data/DGPs_preprocessed.csv @@ -0,0 +1,1601 @@ 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diff --git a/doc/examples/data/high42.CSV b/doc/examples/data/high42.CSV index 7e6e0941..e7f80a19 100644 --- a/doc/examples/data/high42.CSV +++ b/doc/examples/data/high42.CSV @@ -1,1001 +1,1001 @@ 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From d7263405ecb9d183286267d6f56dce51aa48650b Mon Sep 17 00:00:00 2001 From: JoshuaFalke <61840730+JoshuaFalke@users.noreply.github.com> Date: Fri, 20 May 2022 23:16:41 +0200 Subject: [PATCH 04/20] Create bla --- doc/examples/.ipynb_checkpoints/bla | 1 + 1 file changed, 1 insertion(+) create mode 100644 doc/examples/.ipynb_checkpoints/bla diff --git a/doc/examples/.ipynb_checkpoints/bla b/doc/examples/.ipynb_checkpoints/bla new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/doc/examples/.ipynb_checkpoints/bla @@ -0,0 +1 @@ + From 6e745dfa0b55d6e7967bd5446182d81e780032f1 Mon Sep 17 00:00:00 2001 From: JoshuaFalke <61840730+JoshuaFalke@users.noreply.github.com> Date: Fri, 20 May 2022 23:17:00 +0200 Subject: [PATCH 05/20] Add files via upload --- .../DGPs_and_Data-checkpoint.ipynb | 247 ++++++++++++++++++ 1 file changed, 247 insertions(+) create mode 100644 doc/examples/.ipynb_checkpoints/DGPs_and_Data-checkpoint.ipynb diff --git 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" + ], + "text/plain": [ + " Renamed Original Scenario DS# Random seed filename DGPid \\\n", + "0 high1 CHDScenario3DS86 NaN 3 0.337781 high1 3 \n", + "1 high10 CHDScenario15DS13 NaN 15 0.218848 high10 15 \n", + "2 high100 CHDScenario3DS72 NaN 3 0.130252 high100 3 \n", + "3 high1000 CHDScenario1DS50 50.0 1 0.425784 high1000 1 \n", + "4 high1001 CHDScenario15DS20 NaN 15 0.307721 high1001 15 \n", + "\n", + " trueATE \n", + "0 -0.80000 \n", + "1 -0.16058 \n", + "2 -0.80000 \n", + "3 0.20000 \n", + "4 -0.16058 " + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas as pd\n", + "\n", + "dgps = pd.read_csv('DGPs_preprocessed.csv', sep=',', na_values=\".\")\n", + "dgps.head()" + ] + }, + { + "cell_type": "markdown", + "id": "distributed-testing", + "metadata": {}, + "source": [ + "Select the DGP with ID `42` - that's the one we use in the case study. " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "labeled-raising", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " Renamed Original Scenario DS# Random seed filename DGPid \\\n", + "0 high1 CHDScenario3DS86 NaN 3 0.337781 high1 3 \n", + "1 high10 CHDScenario15DS13 NaN 15 0.218848 high10 15 \n", + "2 high100 CHDScenario3DS72 NaN 3 0.130252 high100 3 \n", + "3 high1000 CHDScenario1DS50 50.0 1 0.425784 high1000 1 \n", + "4 high1001 CHDScenario15DS20 NaN 15 0.307721 high1001 15 \n", + "\n", + " trueATE \n", + "0 -0.80000 \n", + "1 -0.16058 \n", + "2 -0.80000 \n", + "3 0.20000 \n", + "4 -0.16058 " + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas as pd\n", + "\n", + "dgps = pd.read_csv('DGPs_preprocessed.csv', sep=',', na_values=\".\")\n", + "dgps.head()" + ] + }, + { + "cell_type": "markdown", + "id": "distributed-testing", + "metadata": {}, + "source": [ + "Select the DGP with ID `42` - that's the one we use in the case study. " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "labeled-raising", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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1 file changed, 1 deletion(-) delete mode 100644 doc/examples/figures/sdf diff --git a/doc/examples/figures/sdf b/doc/examples/figures/sdf deleted file mode 100644 index 8b137891..00000000 --- a/doc/examples/figures/sdf +++ /dev/null @@ -1 +0,0 @@ - From 9832088f31752df52ddda9e1ca3331431d7c6c54 Mon Sep 17 00:00:00 2001 From: Philipp Bach Date: Wed, 1 Jun 2022 13:03:37 +0200 Subject: [PATCH 14/20] drop files that are not required --- .../DGPs_and_Data-checkpoint.ipynb | 247 - doc/examples/data/DGPs_and_Data.ipynb | 247 - doc/examples/data/DGPs_preprocessed.csv | 1601 ------- doc/examples/data/high1.CSV | 1001 ---- doc/examples/data/high2.CSV | 2001 -------- doc/examples/data/high3.CSV | 1001 ---- .../py_double_ml_abtest_no_split_linreg.ipynb | 4059 ----------------- doc/examples/py_double_ml_abtest_tuning.ipynb | 1931 -------- 8 files changed, 12088 deletions(-) delete mode 100644 doc/examples/data/.ipynb_checkpoints/DGPs_and_Data-checkpoint.ipynb delete mode 100644 doc/examples/data/DGPs_and_Data.ipynb delete mode 100644 doc/examples/data/DGPs_preprocessed.csv delete mode 100644 doc/examples/data/high1.CSV delete mode 100644 doc/examples/data/high2.CSV delete mode 100644 doc/examples/data/high3.CSV delete mode 100644 doc/examples/py_double_ml_abtest_no_split_linreg.ipynb delete mode 100644 doc/examples/py_double_ml_abtest_tuning.ipynb diff --git a/doc/examples/data/.ipynb_checkpoints/DGPs_and_Data-checkpoint.ipynb b/doc/examples/data/.ipynb_checkpoints/DGPs_and_Data-checkpoint.ipynb deleted file mode 100644 index 6d2a1a7e..00000000 --- a/doc/examples/data/.ipynb_checkpoints/DGPs_and_Data-checkpoint.ipynb +++ /dev/null @@ -1,247 +0,0 @@ -{ - 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" - ], - "text/plain": [ - " Renamed Original Scenario DS# Random seed filename DGPid \\\n", - "0 high1 CHDScenario3DS86 NaN 3 0.337781 high1 3 \n", - "1 high10 CHDScenario15DS13 NaN 15 0.218848 high10 15 \n", - "2 high100 CHDScenario3DS72 NaN 3 0.130252 high100 3 \n", - "3 high1000 CHDScenario1DS50 50.0 1 0.425784 high1000 1 \n", - "4 high1001 CHDScenario15DS20 NaN 15 0.307721 high1001 15 \n", - "\n", - " trueATE \n", - "0 -0.80000 \n", - "1 -0.16058 \n", - "2 -0.80000 \n", - "3 0.20000 \n", - "4 -0.16058 " - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import pandas as pd\n", - "\n", - "dgps = pd.read_csv('DGPs_preprocessed.csv', sep=',', na_values=\".\")\n", - "dgps.head()" - ] - }, - { - "cell_type": "markdown", - "id": "distributed-testing", - "metadata": {}, - "source": [ - "Select the DGP with ID `42` - that's the one we use in the case study. " - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "labeled-raising", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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RenamedOriginalScenarioDS#Random seedfilenameDGPidtrueATE
957high42CHDScenario2DS24124.020.752854high4220.8
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" - ], - "text/plain": [ - " Renamed Original Scenario DS# Random seed filename DGPid \\\n", - "957 high42 CHDScenario2DS24 124.0 2 0.752854 high42 2 \n", - "\n", - " trueATE \n", - "957 0.8 " - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "dgps.loc[dgps.Renamed == 'high42']" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.10" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/doc/examples/data/DGPs_preprocessed.csv b/doc/examples/data/DGPs_preprocessed.csv deleted file mode 100644 index cad39317..00000000 --- a/doc/examples/data/DGPs_preprocessed.csv +++ /dev/null @@ -1,1601 +0,0 @@ -Renamed,Original,Scenario,DS#,Random seed,filename,DGPid,trueATE -high1,CHDScenario3DS86,,3,0.337780775229441,high1,3,-0.800000000000001 -high10,CHDScenario15DS13,,15,0.218848277916799,high10,15,-0.16058 -high100,CHDScenario3DS72,,3,0.130251744231591,high100,3,-0.800000000000001 -high1000,CHDScenario1DS50,50,1,0.425784461576418,high1000,1,0.2 -high1001,CHDScenario15DS20,,15,0.307721358167384,high1001,15,-0.16058 -high1002,CHDScenario6DS1,,6,0.567807174304433,high1002,6,-1.1039 -high1003,CHDScenario6DS75,,6,0.407714658941775,high1003,6,-1.1039 -high1004,CHDScenario14DS13,,14,0.35351650646737,high1004,14,61.11 -high1005,CHDScenario6DS11,,6,0.974535436313897,high1005,6,-1.1039 -high1006,CHDScenario9DS42,,9,0.739619904174329,high1006,9,12.62 -high1007,CHDScenario16DS66,,16,0.81030013659789,high1007,16,1 -high1008,CHDScenario1DS15,15,1,0.150957145309245,high1008,1,0.2 -high1009,CHDScenario7DS81,,7,0.600630104769901,high1009,7,0 -high101,CHDScenario16DS78,,16,0.0819751007528389,high101,16,1 -high1010,CHDScenario11DS82,,11,0.596790355026503,high1010,11,10.77 -high1011,CHDScenario10DS22,,10,0.208092197688178,high1011,10,9.134 -high1012,CHDScenario14DS99,,14,0.529019939925166,high1012,14,61.11 -high1013,CHDScenario16DS99,,16,0.793425278419162,high1013,16,1 -high1014,CHDScenario15DS81,,15,0.531881183141435,high1014,15,-0.16058 -high1015,CHDScenario5DS61,,5,0.196632364989263,high1015,5,-0.3429 -high1016,CHDScenario11DS12,,11,0.547173382293564,high1016,11,10.77 -high1017,CHDScenario16DS37,,16,0.19481150600344,high1017,16,1 -high1018,CHDScenario14DS17,,14,0.0614804597967079,high1018,14,61.11 -high1019,CHDScenario2DS86,186,2,0.657445233311644,high1019,2,0.8 -high102,CHDScenario3DS77,,3,0.139950581900858,high102,3,-0.800000000000001 -high1020,CHDScenario8DS41,,8,0.423596592487275,high1020,8,-1.432 -high1021,CHDScenario8DS31,,8,0.77556617994587,high1021,8,-1.432 -high1022,CHDScenario2DS58,158,2,0.749658794020654,high1022,2,0.8 -high1023,CHDScenario10DS24,,10,0.995019899720868,high1023,10,9.134 -high1024,CHDScenario14DS18,,14,0.188195221787496,high1024,14,61.11 -high1025,CHDScenario12DS31,,12,0.602941530911272,high1025,12,-3.159 -high1026,CHDScenario2DS54,154,2,0.351513862310505,high1026,2,0.8 -high1027,CHDScenario3DS14,,3,0.00334679342425703,high1027,3,-0.800000000000001 -high1028,CHDScenario8DS71,,8,0.520155222935355,high1028,8,-1.432 -high1029,CHDScenario11DS81,,11,0.602313658756335,high1029,11,10.77 -high103,CHDScenario13DS14,,13,0.786665828924802,high103,13,-0.8486 -high1030,CHDScenario5DS42,,5,0.759698853876239,high1030,5,-0.3429 -high1031,CHDScenario10DS79,,10,0.0659304923632662,high1031,10,9.134 -high1032,CHDScenario2DS81,181,2,0.275789390060156,high1032,2,0.8 -high1033,CHDScenario13DS75,,13,0.601140307943352,high1033,13,-0.8486 -high1034,CHDScenario2DS32,132,2,0.458639775505428,high1034,2,0.8 -high1035,CHDScenario14DS77,,14,0.588795458648423,high1035,14,61.11 -high1036,CHDScenario7DS44,,7,0.196176577017585,high1036,7,0 -high1037,CHDScenario3DS98,,3,0.985152436724717,high1037,3,-0.800000000000001 -high1038,CHDScenario13DS82,,13,0.237837565618738,high1038,13,-0.8486 -high1039,CHDScenario9DS97,,9,0.368762205854095,high1039,9,12.62 -high104,CHDScenario13DS4,,13,0.834201618351954,high104,13,-0.8486 -high1040,CHDScenario10DS62,,10,0.0971558942871727,high1040,10,9.134 -high1041,CHDScenario2DS20,120,2,0.880671188613506,high1041,2,0.8 -high1042,CHDScenario13DS76,,13,0.343070824510479,high1042,13,-0.8486 -high1043,CHDScenario5DS4,,5,0.562298899844868,high1043,5,-0.3429 -high1044,CHDScenario11DS33,,11,0.372472084303859,high1044,11,10.77 -high1045,CHDScenario8DS89,,8,0.516207083198759,high1045,8,-1.432 -high1046,CHDScenario15DS8,,15,0.799908521604526,high1046,15,-0.16058 -high1047,CHDScenario15DS73,,15,0.392157010142749,high1047,15,-0.16058 -high1048,CHDScenario9DS30,,9,0.444761991474045,high1048,9,12.62 -high1049,CHDScenario1DS17,17,1,0.0267405343577791,high1049,1,0.2 -high105,CHDScenario6DS36,,6,0.485557869477313,high105,6,-1.1039 -high1050,CHDScenario12DS57,,12,0.0264439091361074,high1050,12,-3.159 -high1051,CHDScenario9DS89,,9,0.854885052752475,high1051,9,12.62 -high1052,CHDScenario11DS3,,11,0.00474626791412824,high1052,11,10.77 -high1053,CHDScenario2DS63,163,2,0.590456306646832,high1053,2,0.8 -high1054,CHDScenario2DS13,113,2,0.531816351878513,high1054,2,0.8 -high1055,CHDScenario4DS93,,4,0.0760829182031981,high1055,4,2.1 -high1056,CHDScenario5DS31,,5,0.288456838845424,high1056,5,-0.3429 -high1057,CHDScenario1DS88,88,1,0.863061914365436,high1057,1,0.2 -high1058,CHDScenario4DS60,,4,0.407171413879671,high1058,4,2.1 -high1059,CHDScenario13DS33,,13,0.576811256226918,high1059,13,-0.8486 -high106,CHDScenario4DS45,,4,0.243471850131124,high106,4,2.1 -high1060,CHDScenario15DS60,,15,0.176190762967908,high1060,15,-0.16058 -high1061,CHDScenario11DS58,,11,0.936449578724795,high1061,11,10.77 -high1062,CHDScenario3DS7,,3,0.92281738307664,high1062,3,-0.800000000000001 -high1063,CHDScenario7DS49,,7,0.0449384850110199,high1063,7,0 -high1064,CHDScenario8DS29,,8,0.268018180627513,high1064,8,-1.432 -high1065,CHDScenario14DS26,,14,0.417841379197451,high1065,14,61.11 -high1066,CHDScenario14DS10,,14,0.83473921981531,high1066,14,61.11 -high1067,CHDScenario3DS32,,3,0.432073951232472,high1067,3,-0.800000000000001 -high1068,CHDScenario14DS87,,14,0.303778562794149,high1068,14,61.11 -high1069,CHDScenario13DS40,,13,0.389522982078963,high1069,13,-0.8486 -high107,CHDScenario7DS52,,7,0.549481479173141,high107,7,0 -high1070,CHDScenario12DS68,,12,0.0512773027554598,high1070,12,-3.159 -high1071,CHDScenario5DS81,,5,0.0964741637675021,high1071,5,-0.3429 -high1072,CHDScenario8DS2,,8,0.874538260721674,high1072,8,-1.432 -high1073,CHDScenario12DS92,,12,0.655631560860177,high1073,12,-3.159 -high1074,CHDScenario16DS57,,16,0.783995858785501,high1074,16,1 -high1075,CHDScenario12DS55,,12,0.334586781107305,high1075,12,-3.159 -high1076,CHDScenario14DS49,,14,0.0663234744817743,high1076,14,61.11 -high1077,CHDScenario1DS13,13,1,0.452227974718498,high1077,1,0.2 -high1078,CHDScenario3DS21,,3,0.223384973971886,high1078,3,-0.800000000000001 -high1079,CHDScenario9DS33,,9,0.195589020778445,high1079,9,12.62 -high108,CHDScenario14DS27,,14,0.293104170151902,high108,14,61.11 -high1080,CHDScenario3DS95,,3,0.161849670600885,high1080,3,-0.800000000000001 -high1081,CHDScenario7DS24,,7,0.0519596034436654,high1081,7,0 -high1082,CHDScenario13DS61,,13,0.425271972411458,high1082,13,-0.8486 -high1083,CHDScenario13DS90,,13,0.988364691110728,high1083,13,-0.8486 -high1084,CHDScenario3DS10,,3,0.510386752091132,high1084,3,-0.800000000000001 -high1085,CHDScenario12DS33,,12,0.8291067510429,high1085,12,-3.159 -high1086,CHDScenario3DS89,,3,0.78835678850244,high1086,3,-0.800000000000001 -high1087,CHDScenario14DS11,,14,0.573387638554379,high1087,14,61.11 -high1088,CHDScenario11DS94,,11,0.601737282416136,high1088,11,10.77 -high1089,CHDScenario8DS79,,8,0.851480148188384,high1089,8,-1.432 -high109,CHDScenario13DS68,,13,0.107639444734679,high109,13,-0.8486 -high1090,CHDScenario1DS19,19,1,0.0314341254394519,high1090,1,0.2 -high1091,CHDScenario10DS45,,10,0.631859427768832,high1091,10,9.134 -high1092,CHDScenario11DS85,,11,0.721798772261927,high1092,11,10.77 -high1093,CHDScenario16DS15,,16,0.486299402100172,high1093,16,1 -high1094,CHDScenario5DS92,,5,0.720883325915072,high1094,5,-0.3429 -high1095,CHDScenario1DS40,40,1,0.706831709208803,high1095,1,0.2 -high1096,CHDScenario8DS24,,8,0.567405028469482,high1096,8,-1.432 -high1097,CHDScenario9DS48,,9,0.902422251768644,high1097,9,12.62 -high1098,CHDScenario15DS36,,15,0.344737898627202,high1098,15,-0.16058 -high1099,CHDScenario16DS25,,16,0.178468768447129,high1099,16,1 -high11,CHDScenario2DS47,147,2,0.428285178574752,high11,2,0.8 -high110,CHDScenario1DS3,3,1,0.519376690017284,high110,1,0.2 -high1100,CHDScenario8DS56,,8,0.937167741803859,high1100,8,-1.432 -high1101,CHDScenario6DS18,,6,0.53772002730088,high1101,6,-1.1039 -high1102,CHDScenario11DS42,,11,0.209723188696126,high1102,11,10.77 -high1103,CHDScenario2DS29,129,2,0.0362823931704166,high1103,2,0.8 -high1104,CHDScenario6DS19,,6,0.0279559841671068,high1104,6,-1.1039 -high1105,CHDScenario4DS73,,4,0.6156299215155,high1105,4,2.1 -high1106,CHDScenario1DS2,2,1,0.133940988035703,high1106,1,0.2 -high1107,CHDScenario9DS60,,9,0.445241177408614,high1107,9,12.62 -high1108,CHDScenario14DS83,,14,0.155505514133711,high1108,14,61.11 -high1109,CHDScenario12DS2,,12,0.0681904278123019,high1109,12,-3.159 -high111,CHDScenario12DS28,,12,0.203777429899351,high111,12,-3.159 -high1110,CHDScenario13DS65,,13,0.328903312715119,high1110,13,-0.8486 -high1111,CHDScenario16DS29,,16,0.7373480239164,high1111,16,1 -high1112,CHDScenario15DS47,,15,0.233499656808054,high1112,15,-0.16058 -high1113,CHDScenario9DS20,,9,0.939786022675987,high1113,9,12.62 -high1114,CHDScenario16DS38,,16,0.570950092132001,high1114,16,1 -high1115,CHDScenario2DS98,,2,0.0181180470071654,high1115,2,0.8 -high1116,CHDScenario4DS37,,4,0.159044696670996,high1116,4,2.1 -high1117,CHDScenario9DS84,,9,0.892715121617937,high1117,9,12.62 -high1118,CHDScenario8DS3,,8,0.150925849223337,high1118,8,-1.432 -high1119,CHDScenario12DS15,,12,0.998483944998819,high1119,12,-3.159 -high112,CHDScenario5DS19,,5,0.276064354218686,high112,5,-0.3429 -high1120,CHDScenario12DS22,,12,0.0215852662623177,high1120,12,-3.159 -high1121,CHDScenario2DS28,128,2,0.0657189270034871,high1121,2,0.8 -high1122,CHDScenario12DS42,,12,0.730460488425698,high1122,12,-3.159 -high1123,CHDScenario2DS43,143,2,0.85605326331909,high1123,2,0.8 -high1124,CHDScenario3DS83,,3,0.127879721368286,high1124,3,-0.800000000000001 -high1125,CHDScenario7DS14,,7,0.423152367098127,high1125,7,0 -high1126,CHDScenario7DS48,,7,0.0236420933108459,high1126,7,0 -high1127,CHDScenario10DS36,,10,0.738524284372959,high1127,10,9.134 -high1128,CHDScenario13DS24,,13,0.885640893573144,high1128,13,-0.8486 -high1129,CHDScenario3DS20,,3,0.0402860148368581,high1129,3,-0.800000000000001 -high113,CHDScenario13DS78,,13,0.316089457825201,high113,13,-0.8486 -high1130,CHDScenario7DS47,,7,0.115065378754668,high1130,7,0 -high1131,CHDScenario13DS45,,13,0.898194443621564,high1131,13,-0.8486 -high1132,CHDScenario9DS79,,9,0.249787216357522,high1132,9,12.62 -high1133,CHDScenario1DS38,38,1,0.774223638283174,high1133,1,0.2 -high1134,CHDScenario2DS6,106,2,0.00444782437226965,high1134,2,0.8 -high1135,CHDScenario5DS18,,5,0.428469147143229,high1135,5,-0.3429 -high1136,CHDScenario2DS80,180,2,0.498395334270851,high1136,2,0.8 -high1137,CHDScenario9DS46,,9,0.100456960674821,high1137,9,12.62 -high1138,CHDScenario10DS21,,10,0.523544056903197,high1138,10,9.134 -high1139,CHDScenario9DS50,,9,0.706148299456092,high1139,9,12.62 -high114,CHDScenario4DS18,,4,0.318397603411393,high114,4,2.1 -high1140,CHDScenario10DS31,,10,0.592394828068924,high1140,10,9.134 -high1141,CHDScenario13DS92,,13,0.144879816091654,high1141,13,-0.8486 -high1142,CHDScenario15DS69,,15,0.0745144071455833,high1142,15,-0.16058 -high1143,CHDScenario11DS68,,11,0.267769466835235,high1143,11,10.77 -high1144,CHDScenario5DS39,,5,0.600269580620375,high1144,5,-0.3429 -high1145,CHDScenario2DS50,150,2,0.189396476867044,high1145,2,0.8 -high1146,CHDScenario9DS99,,9,0.597677803256978,high1146,9,12.62 -high1147,CHDScenario4DS58,,4,0.787309272983259,high1147,4,2.1 -high1148,CHDScenario16DS45,,16,0.43212239544347,high1148,16,1 -high1149,CHDScenario12DS7,,12,0.410021682688189,high1149,12,-3.159 -high115,CHDScenario12DS96,,12,0.950636955061979,high115,12,-3.159 -high1150,CHDScenario1DS32,32,1,0.668299142289826,high1150,1,0.2 -high1151,CHDScenario6DS20,,6,0.27423112560813,high1151,6,-1.1039 -high1152,CHDScenario10DS72,,10,0.720061547339887,high1152,10,9.134 -high1153,CHDScenario14DS4,,14,0.0212851522387009,high1153,14,61.11 -high1154,CHDScenario15DS24,,15,0.17394916009037,high1154,15,-0.16058 -high1155,CHDScenario13DS79,,13,0.823040698260897,high1155,13,-0.8486 -high1156,CHDScenario9DS61,,9,0.943038539192908,high1156,9,12.62 -high1157,CHDScenario13DS51,,13,0.806009972687956,high1157,13,-0.8486 -high1158,CHDScenario7DS17,,7,0.349053806166979,high1158,7,0 -high1159,CHDScenario2DS46,146,2,0.717744685257034,high1159,2,0.8 -high116,CHDScenario4DS56,,4,0.271364056696688,high116,4,2.1 -high1160,CHDScenario15DS64,,15,0.714077478641164,high1160,15,-0.16058 -high1161,CHDScenario6DS91,,6,0.0401634986436529,high1161,6,-1.1039 -high1162,CHDScenario6DS65,,6,0.360598221022628,high1162,6,-1.1039 -high1163,CHDScenario8DS57,,8,0.0713725752511257,high1163,8,-1.432 -high1164,CHDScenario9DS7,,9,0.591216571672305,high1164,9,12.62 -high1165,CHDScenario12DS39,,12,0.986335428128643,high1165,12,-3.159 -high1166,CHDScenario15DS77,,15,0.298951216883328,high1166,15,-0.16058 -high1167,CHDScenario11DS19,,11,0.685475427900255,high1167,11,10.77 -high1168,CHDScenario12DS98,,12,0.841219992214664,high1168,12,-3.159 -high1169,CHDScenario13DS26,,13,0.642675165561385,high1169,13,-0.8486 -high117,CHDScenario15DS16,,15,0.43356165236325,high117,15,-0.16058 -high1170,CHDScenario13DS64,,13,0.718516344097359,high1170,13,-0.8486 -high1171,CHDScenario8DS80,,8,0.160409360089584,high1171,8,-1.432 -high1172,CHDScenario4DS36,,4,0.79093549030243,high1172,4,2.1 -high1173,CHDScenario9DS54,,9,0.186816927089823,high1173,9,12.62 -high1174,CHDScenario15DS18,,15,0.556397022350562,high1174,15,-0.16058 -high1175,CHDScenario11DS29,,11,0.441608226493395,high1175,11,10.77 -high1176,CHDScenario14DS80,,14,0.239917569192923,high1176,14,61.11 -high1177,CHDScenario8DS4,,8,0.254242584273791,high1177,8,-1.432 -high1178,CHDScenario10DS93,,10,0.658595526162661,high1178,10,9.134 -high1179,CHDScenario4DS23,,4,0.536110453213903,high1179,4,2.1 -high118,CHDScenario5DS41,,5,0.737399150211126,high118,5,-0.3429 -high1180,CHDScenario2DS75,175,2,0.272329279231709,high1180,2,0.8 -high1181,CHDScenario2DS36,136,2,0.968282619428495,high1181,2,0.8 -high1182,CHDScenario12DS24,,12,0.816236066961291,high1182,12,-3.159 -high1183,CHDScenario16DS96,,16,0.38710033001633,high1183,16,1 -high1184,CHDScenario15DS99,,15,0.379301838716334,high1184,15,-0.16058 -high1185,CHDScenario9DS59,,9,0.385169440164549,high1185,9,12.62 -high1186,CHDScenario3DS6,,3,0.0304050428634866,high1186,3,-0.800000000000001 -high1187,CHDScenario12DS36,,12,0.0998615413642129,high1187,12,-3.159 -high1188,CHDScenario7DS84,,7,0.902726383740693,high1188,7,0 -high1189,CHDScenario11DS39,,11,0.860573370909725,high1189,11,10.77 -high119,CHDScenario15DS51,,15,0.212437302908217,high119,15,-0.16058 -high1190,CHDScenario5DS6,,5,0.33764007167351,high1190,5,-0.3429 -high1191,CHDScenario16DS20,,16,0.937489487385073,high1191,16,1 -high1192,CHDScenario8DS100,,8,0.29817709791055,high1192,8,-1.432 -high1193,CHDScenario6DS30,,6,0.732115053248049,high1193,6,-1.1039 -high1194,CHDScenario16DS69,,16,0.227197113288199,high1194,16,1 -high1195,CHDScenario4DS19,,4,0.993166403243154,high1195,4,2.1 -high1196,CHDScenario3DS19,,3,0.43238226046697,high1196,3,-0.800000000000001 -high1197,CHDScenario15DS32,,15,0.209863568638017,high1197,15,-0.16058 -high1198,CHDScenario11DS17,,11,0.874445241864984,high1198,11,10.77 -high1199,CHDScenario6DS48,,6,0.532229352003559,high1199,6,-1.1039 -high12,CHDScenario4DS12,,4,0.483784933664219,high12,4,2.1 -high120,CHDScenario1DS60,60,1,0.052771891733193,high120,1,0.2 -high1200,CHDScenario14DS69,,14,0.874964737238354,high1200,14,61.11 -high1201,CHDScenario6DS21,,6,0.252791527132332,high1201,6,-1.1039 -high1202,CHDScenario4DS44,,4,0.669872177257179,high1202,4,2.1 -high1203,CHDScenario12DS5,,12,0.798179082899129,high1203,12,-3.159 -high1204,CHDScenario6DS67,,6,0.0326751170221526,high1204,6,-1.1039 -high1205,CHDScenario16DS90,,16,0.798847040821538,high1205,16,1 -high1206,CHDScenario7DS76,,7,0.131411372161652,high1206,7,0 -high1207,CHDScenario16DS64,,16,0.522120690492279,high1207,16,1 -high1208,CHDScenario13DS5,,13,0.273092183157546,high1208,13,-0.8486 -high1209,CHDScenario12DS80,,12,0.296476483374666,high1209,12,-3.159 -high121,CHDScenario9DS66,,9,0.419818656460346,high121,9,12.62 -high1210,CHDScenario7DS77,,7,0.177222578636001,high1210,7,0 -high1211,CHDScenario10DS97,,10,0.252994213466914,high1211,10,9.134 -high1212,CHDScenario9DS91,,9,0.754843340243231,high1212,9,12.62 -high1213,CHDScenario15DS17,,15,0.772110308228152,high1213,15,-0.16058 -high1214,CHDScenario13DS15,,13,0.048020900037152,high1214,13,-0.8486 -high1215,CHDScenario12DS78,,12,0.509797509410408,high1215,12,-3.159 -high1216,CHDScenario2DS7,107,2,0.664121775812928,high1216,2,0.8 -high1217,CHDScenario15DS31,,15,0.926521481267946,high1217,15,-0.16058 -high1218,CHDScenario8DS68,,8,0.0109741193260886,high1218,8,-1.432 -high1219,CHDScenario3DS8,,3,0.63297684916843,high1219,3,-0.800000000000001 -high122,CHDScenario5DS45,,5,0.894166861601486,high122,5,-0.3429 -high1220,CHDScenario10DS20,,10,0.977128987020182,high1220,10,9.134 -high1221,CHDScenario13DS12,,13,0.703398284602755,high1221,13,-0.8486 -high1222,CHDScenario16DS16,,16,0.0968216996036865,high1222,16,1 -high1223,CHDScenario7DS82,,7,0.0313407383028124,high1223,7,0 -high1224,CHDScenario1DS46,46,1,0.0215852582875516,high1224,1,0.2 -high1225,CHDScenario9DS53,,9,0.804663603797392,high1225,9,12.62 -high1226,CHDScenario14DS40,,14,0.508718241778825,high1226,14,61.11 -high1227,CHDScenario7DS89,,7,0.499093589320275,high1227,7,0 -high1228,CHDScenario12DS71,,12,0.920957072279458,high1228,12,-3.159 -high1229,CHDScenario9DS23,,9,0.480029426749142,high1229,9,12.62 -high123,CHDScenario1DS24,24,1,0.420257736798751,high123,1,0.2 -high1230,CHDScenario5DS10,,5,0.274369727998614,high1230,5,-0.3429 -high1231,CHDScenario12DS95,,12,0.181512197043512,high1231,12,-3.159 -high1232,CHDScenario16DS48,,16,0.698015175022802,high1232,16,1 -high1233,CHDScenario2DS48,148,2,0.164226870200525,high1233,2,0.8 -high1234,CHDScenario15DS74,,15,0.789818783218837,high1234,15,-0.16058 -high1235,CHDScenario7DS70,,7,0.219825939347054,high1235,7,0 -high1236,CHDScenario6DS87,,6,0.343033355509491,high1236,6,-1.1039 -high1237,CHDScenario7DS96,,7,0.649537633899481,high1237,7,0 -high1238,CHDScenario9DS77,,9,0.158632523298515,high1238,9,12.62 -high1239,CHDScenario15DS2,,15,0.244530891579737,high1239,15,-0.16058 -high124,CHDScenario8DS65,,8,0.124843810346694,high124,8,-1.432 -high1240,CHDScenario7DS31,,7,0.174082920184682,high1240,7,0 -high1241,CHDScenario2DS83,183,2,0.183367963591173,high1241,2,0.8 -high1242,CHDScenario3DS46,,3,0.412303689044964,high1242,3,-0.800000000000001 -high1243,CHDScenario11DS91,,11,0.137543013490792,high1243,11,10.77 -high1244,CHDScenario14DS89,,14,0.644314041800936,high1244,14,61.11 -high1245,CHDScenario15DS33,,15,0.0608582955098359,high1245,15,-0.16058 -high1246,CHDScenario6DS41,,6,0.401935563055607,high1246,6,-1.1039 -high1247,CHDScenario12DS34,,12,0.489965871094628,high1247,12,-3.159 -high1248,CHDScenario10DS48,,10,0.00171942405982695,high1248,10,9.134 -high1249,CHDScenario16DS71,,16,0.784755723813998,high1249,16,1 -high125,CHDScenario10DS77,,10,0.931659706551861,high125,10,9.134 -high1250,CHDScenario12DS20,,12,0.193280025499318,high1250,12,-3.159 -high1251,CHDScenario14DS43,,14,0.688246118339246,high1251,14,61.11 -high1252,CHDScenario10DS87,,10,0.724240937232851,high1252,10,9.134 -high1253,CHDScenario10DS76,,10,0.245336868066577,high1253,10,9.134 -high1254,CHDScenario16DS41,,16,0.401774292341588,high1254,16,1 -high1255,CHDScenario7DS53,,7,0.720149985040962,high1255,7,0 -high1256,CHDScenario6DS40,,6,0.678328632074775,high1256,6,-1.1039 -high1257,CHDScenario6DS86,,6,0.701326352410854,high1257,6,-1.1039 -high1258,CHDScenario13DS29,,13,0.444298368373274,high1258,13,-0.8486 -high1259,CHDScenario5DS24,,5,0.417712196152576,high1259,5,-0.3429 -high126,CHDScenario13DS49,,13,0.337035949119597,high126,13,-0.8486 -high1260,CHDScenario7DS88,,7,0.209093575876156,high1260,7,0 -high1261,CHDScenario8DS92,,8,0.755559902097965,high1261,8,-1.432 -high1262,CHDScenario1DS23,23,1,0.645954327605383,high1262,1,0.2 -high1263,CHDScenario5DS66,,5,0.324295630053505,high1263,5,-0.3429 -high1264,CHDScenario10DS59,,10,0.461526634128277,high1264,10,9.134 -high1265,CHDScenario8DS34,,8,0.101183907499297,high1265,8,-1.432 -high1266,CHDScenario12DS49,,12,0.0312713533901997,high1266,12,-3.159 -high1267,CHDScenario1DS31,31,1,0.984191871454051,high1267,1,0.2 -high1268,CHDScenario14DS84,,14,0.137279166395901,high1268,14,61.11 -high1269,CHDScenario3DS61,,3,0.87067984305866,high1269,3,-0.800000000000001 -high127,CHDScenario9DS96,,9,0.480778826549658,high127,9,12.62 -high1270,CHDScenario6DS44,,6,0.224943583167503,high1270,6,-1.1039 -high1271,CHDScenario6DS12,,6,0.922471367778693,high1271,6,-1.1039 -high1272,CHDScenario14DS93,,14,0.258303809980214,high1272,14,61.11 -high1273,CHDScenario8DS47,,8,0.471091169668472,high1273,8,-1.432 -high1274,CHDScenario9DS27,,9,0.887606188530163,high1274,9,12.62 -high1275,CHDScenario16DS5,,16,0.46199930107476,high1275,16,1 -high1276,CHDScenario1DS6,6,1,0.360537662289559,high1276,1,0.2 -high1277,CHDScenario7DS71,,7,0.795572850096788,high1277,7,0 -high1278,CHDScenario6DS85,,6,0.836357259613016,high1278,6,-1.1039 -high1279,CHDScenario15DS21,,15,0.0410614888921821,high1279,15,-0.16058 -high128,CHDScenario8DS75,,8,0.900016157708798,high128,8,-1.432 -high1280,CHDScenario12DS89,,12,0.541909527399196,high1280,12,-3.159 -high1281,CHDScenario7DS69,,7,0.968338703618825,high1281,7,0 -high1282,CHDScenario4DS90,,4,0.769182838073398,high1282,4,2.1 -high1283,CHDScenario1DS25,25,1,0.620627704973578,high1283,1,0.2 -high1284,CHDScenario2DS38,138,2,0.791253103630732,high1284,2,0.8 -high1285,CHDScenario16DS32,,16,0.0200549424597295,high1285,16,1 -high1286,CHDScenario16DS65,,16,0.756633472689809,high1286,16,1 -high1287,CHDScenario7DS36,,7,0.231201264236555,high1287,7,0 -high1288,CHDScenario7DS57,,7,0.600292622811429,high1288,7,0 -high1289,CHDScenario5DS32,,5,0.788143756804668,high1289,5,-0.3429 -high129,CHDScenario7DS27,,7,0.816948518515882,high129,7,0 -high1290,CHDScenario7DS13,,7,0.800488439847941,high1290,7,0 -high1291,CHDScenario11DS62,,11,0.178459770167336,high1291,11,10.77 -high1292,CHDScenario4DS28,,4,0.0242586199710777,high1292,4,2.1 -high1293,CHDScenario10DS14,,10,0.834124084354753,high1293,10,9.134 -high1294,CHDScenario1DS16,16,1,0.591855107891642,high1294,1,0.2 -high1295,CHDScenario1DS34,34,1,0.0244180321579623,high1295,1,0.2 -high1296,CHDScenario16DS67,,16,0.712844990021247,high1296,16,1 -high1297,CHDScenario5DS79,,5,0.963472363478266,high1297,5,-0.3429 -high1298,CHDScenario1DS12,12,1,0.356727572871212,high1298,1,0.2 -high1299,CHDScenario11DS69,,11,0.0986827699015123,high1299,11,10.77 -high13,CHDScenario3DS91,,3,0.426857355536313,high13,3,-0.800000000000001 -high130,CHDScenario5DS30,,5,0.500295636717072,high130,5,-0.3429 -high1300,CHDScenario15DS72,,15,0.326134150923283,high1300,15,-0.16058 -high1301,CHDScenario4DS25,,4,0.42245919653921,high1301,4,2.1 -high1302,CHDScenario11DS18,,11,0.2161279927275,high1302,11,10.77 -high1303,CHDScenario13DS87,,13,0.606408581602139,high1303,13,-0.8486 -high1304,CHDScenario9DS51,,9,0.438235502228673,high1304,9,12.62 -high1305,CHDScenario11DS100,,11,0.345067659770242,high1305,11,10.77 -high1306,CHDScenario3DS38,,3,0.37514513138201,high1306,3,-0.800000000000001 -high1307,CHDScenario2DS66,166,2,0.566905086659951,high1307,2,0.8 -high1308,CHDScenario16DS2,,16,0.413083466518714,high1308,16,1 -high1309,CHDScenario13DS18,,13,0.317698920477582,high1309,13,-0.8486 -high131,CHDScenario4DS33,,4,0.56824213651679,high131,4,2.1 -high1310,CHDScenario11DS90,,11,0.638000840505732,high1310,11,10.77 -high1311,CHDScenario4DS39,,4,0.228799190210428,high1311,4,2.1 -high1312,CHDScenario15DS71,,15,0.993296604988826,high1312,15,-0.16058 -high1313,CHDScenario16DS47,,16,0.948699674968075,high1313,16,1 -high1314,CHDScenario4DS97,,4,0.0148650398793737,high1314,4,2.1 -high1315,CHDScenario2DS89,189,2,0.574595774123762,high1315,2,0.8 -high1316,CHDScenario1DS22,22,1,0.241095341399902,high1316,1,0.2 -high1317,CHDScenario5DS99,,5,0.755635723793773,high1317,5,-0.3429 -high1318,CHDScenario3DS28,,3,0.199679242628092,high1318,3,-0.800000000000001 -high1319,CHDScenario12DS51,,12,0.269290680872548,high1319,12,-3.159 -high132,CHDScenario15DS45,,15,0.710893368645197,high132,15,-0.16058 -high1320,CHDScenario14DS46,,14,0.313327003859393,high1320,14,61.11 -high1321,CHDScenario1DS55,55,1,0.840748409128134,high1321,1,0.2 -high1322,CHDScenario6DS24,,6,0.795853219755053,high1322,6,-1.1039 -high1323,CHDScenario12DS94,,12,0.630790378991665,high1323,12,-3.159 -high1324,CHDScenario9DS70,,9,0.949252113549219,high1324,9,12.62 -high1325,CHDScenario6DS84,,6,0.806899368696846,high1325,6,-1.1039 -high1326,CHDScenario6DS59,,6,0.378715086990864,high1326,6,-1.1039 -high1327,CHDScenario5DS5,,5,0.711015902458656,high1327,5,-0.3429 -high1328,CHDScenario10DS58,,10,0.336975508120108,high1328,10,9.134 -high1329,CHDScenario11DS49,,11,0.984004034429531,high1329,11,10.77 -high133,CHDScenario13DS44,,13,0.0152486961186249,high133,13,-0.8486 -high1330,CHDScenario11DS64,,11,0.423748632861306,high1330,11,10.77 -high1331,CHDScenario10DS49,,10,0.934320319223369,high1331,10,9.134 -high1332,CHDScenario4DS8,,4,0.0506221412051291,high1332,4,2.1 -high1333,CHDScenario8DS32,,8,0.59610231334235,high1333,8,-1.432 -high1334,CHDScenario3DS66,,3,0.580348202500632,high1334,3,-0.800000000000001 -high1335,CHDScenario10DS29,,10,0.173052041300839,high1335,10,9.134 -high1336,CHDScenario14DS64,,14,0.54234306708417,high1336,14,61.11 -high1337,CHDScenario7DS64,,7,0.28775946732999,high1337,7,0 -high1338,CHDScenario8DS93,,8,0.75740781997805,high1338,8,-1.432 -high1339,CHDScenario4DS5,,4,0.534206960670887,high1339,4,2.1 -high134,CHDScenario13DS72,,13,0.118618284721718,high134,13,-0.8486 -high1340,CHDScenario10DS86,,10,0.61870258020983,high1340,10,9.134 -high1341,CHDScenario6DS37,,6,0.188910490255967,high1341,6,-1.1039 -high1342,CHDScenario8DS98,,8,0.776881983737205,high1342,8,-1.432 -high1343,CHDScenario11DS8,,11,0.397560798742873,high1343,11,10.77 -high1344,CHDScenario10DS88,,10,0.966171294304013,high1344,10,9.134 -high1345,CHDScenario11DS55,,11,0.876621373396101,high1345,11,10.77 -high1346,CHDScenario14DS90,,14,0.973854893821626,high1346,14,61.11 -high1347,CHDScenario8DS69,,8,0.260620114425453,high1347,8,-1.432 -high1348,CHDScenario11DS40,,11,0.872218112707024,high1348,11,10.77 -high1349,CHDScenario14DS97,,14,0.819383836624903,high1349,14,61.11 -high135,CHDScenario16DS43,,16,0.850269367905174,high135,16,1 -high1350,CHDScenario5DS40,,5,0.492244717142346,high1350,5,-0.3429 -high1351,CHDScenario13DS16,,13,0.279103084580902,high1351,13,-0.8486 -high1352,CHDScenario4DS68,,4,0.384160654156903,high1352,4,2.1 -high1353,CHDScenario7DS9,,7,0.0221647749965727,high1353,7,0 -high1354,CHDScenario1DS47,47,1,0.364644683781622,high1354,1,0.2 -high1355,CHDScenario16DS21,,16,0.712408131278295,high1355,16,1 -high1356,CHDScenario14DS88,,14,0.982635535406508,high1356,14,61.11 -high1357,CHDScenario13DS17,,13,0.711934904178133,high1357,13,-0.8486 -high1358,CHDScenario3DS15,,3,0.0892216000823429,high1358,3,-0.800000000000001 -high1359,CHDScenario10DS55,,10,0.422300518777245,high1359,10,9.134 -high136,CHDScenario10DS33,,10,0.10256867161051,high136,10,9.134 -high1360,CHDScenario11DS15,,11,0.752992430867405,high1360,11,10.77 -high1361,CHDScenario9DS15,,9,0.584949600179277,high1361,9,12.62 -high1362,CHDScenario12DS1,,12,0.714585312661169,high1362,12,-3.159 -high1363,CHDScenario11DS84,,11,0.388743186254897,high1363,11,10.77 -high1364,CHDScenario8DS36,,8,0.574063973927562,high1364,8,-1.432 -high1365,CHDScenario13DS94,,13,0.137245163298667,high1365,13,-0.8486 -high1366,CHDScenario4DS27,,4,0.880756885852845,high1366,4,2.1 -high1367,CHDScenario7DS54,,7,0.604137536784998,high1367,7,0 -high1368,CHDScenario1DS43,43,1,0.517711140561202,high1368,1,0.2 -high1369,CHDScenario4DS59,,4,0.877842650424615,high1369,4,2.1 -high137,CHDScenario1DS96,96,1,0.179729628145593,high137,1,0.2 -high1370,CHDScenario10DS16,,10,0.534416668209644,high1370,10,9.134 -high1371,CHDScenario14DS79,,14,0.439963706992798,high1371,14,61.11 -high1372,CHDScenario16DS75,,16,0.781463536125285,high1372,16,1 -high1373,CHDScenario3DS52,,3,0.959283782117969,high1373,3,-0.800000000000001 -high1374,CHDScenario13DS95,,13,0.483074393405447,high1374,13,-0.8486 -high1375,CHDScenario10DS90,,10,0.615869339682538,high1375,10,9.134 -high1376,CHDScenario14DS9,,14,0.552477573471083,high1376,14,61.11 -high1377,CHDScenario9DS86,,9,0.619232135591794,high1377,9,12.62 -high1378,CHDScenario3DS34,,3,0.98994771813349,high1378,3,-0.800000000000001 -high1379,CHDScenario14DS56,,14,0.644942676868057,high1379,14,61.11 -high138,CHDScenario1DS11,11,1,0.770238478496038,high138,1,0.2 -high1380,CHDScenario2DS64,164,2,0.779121948032244,high1380,2,0.8 -high1381,CHDScenario6DS66,,6,0.510254212905758,high1381,6,-1.1039 -high1382,CHDScenario3DS71,,3,0.12539909102225,high1382,3,-0.800000000000001 -high1383,CHDScenario9DS26,,9,0.252299431592565,high1383,9,12.62 -high1384,CHDScenario2DS8,108,2,0.885458394025425,high1384,2,0.8 -high1385,CHDScenario1DS67,67,1,0.373981111985904,high1385,1,0.2 -high1386,CHDScenario5DS13,,5,0.5231781115442,high1386,5,-0.3429 -high1387,CHDScenario14DS67,,14,0.232167681637724,high1387,14,61.11 -high1388,CHDScenario7DS3,,7,0.787954567531111,high1388,7,0 -high1389,CHDScenario13DS30,,13,0.390919306794492,high1389,13,-0.8486 -high139,CHDScenario15DS29,,15,0.635950949204644,high139,15,-0.16058 -high1390,CHDScenario1DS59,59,1,0.654444326714411,high1390,1,0.2 -high1391,CHDScenario6DS61,,6,0.840914494587774,high1391,6,-1.1039 -high1392,CHDScenario16DS49,,16,0.0788833607894715,high1392,16,1 -high1393,CHDScenario10DS39,,10,0.687498485276147,high1393,10,9.134 -high1394,CHDScenario16DS23,,16,0.107470069413426,high1394,16,1 -high1395,CHDScenario11DS75,,11,0.62366336231225,high1395,11,10.77 -high1396,CHDScenario2DS18,118,2,0.929655624627855,high1396,2,0.8 -high1397,CHDScenario11DS50,,11,0.0692049155074043,high1397,11,10.77 -high1398,CHDScenario10DS5,,10,0.290937657544374,high1398,10,9.134 -high1399,CHDScenario3DS75,,3,0.970349671944704,high1399,3,-0.800000000000001 -high14,CHDScenario1DS93,93,1,0.733928300301755,high14,1,0.2 -high140,CHDScenario1DS90,90,1,0.877445302432743,high140,1,0.2 -high1400,CHDScenario16DS85,,16,0.30704728638392,high1400,16,1 -high1401,CHDScenario8DS99,,8,0.780793872303104,high1401,8,-1.432 -high1402,CHDScenario1DS79,79,1,0.0982934980524716,high1402,1,0.2 -high1403,CHDScenario6DS39,,6,0.0282947692803583,high1403,6,-1.1039 -high1404,CHDScenario16DS34,,16,0.213963450126179,high1404,16,1 -high1405,CHDScenario3DS29,,3,0.0306623719871647,high1405,3,-0.800000000000001 -high1406,CHDScenario5DS75,,5,0.107002008033852,high1406,5,-0.3429 -high1407,CHDScenario15DS96,,15,0.0918319698759764,high1407,15,-0.16058 -high1408,CHDScenario12DS85,,12,0.337155608654655,high1408,12,-3.159 -high1409,CHDScenario1DS63,63,1,0.602326414325243,high1409,1,0.2 -high141,CHDScenario10DS17,,10,0.252521532662761,high141,10,9.134 -high1410,CHDScenario2DS67,167,2,0.688858575180738,high1410,2,0.8 -high1411,CHDScenario15DS44,,15,0.675983004711563,high1411,15,-0.16058 -high1412,CHDScenario12DS60,,12,0.345212625029803,high1412,12,-3.159 -high1413,CHDScenario5DS28,,5,0.578795041435251,high1413,5,-0.3429 -high1414,CHDScenario11DS88,,11,0.0324461272046459,high1414,11,10.77 -high1415,CHDScenario8DS61,,8,0.0806927025545889,high1415,8,-1.432 -high1416,CHDScenario16DS94,,16,0.0456061510189482,high1416,16,1 -high1417,CHDScenario1DS75,75,1,0.448137364345903,high1417,1,0.2 -high1418,CHDScenario4DS91,,4,0.704139781463693,high1418,4,2.1 -high1419,CHDScenario1DS68,68,1,0.341109261331486,high1419,1,0.2 -high142,CHDScenario4DS66,,4,0.408946837714798,high142,4,2.1 -high1420,CHDScenario5DS7,,5,0.692431273444418,high1420,5,-0.3429 -high1421,CHDScenario1DS4,4,1,0.647511192704421,high1421,1,0.2 -high1422,CHDScenario10DS26,,10,0.567441295784633,high1422,10,9.134 -high1423,CHDScenario9DS69,,9,0.484137223236274,high1423,9,12.62 -high1424,CHDScenario13DS52,,13,0.100296742312144,high1424,13,-0.8486 -high1425,CHDScenario13DS100,,13,0.318344574682719,high1425,13,-0.8486 -high1426,CHDScenario7DS26,,7,0.877919231762069,high1426,7,0 -high1427,CHDScenario9DS21,,9,0.597134327208093,high1427,9,12.62 -high1428,CHDScenario9DS82,,9,0.889404809054033,high1428,9,12.62 -high1429,CHDScenario16DS31,,16,0.924647072171666,high1429,16,1 -high143,CHDScenario3DS96,,3,0.0115198583944005,high143,3,-0.800000000000001 -high1430,CHDScenario9DS44,,9,0.111969579885144,high1430,9,12.62 -high1431,CHDScenario14DS72,,14,0.610717543610316,high1431,14,61.11 -high1432,CHDScenario12DS58,,12,0.385039386168727,high1432,12,-3.159 -high1433,CHDScenario13DS27,,13,0.0685597369862162,high1433,13,-0.8486 -high1434,CHDScenario12DS63,,12,0.86081966857956,high1434,12,-3.159 -high1435,CHDScenario13DS69,,13,0.0342713726623316,high1435,13,-0.8486 -high1436,CHDScenario15DS42,,15,0.806240648415707,high1436,15,-0.16058 -high1437,CHDScenario5DS65,,5,0.707142831710697,high1437,5,-0.3429 -high1438,CHDScenario10DS34,,10,0.48187678021985,high1438,10,9.134 -high1439,CHDScenario1DS57,57,1,0.754259109133828,high1439,1,0.2 -high144,CHDScenario16DS1,,16,0.745763416544201,high144,16,1 -high1440,CHDScenario16DS42,,16,0.135315999575793,high1440,16,1 -high1441,CHDScenario2DS44,144,2,0.547478077259369,high1441,2,0.8 -high1442,CHDScenario4DS82,,4,0.109339850860535,high1442,4,2.1 -high1443,CHDScenario12DS86,,12,0.803308170010038,high1443,12,-3.159 -high1444,CHDScenario15DS35,,15,0.755148921104075,high1444,15,-0.16058 -high1445,CHDScenario14DS35,,14,0.967977478173642,high1445,14,61.11 -high1446,CHDScenario9DS40,,9,0.496302743052049,high1446,9,12.62 -high1447,CHDScenario16DS22,,16,0.340926388122935,high1447,16,1 -high1448,CHDScenario10DS30,,10,0.703283293459889,high1448,10,9.134 -high1449,CHDScenario4DS35,,4,0.632175936740894,high1449,4,2.1 -high145,CHDScenario8DS22,,8,0.862692091419877,high145,8,-1.432 -high1450,CHDScenario2DS94,194,2,0.0302733894182519,high1450,2,0.8 -high1451,CHDScenario8DS54,,8,0.882072164115293,high1451,8,-1.432 -high1452,CHDScenario2DS62,162,2,0.763309166894405,high1452,2,0.8 -high1453,CHDScenario16DS89,,16,0.478731545365664,high1453,16,1 -high1454,CHDScenario4DS22,,4,0.257087929954142,high1454,4,2.1 -high1455,CHDScenario8DS82,,8,0.385867813014958,high1455,8,-1.432 -high1456,CHDScenario12DS46,,12,0.130254465954357,high1456,12,-3.159 -high1457,CHDScenario11DS52,,11,0.815653464608212,high1457,11,10.77 -high1458,CHDScenario15DS46,,15,0.223954402392207,high1458,15,-0.16058 -high1459,CHDScenario15DS41,,15,0.83032441004399,high1459,15,-0.16058 -high146,CHDScenario1DS26,26,1,0.888588590449459,high146,1,0.2 -high1460,CHDScenario12DS79,,12,0.387637178277752,high1460,12,-3.159 -high1461,CHDScenario3DS44,,3,0.474208389826887,high1461,3,-0.800000000000001 -high1462,CHDScenario10DS25,,10,0.267171537083225,high1462,10,9.134 -high1463,CHDScenario6DS63,,6,0.666409966236134,high1463,6,-1.1039 -high1464,CHDScenario2DS61,161,2,0.0775064973971119,high1464,2,0.8 -high1465,CHDScenario10DS61,,10,0.813063200946596,high1465,10,9.134 -high1466,CHDScenario5DS93,,5,0.517585943442933,high1466,5,-0.3429 -high1467,CHDScenario6DS47,,6,0.577130677503235,high1467,6,-1.1039 -high1468,CHDScenario7DS5,,7,0.541378421119982,high1468,7,0 -high1469,CHDScenario13DS20,,13,0.413405803980859,high1469,13,-0.8486 -high147,CHDScenario15DS22,,15,0.438145334217524,high147,15,-0.16058 -high1470,CHDScenario14DS39,,14,0.970753244866235,high1470,14,61.11 -high1471,CHDScenario12DS59,,12,0.740572357024024,high1471,12,-3.159 -high1472,CHDScenario7DS97,,7,0.101032872557209,high1472,7,0 -high1473,CHDScenario12DS11,,12,0.696582791748388,high1473,12,-3.159 -high1474,CHDScenario15DS70,,15,0.73346990219846,high1474,15,-0.16058 -high1475,CHDScenario5DS15,,5,0.542763009275313,high1475,5,-0.3429 -high1476,CHDScenario14DS12,,14,0.0354877032539099,high1476,14,61.11 -high1477,CHDScenario2DS15,115,2,0.290901306452606,high1477,2,0.8 -high1478,CHDScenario3DS84,,3,0.828738312459772,high1478,3,-0.800000000000001 -high1479,CHDScenario2DS19,119,2,0.295651057198497,high1479,2,0.8 -high148,CHDScenario16DS52,,16,0.321303151515995,high148,16,1 -high1480,CHDScenario11DS71,,11,0.650573406310995,high1480,11,10.77 -high1481,CHDScenario10DS73,,10,0.0172113373855209,high1481,10,9.134 -high1482,CHDScenario2DS12,112,2,0.208140258500021,high1482,2,0.8 -high1483,CHDScenario2DS87,187,2,0.256265805287597,high1483,2,0.8 -high1484,CHDScenario11DS72,,11,0.862767111638763,high1484,11,10.77 -high1485,CHDScenario11DS60,,11,0.973485207853211,high1485,11,10.77 -high1486,CHDScenario16DS30,,16,0.207565964087653,high1486,16,1 -high1487,CHDScenario6DS73,,6,0.0844299607493975,high1487,6,-1.1039 -high1488,CHDScenario9DS34,,9,0.528898028076974,high1488,9,12.62 -high1489,CHDScenario15DS62,,15,0.00172006975133188,high1489,15,-0.16058 -high149,CHDScenario6DS90,,6,0.283801714833648,high149,6,-1.1039 -high1490,CHDScenario3DS65,,3,0.277570156618181,high1490,3,-0.800000000000001 -high1491,CHDScenario13DS81,,13,0.845294222527054,high1491,13,-0.8486 -high1492,CHDScenario7DS66,,7,0.66945076554831,high1492,7,0 -high1493,CHDScenario10DS84,,10,0.0624914412708472,high1493,10,9.134 -high1494,CHDScenario13DS93,,13,0.545322165278966,high1494,13,-0.8486 -high1495,CHDScenario7DS90,,7,0.024859129692908,high1495,7,0 -high1496,CHDScenario9DS58,,9,0.195369358316005,high1496,9,12.62 -high1497,CHDScenario5DS63,,5,0.753214344498185,high1497,5,-0.3429 -high1498,CHDScenario9DS12,,9,0.398088038841905,high1498,9,12.62 -high1499,CHDScenario14DS5,,14,0.706072723605049,high1499,14,61.11 -high15,CHDScenario6DS60,,6,0.490771709508552,high15,6,-1.1039 -high150,CHDScenario9DS47,,9,0.377179570566033,high150,9,12.62 -high1500,CHDScenario15DS61,,15,0.4574739430092,high1500,15,-0.16058 -high1501,CHDScenario5DS34,,5,0.990813990241973,high1501,5,-0.3429 -high1502,CHDScenario11DS66,,11,0.847605337560866,high1502,11,10.77 -high1503,CHDScenario7DS18,,7,0.466756656190266,high1503,7,0 -high1504,CHDScenario9DS62,,9,0.336900856952709,high1504,9,12.62 -high1505,CHDScenario10DS66,,10,0.116111284449346,high1505,10,9.134 -high1506,CHDScenario10DS98,,10,0.583013511484775,high1506,10,9.134 -high1507,CHDScenario11DS44,,11,0.575405435000411,high1507,11,10.77 -high1508,CHDScenario11DS48,,11,0.965889156423422,high1508,11,10.77 -high1509,CHDScenario14DS19,,14,0.283538787487173,high1509,14,61.11 -high151,CHDScenario8DS7,,8,0.296980173347249,high151,8,-1.432 -high1510,CHDScenario8DS86,,8,0.710883808745238,high1510,8,-1.432 -high1511,CHDScenario5DS80,,5,0.0963290079027446,high1511,5,-0.3429 -high1512,CHDScenario12DS54,,12,0.742412803765845,high1512,12,-3.159 -high1513,CHDScenario3DS49,,3,0.818868899481982,high1513,3,-0.800000000000001 -high1514,CHDScenario14DS34,,14,0.515311799033201,high1514,14,61.11 -high1515,CHDScenario4DS34,,4,0.949192800411057,high1515,4,2.1 -high1516,CHDScenario1DS10,10,1,0.183253491988387,high1516,1,0.2 -high1517,CHDScenario9DS38,,9,0.600118807803619,high1517,9,12.62 -high1518,CHDScenario1DS65,65,1,0.989609154994269,high1518,1,0.2 -high1519,CHDScenario5DS11,,5,0.582223913768929,high1519,5,-0.3429 -high152,CHDScenario15DS28,,15,0.279677428262561,high152,15,-0.16058 -high1520,CHDScenario2DS42,142,2,0.392068910287094,high1520,2,0.8 -high1521,CHDScenario10DS23,,10,0.204673928129469,high1521,10,9.134 -high1522,CHDScenario3DS69,,3,0.821010052781045,high1522,3,-0.800000000000001 -high1523,CHDScenario14DS3,,14,0.0379359101337419,high1523,14,61.11 -high1524,CHDScenario6DS74,,6,0.22839784215477,high1524,6,-1.1039 -high1525,CHDScenario4DS11,,4,0.235895271154157,high1525,4,2.1 -high1526,CHDScenario2DS33,133,2,0.112064945515864,high1526,2,0.8 -high1527,CHDScenario9DS29,,9,0.135130228176393,high1527,9,12.62 -high1528,CHDScenario14DS71,,14,0.853950774205793,high1528,14,61.11 -high1529,CHDScenario9DS81,,9,0.591219910384327,high1529,9,12.62 -high153,CHDScenario15DS9,,15,0.880700239459581,high153,15,-0.16058 -high1530,CHDScenario3DS62,,3,0.737384201540851,high1530,3,-0.800000000000001 -high1531,CHDScenario2DS76,176,2,0.0576374926232347,high1531,2,0.8 -high1532,CHDScenario16DS46,,16,0.551014892635409,high1532,16,1 -high1533,CHDScenario16DS98,,16,0.375793699420895,high1533,16,1 -high1534,CHDScenario13DS21,,13,0.477341403740741,high1534,13,-0.8486 -high1535,CHDScenario3DS37,,3,0.547488605922527,high1535,3,-0.800000000000001 -high1536,CHDScenario12DS82,,12,0.59619463215961,high1536,12,-3.159 -high1537,CHDScenario5DS2,,5,0.156775452910488,high1537,5,-0.3429 -high1538,CHDScenario8DS43,,8,0.0832279730207504,high1538,8,-1.432 -high1539,CHDScenario12DS44,,12,0.778566925100866,high1539,12,-3.159 -high154,CHDScenario4DS21,,4,0.843155134621177,high154,4,2.1 -high1540,CHDScenario8DS45,,8,0.960846398075122,high1540,8,-1.432 -high1541,CHDScenario8DS84,,8,0.667714864866233,high1541,8,-1.432 -high1542,CHDScenario9DS25,,9,0.632069826422897,high1542,9,12.62 -high1543,CHDScenario7DS12,,7,0.576199911230363,high1543,7,0 -high1544,CHDScenario16DS87,,16,0.123595103317239,high1544,16,1 -high1545,CHDScenario8DS55,,8,0.23130197570701,high1545,8,-1.432 -high1546,CHDScenario10DS99,,10,0.27697336948902,high1546,10,9.134 -high1547,CHDScenario5DS82,,5,0.605457227412842,high1547,5,-0.3429 -high1548,CHDScenario12DS67,,12,0.897153691598998,high1548,12,-3.159 -high1549,CHDScenario14DS30,,14,0.64813423627961,high1549,14,61.11 -high155,CHDScenario10DS28,,10,0.126119966050734,high155,10,9.134 -high1550,CHDScenario16DS6,,16,0.391258833495988,high1550,16,1 -high1551,CHDScenario14DS29,,14,0.813668728451154,high1551,14,61.11 -high1552,CHDScenario15DS25,,15,0.411214548766532,high1552,15,-0.16058 -high1553,CHDScenario8DS38,,8,0.836677075851345,high1553,8,-1.432 -high1554,CHDScenario13DS99,,13,0.283251725723271,high1554,13,-0.8486 -high1555,CHDScenario15DS57,,15,0.230736464672807,high1555,15,-0.16058 -high1556,CHDScenario7DS1,,7,0.249569863405339,high1556,7,0 -high1557,CHDScenario14DS96,,14,0.0870198533568842,high1557,14,61.11 -high1558,CHDScenario8DS88,,8,0.0782744845579306,high1558,8,-1.432 -high1559,CHDScenario1DS69,69,1,0.700092788096958,high1559,1,0.2 -high156,CHDScenario1DS44,44,1,0.0425042260687667,high156,1,0.2 -high1560,CHDScenario1DS98,98,1,0.0386636667067275,high1560,1,0.2 -high1561,CHDScenario7DS39,,7,0.243319593205978,high1561,7,0 -high1562,CHDScenario11DS25,,11,0.600187379897603,high1562,11,10.77 -high1563,CHDScenario11DS61,,11,0.104469564798822,high1563,11,10.77 -high1564,CHDScenario8DS25,,8,0.901564298182334,high1564,8,-1.432 -high1565,CHDScenario9DS3,,9,0.722806953438727,high1565,9,12.62 -high1566,CHDScenario13DS37,,13,0.67585006382703,high1566,13,-0.8486 -high1567,CHDScenario5DS29,,5,0.004995763358148,high1567,5,-0.3429 -high1568,CHDScenario5DS50,,5,0.273953376314788,high1568,5,-0.3429 -high1569,CHDScenario4DS10,,4,0.695497700369336,high1569,4,2.1 -high157,CHDScenario11DS37,,11,0.596556032842957,high157,11,10.77 -high1570,CHDScenario1DS36,36,1,0.133707822908362,high1570,1,0.2 -high1571,CHDScenario5DS56,,5,0.756674145614511,high1571,5,-0.3429 -high1572,CHDScenario2DS57,157,2,0.884950292947265,high1572,2,0.8 -high1573,CHDScenario8DS51,,8,0.817063292124167,high1573,8,-1.432 -high1574,CHDScenario12DS61,,12,0.953014090889256,high1574,12,-3.159 -high1575,CHDScenario12DS40,,12,0.585399730445738,high1575,12,-3.159 -high1576,CHDScenario11DS30,,11,0.949686841496509,high1576,11,10.77 -high1577,CHDScenario14DS15,,14,0.999651878532208,high1577,14,61.11 -high1578,CHDScenario13DS74,,13,0.983329508768902,high1578,13,-0.8486 -high1579,CHDScenario4DS79,,4,0.325453892424747,high1579,4,2.1 -high158,CHDScenario12DS77,,12,0.78944212097022,high158,12,-3.159 -high1580,CHDScenario4DS70,,4,0.525948332136428,high1580,4,2.1 -high1581,CHDScenario14DS20,,14,0.247482670343935,high1581,14,61.11 -high1582,CHDScenario13DS34,,13,0.252587427379209,high1582,13,-0.8486 -high1583,CHDScenario2DS2,102,2,0.641099277942318,high1583,2,0.8 -high1584,CHDScenario10DS35,,10,0.0261394409999741,high1584,10,9.134 -high1585,CHDScenario7DS2,,7,0.602016985882892,high1585,7,0 -high1586,CHDScenario1DS89,89,1,0.798553269742052,high1586,1,0.2 -high1587,CHDScenario16DS60,,16,0.231601893257625,high1587,16,1 -high1588,CHDScenario7DS80,,7,0.695173752981298,high1588,7,0 -high1589,CHDScenario7DS10,,7,0.16831099943291,high1589,7,0 -high159,CHDScenario15DS12,,15,0.968994087096278,high159,15,-0.16058 -high1590,CHDScenario7DS86,,7,0.854597331721967,high1590,7,0 -high1591,CHDScenario3DS76,,3,0.936240846397151,high1591,3,-0.800000000000001 -high1592,CHDScenario8DS16,,8,0.898095398259781,high1592,8,-1.432 -high1593,CHDScenario6DS80,,6,0.859267733146932,high1593,6,-1.1039 -high1594,CHDScenario15DS30,,15,0.280595613057916,high1594,15,-0.16058 -high1595,CHDScenario6DS98,,6,0.613866953410444,high1595,6,-1.1039 -high1596,CHDScenario10DS54,,10,0.764971449646786,high1596,10,9.134 -high1597,CHDScenario15DS49,,15,0.922383206431799,high1597,15,-0.16058 -high1598,CHDScenario11DS53,,11,0.664518447558878,high1598,11,10.77 -high1599,CHDScenario10DS32,,10,0.11699339584066,high1599,10,9.134 -high16,CHDScenario16DS86,,16,0.802073396585599,high16,16,1 -high160,CHDScenario4DS9,,4,0.0145135507812845,high160,4,2.1 -high1600,CHDScenario7DS60,,7,0.595766834195145,high1600,7,0 -high161,CHDScenario2DS41,141,2,0.672118902802489,high161,2,0.8 -high162,CHDScenario3DS64,,3,0.241015554015027,high162,3,-0.800000000000001 -high163,CHDScenario8DS73,,8,0.398776923606122,high163,8,-1.432 -high164,CHDScenario10DS85,,10,0.228153282719142,high164,10,9.134 -high165,CHDScenario11DS89,,11,0.53731857174923,high165,11,10.77 -high166,CHDScenario4DS75,,4,0.914842507677263,high166,4,2.1 -high167,CHDScenario9DS85,,9,0.301275070902773,high167,9,12.62 -high168,CHDScenario10DS92,,10,0.665059561925877,high168,10,9.134 -high169,CHDScenario6DS82,,6,0.766230323955876,high169,6,-1.1039 -high17,CHDScenario8DS14,,8,0.861116531305415,high17,8,-1.432 -high170,CHDScenario5DS3,,5,0.670308155020029,high170,5,-0.3429 -high171,CHDScenario7DS61,,7,0.807693330009248,high171,7,0 -high172,CHDScenario3DS81,,3,0.23639506840334,high172,3,-0.800000000000001 -high173,CHDScenario6DS7,,6,0.627160990413978,high173,6,-1.1039 -high174,CHDScenario14DS53,,14,0.925122758570472,high174,14,61.11 -high175,CHDScenario3DS24,,3,0.899108296886652,high175,3,-0.800000000000001 -high176,CHDScenario14DS16,,14,0.11229526445009,high176,14,61.11 -high177,CHDScenario9DS22,,9,0.380346780215854,high177,9,12.62 -high178,CHDScenario3DS63,,3,0.452195492268575,high178,3,-0.800000000000001 -high179,CHDScenario7DS25,,7,0.423480295251845,high179,7,0 -high18,CHDScenario1DS97,97,1,0.573001331526369,high18,1,0.2 -high180,CHDScenario15DS85,,15,0.611436540889293,high180,15,-0.16058 -high181,CHDScenario12DS87,,12,0.772740711301988,high181,12,-3.159 -high182,CHDScenario16DS51,,16,0.603524452458371,high182,16,1 -high183,CHDScenario4DS30,,4,0.788583502333146,high183,4,2.1 -high184,CHDScenario14DS8,,14,0.393966745819767,high184,14,61.11 -high185,CHDScenario10DS19,,10,0.40541952525796,high185,10,9.134 -high186,CHDScenario1DS51,51,1,0.582505183340322,high186,1,0.2 -high187,CHDScenario2DS16,116,2,0.412753394643189,high187,2,0.8 -high188,CHDScenario14DS14,,14,0.968744291740788,high188,14,61.11 -high189,CHDScenario15DS56,,15,0.468321264525443,high189,15,-0.16058 -high19,CHDScenario2DS52,152,2,0.383254711524952,high19,2,0.8 -high190,CHDScenario14DS45,,14,0.487116121895164,high190,14,61.11 -high191,CHDScenario16DS68,,16,0.403778133360652,high191,16,1 -high192,CHDScenario7DS68,,7,0.308324092782408,high192,7,0 -high193,CHDScenario1DS20,20,1,0.75407912733529,high193,1,0.2 -high194,CHDScenario14DS31,,14,0.17079090025395,high194,14,61.11 -high195,CHDScenario16DS81,,16,0.563982107582004,high195,16,1 -high196,CHDScenario2DS99,,2,0.73101555855424,high196,2,0.8 -high197,CHDScenario16DS18,,16,0.593600064316978,high197,16,1 -high198,CHDScenario2DS35,135,2,0.192319810214997,high198,2,0.8 -high199,CHDScenario13DS71,,13,0.566761910020368,high199,13,-0.8486 -high2,CHDScenario12DS26,,12,0.857787927973498,high2,12,-3.159 -high20,CHDScenario2DS92,192,2,0.752337946514084,high20,2,0.8 -high200,CHDScenario13DS38,,13,0.463905941252795,high200,13,-0.8486 -high201,CHDScenario6DS6,,6,0.552046772613034,high201,6,-1.1039 -high202,CHDScenario4DS94,,4,0.18321676318374,high202,4,2.1 -high203,CHDScenario10DS80,,10,0.0252758180077769,high203,10,9.134 -high204,CHDScenario3DS18,,3,0.11703705160871,high204,3,-0.800000000000001 -high205,CHDScenario13DS35,,13,0.335747803567447,high205,13,-0.8486 -high206,CHDScenario1DS30,30,1,0.334456145670721,high206,1,0.2 -high207,CHDScenario15DS5,,15,0.713971198911297,high207,15,-0.16058 -high208,CHDScenario9DS16,,9,0.962277217388221,high208,9,12.62 -high209,CHDScenario13DS63,,13,0.923251983429596,high209,13,-0.8486 -high21,CHDScenario6DS2,,6,0.0465576154642606,high21,6,-1.1039 -high210,CHDScenario3DS70,,3,0.0658448458204028,high210,3,-0.800000000000001 -high211,CHDScenario6DS33,,6,0.921452022941164,high211,6,-1.1039 -high212,CHDScenario5DS47,,5,0.560964506898379,high212,5,-0.3429 -high213,CHDScenario7DS30,,7,0.341236997032229,high213,7,0 -high214,CHDScenario4DS51,,4,0.401116333696506,high214,4,2.1 -high215,CHDScenario12DS65,,12,0.981699616965696,high215,12,-3.159 -high216,CHDScenario15DS43,,15,0.895656607502581,high216,15,-0.16058 -high217,CHDScenario3DS100,,3,0.0896906689484993,high217,3,-0.800000000000001 -high218,CHDScenario9DS98,,9,0.0763621089831896,high218,9,12.62 -high219,CHDScenario9DS36,,9,0.94411981571986,high219,9,12.62 -high22,CHDScenario4DS3,,4,0.0147715389105676,high22,4,2.1 -high220,CHDScenario7DS42,,7,0.487460434746109,high220,7,0 -high221,CHDScenario14DS86,,14,0.752545582003203,high221,14,61.11 -high222,CHDScenario15DS82,,15,0.576516560810694,high222,15,-0.16058 -high223,CHDScenario8DS53,,8,0.887467437375394,high223,8,-1.432 -high224,CHDScenario13DS80,,13,0.446169117357089,high224,13,-0.8486 -high225,CHDScenario7DS73,,7,0.980694434989614,high225,7,0 -high226,CHDScenario1DS61,61,1,0.216406236361318,high226,1,0.2 -high227,CHDScenario11DS78,,11,0.752160200026954,high227,11,10.77 -high228,CHDScenario8DS6,,8,0.28444251251534,high228,8,-1.432 -high229,CHDScenario3DS93,,3,0.20617545478732,high229,3,-0.800000000000001 -high23,CHDScenario16DS55,,16,0.919672667502656,high23,16,1 -high230,CHDScenario11DS70,,11,0.642390029208368,high230,11,10.77 -high231,CHDScenario10DS67,,10,0.77883311711904,high231,10,9.134 -high232,CHDScenario4DS53,,4,0.633108036145099,high232,4,2.1 -high233,CHDScenario11DS83,,11,0.965452546684978,high233,11,10.77 -high234,CHDScenario10DS4,,10,0.174248540208809,high234,10,9.134 -high235,CHDScenario13DS50,,13,0.072621784489297,high235,13,-0.8486 -high236,CHDScenario6DS69,,6,0.342897612153254,high236,6,-1.1039 -high237,CHDScenario5DS59,,5,0.724356582200039,high237,5,-0.3429 -high238,CHDScenario1DS28,28,1,0.702404008512367,high238,1,0.2 -high239,CHDScenario13DS2,,13,0.968282156899366,high239,13,-0.8486 -high24,CHDScenario2DS9,109,2,0.136178493636897,high24,2,0.8 -high240,CHDScenario11DS45,,11,0.720659900850852,high240,11,10.77 -high241,CHDScenario9DS43,,9,0.282120808247818,high241,9,12.62 -high242,CHDScenario4DS20,,4,0.373326705853749,high242,4,2.1 -high243,CHDScenario5DS88,,5,0.557228925225526,high243,5,-0.3429 -high244,CHDScenario6DS4,,6,0.651596935188876,high244,6,-1.1039 -high245,CHDScenario11DS77,,11,0.469294115648728,high245,11,10.77 -high246,CHDScenario7DS95,,7,0.957958210472387,high246,7,0 -high247,CHDScenario5DS68,,5,0.232994683466242,high247,5,-0.3429 -high248,CHDScenario13DS48,,13,0.867873692045976,high248,13,-0.8486 -high249,CHDScenario7DS23,,7,0.230497819207704,high249,7,0 -high25,CHDScenario1DS94,94,1,0.179510394816754,high25,1,0.2 -high250,CHDScenario15DS39,,15,0.62039325280469,high250,15,-0.16058 -high251,CHDScenario9DS67,,9,0.310840714033791,high251,9,12.62 -high252,CHDScenario16DS7,,16,0.380364656234924,high252,16,1 -high253,CHDScenario6DS77,,6,0.546548041750014,high253,6,-1.1039 -high254,CHDScenario7DS16,,7,0.38179389895116,high254,7,0 -high255,CHDScenario8DS48,,8,0.335026866010317,high255,8,-1.432 -high256,CHDScenario5DS12,,5,0.419734772786803,high256,5,-0.3429 -high257,CHDScenario7DS85,,7,0.331805523401503,high257,7,0 -high258,CHDScenario3DS56,,3,0.210365728373295,high258,3,-0.800000000000001 -high259,CHDScenario15DS83,,15,0.337317617300555,high259,15,-0.16058 -high26,CHDScenario8DS21,,8,0.466574949159229,high26,8,-1.432 -high260,CHDScenario8DS52,,8,0.670035310733492,high260,8,-1.432 -high261,CHDScenario7DS51,,7,0.195722729933706,high261,7,0 -high262,CHDScenario4DS81,,4,0.858938828696149,high262,4,2.1 -high263,CHDScenario14DS59,,14,0.836219243058524,high263,14,61.11 -high264,CHDScenario10DS15,,10,0.506167315203539,high264,10,9.134 -high265,CHDScenario10DS70,,10,0.848713202503108,high265,10,9.134 -high266,CHDScenario7DS55,,7,0.223481644248209,high266,7,0 -high267,CHDScenario3DS9,,3,0.0492709840749667,high267,3,-0.800000000000001 -high268,CHDScenario14DS95,,14,0.580021653102126,high268,14,61.11 -high269,CHDScenario10DS27,,10,0.926391893120475,high269,10,9.134 -high27,CHDScenario9DS74,,9,0.827631366813395,high27,9,12.62 -high270,CHDScenario5DS9,,5,0.922056072322188,high270,5,-0.3429 -high271,CHDScenario9DS28,,9,0.343511755319526,high271,9,12.62 -high272,CHDScenario8DS77,,8,0.495556230604372,high272,8,-1.432 -high273,CHDScenario12DS38,,12,0.277961854958125,high273,12,-3.159 -high274,CHDScenario11DS4,,11,0.0765177452933951,high274,11,10.77 -high275,CHDScenario9DS52,,9,0.349508193919684,high275,9,12.62 -high276,CHDScenario9DS92,,9,0.638178086961129,high276,9,12.62 -high277,CHDScenario6DS92,,6,0.0456576687488336,high277,6,-1.1039 -high278,CHDScenario12DS9,,12,0.0932370394856763,high278,12,-3.159 -high279,CHDScenario13DS39,,13,0.71288893290764,high279,13,-0.8486 -high28,CHDScenario8DS76,,8,0.0907353935808295,high28,8,-1.432 -high280,CHDScenario3DS31,,3,0.152206406285797,high280,3,-0.800000000000001 -high281,CHDScenario16DS82,,16,0.96159556461531,high281,16,1 -high282,CHDScenario6DS56,,6,0.834804356853768,high282,6,-1.1039 -high283,CHDScenario6DS8,,6,0.510863451926649,high283,6,-1.1039 -high284,CHDScenario10DS43,,10,0.505592496920344,high284,10,9.134 -high285,CHDScenario3DS12,,3,0.987992955772065,high285,3,-0.800000000000001 -high286,CHDScenario9DS45,,9,0.979797027967632,high286,9,12.62 -high287,CHDScenario4DS57,,4,0.281194301830872,high287,4,2.1 -high288,CHDScenario10DS75,,10,0.163899942826918,high288,10,9.134 -high289,CHDScenario14DS70,,14,0.1925924851246,high289,14,61.11 -high29,CHDScenario4DS72,,4,0.516719526730656,high29,4,2.1 -high290,CHDScenario5DS27,,5,0.644848209330111,high290,5,-0.3429 -high291,CHDScenario13DS46,,13,0.747655258752767,high291,13,-0.8486 -high292,CHDScenario12DS50,,12,0.346849313446997,high292,12,-3.159 -high293,CHDScenario5DS1,,5,0.235132027009392,high293,5,-0.3429 -high294,CHDScenario15DS75,,15,0.347505466942679,high294,15,-0.16058 -high295,CHDScenario2DS1,101,2,0.220531553539279,high295,2,0.8 -high296,CHDScenario10DS10,,10,0.417542213261394,high296,10,9.134 -high297,CHDScenario3DS87,,3,0.0512930837672926,high297,3,-0.800000000000001 -high298,CHDScenario10DS9,,10,0.825266407056857,high298,10,9.134 -high299,CHDScenario6DS5,,6,0.634752451184856,high299,6,-1.1039 -high3,CHDScenario6DS3,,6,0.15352984787631,high3,6,-1.1039 -high30,CHDScenario9DS75,,9,0.854927332576397,high30,9,12.62 -high300,CHDScenario3DS23,,3,0.205226212905997,high300,3,-0.800000000000001 -high301,CHDScenario9DS49,,9,0.718254876320544,high301,9,12.62 -high302,CHDScenario14DS82,,14,0.329486006091177,high302,14,61.11 -high303,CHDScenario5DS36,,5,0.926502939399835,high303,5,-0.3429 -high304,CHDScenario10DS50,,10,0.223396991812696,high304,10,9.134 -high305,CHDScenario12DS29,,12,0.654217455123628,high305,12,-3.159 -high306,CHDScenario6DS64,,6,0.742693812645761,high306,6,-1.1039 -high307,CHDScenario11DS51,,11,0.567387502890601,high307,11,10.77 -high308,CHDScenario7DS35,,7,0.800840814903132,high308,7,0 -high309,CHDScenario12DS62,,12,0.0412755238545367,high309,12,-3.159 -high31,CHDScenario5DS25,,5,0.171968386743747,high31,5,-0.3429 -high310,CHDScenario10DS42,,10,0.0805145763600996,high310,10,9.134 -high311,CHDScenario12DS69,,12,0.509139545307314,high311,12,-3.159 -high312,CHDScenario4DS41,,4,0.213069290667434,high312,4,2.1 -high313,CHDScenario12DS93,,12,0.614305997661501,high313,12,-3.159 -high314,CHDScenario4DS62,,4,0.34683710500891,high314,4,2.1 -high315,CHDScenario15DS6,,15,0.780053259498275,high315,15,-0.16058 -high316,CHDScenario2DS34,134,2,0.629789137440786,high316,2,0.8 -high317,CHDScenario11DS5,,11,0.479257079638974,high317,11,10.77 -high318,CHDScenario6DS27,,6,0.169933667496581,high318,6,-1.1039 -high319,CHDScenario8DS50,,8,0.541276968412079,high319,8,-1.432 -high32,CHDScenario13DS67,,13,0.527190644273057,high32,13,-0.8486 -high320,CHDScenario15DS38,,15,0.173738702572525,high320,15,-0.16058 -high321,CHDScenario3DS33,,3,0.123055429167686,high321,3,-0.800000000000001 -high322,CHDScenario13DS28,,13,0.13714961465808,high322,13,-0.8486 -high323,CHDScenario14DS74,,14,0.834274892302218,high323,14,61.11 -high324,CHDScenario4DS48,,4,0.719886127403484,high324,4,2.1 -high325,CHDScenario16DS10,,16,0.37519333830776,high325,16,1 -high326,CHDScenario7DS21,,7,0.506516100438446,high326,7,0 -high327,CHDScenario3DS97,,3,0.00633671050626183,high327,3,-0.800000000000001 -high328,CHDScenario9DS93,,9,0.846816726618093,high328,9,12.62 -high329,CHDScenario15DS55,,15,0.00371004957640853,high329,15,-0.16058 -high33,CHDScenario13DS22,,13,0.912676474638168,high33,13,-0.8486 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-high344,CHDScenario12DS73,,12,0.318863718660718,high344,12,-3.159 -high345,CHDScenario16DS39,,16,0.342641840157336,high345,16,1 -high346,CHDScenario6DS88,,6,0.263027735019244,high346,6,-1.1039 -high347,CHDScenario11DS6,,11,0.538863030837184,high347,11,10.77 -high348,CHDScenario12DS52,,12,0.118219183701744,high348,12,-3.159 -high349,CHDScenario7DS41,,7,0.626727062259228,high349,7,0 -high35,CHDScenario8DS49,,8,0.422755074625866,high35,8,-1.432 -high350,CHDScenario4DS15,,4,0.237124710187244,high350,4,2.1 -high351,CHDScenario3DS42,,3,0.414693219478036,high351,3,-0.800000000000001 -high352,CHDScenario12DS30,,12,0.0728889698713707,high352,12,-3.159 -high353,CHDScenario4DS88,,4,0.412897049969469,high353,4,2.1 -high354,CHDScenario16DS53,,16,0.821384323945324,high354,16,1 -high355,CHDScenario13DS3,,13,0.00751826836826131,high355,13,-0.8486 -high356,CHDScenario6DS28,,6,0.365657884319821,high356,6,-1.1039 -high357,CHDScenario6DS96,,6,0.673098070644967,high357,6,-1.1039 -high358,CHDScenario4DS2,,4,0.00531836750146175,high358,4,2.1 -high359,CHDScenario11DS56,,11,0.509506360102211,high359,11,10.77 -high36,CHDScenario1DS99,99,1,0.655929296330303,high36,1,0.2 -high360,CHDScenario8DS70,,8,0.470622146407494,high360,8,-1.432 -high361,CHDScenario16DS9,,16,0.458161998513913,high361,16,1 -high362,CHDScenario11DS47,,11,0.726952658599691,high362,11,10.77 -high363,CHDScenario4DS92,,4,0.400240447100632,high363,4,2.1 -high364,CHDScenario9DS56,,9,0.0463627202753441,high364,9,12.62 -high365,CHDScenario5DS97,,5,0.263242518147115,high365,5,-0.3429 -high366,CHDScenario1DS92,92,1,0.200753658699129,high366,1,0.2 -high367,CHDScenario6DS10,,6,0.695907458479353,high367,6,-1.1039 -high368,CHDScenario13DS56,,13,0.3392403923062,high368,13,-0.8486 -high369,CHDScenario16DS61,,16,0.299116583768855,high369,16,1 -high37,CHDScenario6DS22,,6,0.0387990354701794,high37,6,-1.1039 -high370,CHDScenario10DS1,,10,0.47254681651088,high370,10,9.134 -high371,CHDScenario6DS89,,6,0.0193127606977482,high371,6,-1.1039 -high372,CHDScenario13DS62,,13,0.709826308982838,high372,13,-0.8486 -high373,CHDScenario13DS1,,13,0.615728871211429,high373,13,-0.8486 -high374,CHDScenario2DS91,191,2,0.54384775604434,high374,2,0.8 -high375,CHDScenario1DS21,21,1,0.98221194104477,high375,1,0.2 -high376,CHDScenario4DS17,,4,0.118169919424968,high376,4,2.1 -high377,CHDScenario2DS40,140,2,0.391102103077305,high377,2,0.8 -high378,CHDScenario3DS25,,3,0.10398657113445,high378,3,-0.800000000000001 -high379,CHDScenario14DS65,,14,0.60682187385648,high379,14,61.11 -high38,CHDScenario12DS10,,12,0.680136889020678,high38,12,-3.159 -high380,CHDScenario12DS48,,12,0.354850062717928,high380,12,-3.159 -high381,CHDScenario12DS4,,12,0.332012907396167,high381,12,-3.159 -high382,CHDScenario1DS77,77,1,0.512054727439169,high382,1,0.2 -high383,CHDScenario8DS18,,8,0.801822825827911,high383,8,-1.432 -high384,CHDScenario13DS83,,13,0.93189466099946,high384,13,-0.8486 -high385,CHDScenario13DS84,,13,0.403851359690104,high385,13,-0.8486 -high386,CHDScenario14DS50,,14,0.0591187768755519,high386,14,61.11 -high387,CHDScenario7DS19,,7,0.934655098043292,high387,7,0 -high388,CHDScenario12DS25,,12,0.0320206943437924,high388,12,-3.159 -high389,CHDScenario9DS63,,9,0.828684199303609,high389,9,12.62 -high39,CHDScenario14DS41,,14,0.75050849312565,high39,14,61.11 -high390,CHDScenario2DS25,125,2,0.932955845334092,high390,2,0.8 -high391,CHDScenario12DS70,,12,0.426762292389681,high391,12,-3.159 -high392,CHDScenario8DS72,,8,0.241181575108149,high392,8,-1.432 -high393,CHDScenario16DS8,,16,0.752206849075518,high393,16,1 -high394,CHDScenario3DS35,,3,0.55155492187855,high394,3,-0.800000000000001 -high395,CHDScenario1DS76,76,1,0.731056242922791,high395,1,0.2 -high396,CHDScenario8DS26,,8,0.189634897962193,high396,8,-1.432 -high397,CHDScenario6DS94,,6,0.129638721352917,high397,6,-1.1039 -high398,CHDScenario5DS77,,5,0.310316822899619,high398,5,-0.3429 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-high411,CHDScenario11DS20,,11,0.575022373835501,high411,11,10.77 -high412,CHDScenario14DS94,,14,0.662620032888984,high412,14,61.11 -high413,CHDScenario8DS64,,8,0.617953634807047,high413,8,-1.432 -high414,CHDScenario9DS72,,9,0.0776358073712473,high414,9,12.62 -high415,CHDScenario9DS6,,9,0.0113909270238658,high415,9,12.62 -high416,CHDScenario12DS90,,12,0.679785285994858,high416,12,-3.159 -high417,CHDScenario7DS94,,7,0.184197632279343,high417,7,0 -high418,CHDScenario8DS8,,8,0.646278288821242,high418,8,-1.432 -high419,CHDScenario3DS85,,3,0.521444321423902,high419,3,-0.800000000000001 -high42,CHDScenario2DS24,124,2,0.752854187429127,high42,2,0.8 -high420,CHDScenario14DS23,,14,0.265154809561438,high420,14,61.11 -high421,CHDScenario13DS43,,13,0.577241150590723,high421,13,-0.8486 -high422,CHDScenario4DS76,,4,0.19580947576214,high422,4,2.1 -high423,CHDScenario8DS12,,8,0.501947233846495,high423,8,-1.432 -high424,CHDScenario1DS29,29,1,0.49492288861686,high424,1,0.2 -high425,CHDScenario11DS57,,11,0.77632932223172,high425,11,10.77 -high426,CHDScenario1DS73,73,1,0.186908328367206,high426,1,0.2 -high427,CHDScenario7DS100,,7,0.109794051024435,high427,7,0 -high428,CHDScenario5DS62,,5,0.825756941017169,high428,5,-0.3429 -high429,CHDScenario6DS35,,6,0.311934298416174,high429,6,-1.1039 -high43,CHDScenario16DS56,,16,0.176513315048266,high43,16,1 -high430,CHDScenario12DS64,,12,0.991994202187358,high430,12,-3.159 -high431,CHDScenario1DS54,54,1,0.609028437959563,high431,1,0.2 -high432,CHDScenario2DS79,179,2,0.814506372888377,high432,2,0.8 -high433,CHDScenario4DS74,,4,0.962918501271776,high433,4,2.1 -high434,CHDScenario12DS99,,12,0.532270906338333,high434,12,-3.159 -high435,CHDScenario1DS95,95,1,0.419063042192182,high435,1,0.2 -high436,CHDScenario3DS11,,3,0.619135327120338,high436,3,-0.800000000000001 -high437,CHDScenario11DS31,,11,0.105207582894152,high437,11,10.77 -high438,CHDScenario4DS6,,4,0.301247682980413,high438,4,2.1 -high439,CHDScenario9DS65,,9,0.692382348402557,high439,9,12.62 -high44,CHDScenario3DS68,,3,0.296594379717273,high44,3,-0.800000000000001 -high440,CHDScenario14DS85,,14,0.607483633551808,high440,14,61.11 -high441,CHDScenario7DS83,,7,0.723438399491506,high441,7,0 -high442,CHDScenario2DS14,114,2,0.85400468065545,high442,2,0.8 -high443,CHDScenario11DS34,,11,0.167389617839326,high443,11,10.77 -high444,CHDScenario4DS86,,4,0.280445211392525,high444,4,2.1 -high445,CHDScenario3DS41,,3,0.843636914488421,high445,3,-0.800000000000001 -high446,CHDScenario1DS37,37,1,0.529304956247763,high446,1,0.2 -high447,CHDScenario3DS50,,3,0.334951010314578,high447,3,-0.800000000000001 -high448,CHDScenario10DS11,,10,0.298171007384925,high448,10,9.134 -high449,CHDScenario14DS48,,14,0.625530610651249,high449,14,61.11 -high45,CHDScenario8DS9,,8,0.221099376242603,high45,8,-1.432 -high450,CHDScenario16DS28,,16,0.912675414027042,high450,16,1 -high451,CHDScenario4DS43,,4,0.117223442070962,high451,4,2.1 -high452,CHDScenario15DS1,,15,0.988289738644269,high452,15,-0.16058 -high453,CHDScenario15DS94,,15,0.441444052994606,high453,15,-0.16058 -high454,CHDScenario2DS85,185,2,0.752923563551304,high454,2,0.8 -high455,CHDScenario10DS95,,10,0.937141932155285,high455,10,9.134 -high456,CHDScenario8DS81,,8,0.705942142973413,high456,8,-1.432 -high457,CHDScenario15DS68,,15,0.826144810861924,high457,15,-0.16058 -high458,CHDScenario9DS83,,9,0.850787548354836,high458,9,12.62 -high459,CHDScenario10DS65,,10,0.18815048288253,high459,10,9.134 -high46,CHDScenario2DS49,149,2,0.0203252184938297,high46,2,0.8 -high460,CHDScenario13DS8,,13,0.842660350231812,high460,13,-0.8486 -high461,CHDScenario7DS91,,7,0.935501521955297,high461,7,0 -high462,CHDScenario16DS27,,16,0.37354144215162,high462,16,1 -high463,CHDScenario16DS92,,16,0.167883533893119,high463,16,1 -high464,CHDScenario15DS19,,15,0.822597993435922,high464,15,-0.16058 -high465,CHDScenario11DS87,,11,0.45279362140095,high465,11,10.77 -high466,CHDScenario8DS95,,8,0.186975581700568,high466,8,-1.432 -high467,CHDScenario2DS59,159,2,0.152298453838544,high467,2,0.8 -high468,CHDScenario15DS92,,15,0.490336214671949,high468,15,-0.16058 -high469,CHDScenario11DS80,,11,0.326971065783199,high469,11,10.77 -high47,CHDScenario15DS58,,15,0.0343593879541048,high47,15,-0.16058 -high470,CHDScenario10DS41,,10,0.224641469326332,high470,10,9.134 -high471,CHDScenario10DS69,,10,0.0050646651148395,high471,10,9.134 -high472,CHDScenario15DS88,,15,0.640290973322588,high472,15,-0.16058 -high473,CHDScenario3DS94,,3,0.137146799596493,high473,3,-0.800000000000001 -high474,CHDScenario11DS92,,11,0.856550730838865,high474,11,10.77 -high475,CHDScenario7DS46,,7,0.630917966101876,high475,7,0 -high476,CHDScenario16DS19,,16,0.30862330702286,high476,16,1 -high477,CHDScenario7DS50,,7,0.532746110744495,high477,7,0 -high478,CHDScenario8DS85,,8,0.294017861512977,high478,8,-1.432 -high479,CHDScenario10DS96,,10,0.658711808770569,high479,10,9.134 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-high681,CHDScenario11DS99,,11,0.0524056556841293,high681,11,10.77 -high682,CHDScenario15DS34,,15,0.624661285286509,high682,15,-0.16058 -high683,CHDScenario2DS26,126,2,0.520640266289356,high683,2,0.8 -high684,CHDScenario7DS37,,7,0.837388711517977,high684,7,0 -high685,CHDScenario1DS64,64,1,0.774619671802653,high685,1,0.2 -high686,CHDScenario4DS98,,4,0.501499249991032,high686,4,2.1 -high687,CHDScenario15DS86,,15,0.449877453782085,high687,15,-0.16058 -high688,CHDScenario7DS65,,7,0.306186096699739,high688,7,0 -high689,CHDScenario13DS10,,13,0.537526816730564,high689,13,-0.8486 -high69,CHDScenario7DS20,,7,0.0513016901299597,high69,7,0 -high690,CHDScenario1DS7,7,1,0.244272585857868,high690,1,0.2 -high691,CHDScenario15DS3,,15,0.75017051653172,high691,15,-0.16058 -high692,CHDScenario9DS10,,9,0.92378430099773,high692,9,12.62 -high693,CHDScenario12DS56,,12,0.950340118014826,high693,12,-3.159 -high694,CHDScenario2DS73,173,2,0.362685024906761,high694,2,0.8 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-high708,CHDScenario11DS95,,11,0.67655893390484,high708,11,10.77 -high709,CHDScenario14DS32,,14,0.894829203149845,high709,14,61.11 -high71,CHDScenario6DS76,,6,0.219708188634353,high71,6,-1.1039 -high710,CHDScenario2DS95,195,2,0.917329576758797,high710,2,0.8 -high711,CHDScenario9DS35,,9,0.569199612875686,high711,9,12.62 -high712,CHDScenario5DS100,,5,0.0656726140334749,high712,5,-0.3429 -high713,CHDScenario7DS87,,7,0.721245365864678,high713,7,0 -high714,CHDScenario14DS75,,14,0.227091555192397,high714,14,61.11 -high715,CHDScenario10DS91,,10,0.607964141304854,high715,10,9.134 -high716,CHDScenario5DS48,,5,0.405870442446972,high716,5,-0.3429 -high717,CHDScenario8DS30,,8,0.554002814076054,high717,8,-1.432 -high718,CHDScenario16DS72,,16,0.670012358789828,high718,16,1 -high719,CHDScenario16DS4,,16,0.199797488390762,high719,16,1 -high72,CHDScenario9DS1,,9,0.599189936455222,high72,9,12.62 -high720,CHDScenario11DS74,,11,0.567289932166077,high720,11,10.77 -high721,CHDScenario8DS42,,8,0.127865360000894,high721,8,-1.432 -high722,CHDScenario7DS33,,7,0.221700581592784,high722,7,0 -high723,CHDScenario1DS8,8,1,0.254858919981865,high723,1,0.2 -high724,CHDScenario11DS59,,11,0.135596075357567,high724,11,10.77 -high725,CHDScenario10DS12,,10,0.852536204659106,high725,10,9.134 -high726,CHDScenario4DS32,,4,0.274578642821297,high726,4,2.1 -high727,CHDScenario3DS80,,3,0.656464133331184,high727,3,-0.800000000000001 -high728,CHDScenario4DS99,,4,0.191370077576826,high728,4,2.1 -high729,CHDScenario14DS37,,14,0.285183521845223,high729,14,61.11 -high73,CHDScenario14DS47,,14,0.362761753971346,high73,14,61.11 -high730,CHDScenario9DS24,,9,0.369026236693806,high730,9,12.62 -high731,CHDScenario4DS80,,4,0.1704674775577,high731,4,2.1 -high732,CHDScenario3DS92,,3,0.0820412390556989,high732,3,-0.800000000000001 -high733,CHDScenario15DS63,,15,0.952646446706991,high733,15,-0.16058 -high734,CHDScenario14DS68,,14,0.0217157834988839,high734,14,61.11 -high735,CHDScenario2DS74,174,2,0.185788611674984,high735,2,0.8 -high736,CHDScenario2DS21,121,2,0.896566224682918,high736,2,0.8 -high737,CHDScenario16DS17,,16,0.620814575790503,high737,16,1 -high738,CHDScenario4DS77,,4,0.988056147521528,high738,4,2.1 -high739,CHDScenario15DS84,,15,0.0757099604912194,high739,15,-0.16058 -high74,CHDScenario9DS9,,9,0.387058705452185,high74,9,12.62 -high740,CHDScenario8DS27,,8,0.422777011655295,high740,8,-1.432 -high741,CHDScenario1DS14,14,1,0.692823725942663,high741,1,0.2 -high742,CHDScenario7DS29,,7,0.24278844101935,high742,7,0 -high743,CHDScenario13DS36,,13,0.755377433124358,high743,13,-0.8486 -high744,CHDScenario3DS39,,3,0.329488144809774,high744,3,-0.800000000000001 -high745,CHDScenario14DS25,,14,0.0141597443883026,high745,14,61.11 -high746,CHDScenario13DS42,,13,0.776730270347359,high746,13,-0.8486 -high747,CHDScenario12DS84,,12,0.0229251053992707,high747,12,-3.159 -high748,CHDScenario5DS14,,5,0.3701511990593,high748,5,-0.3429 -high749,CHDScenario1DS58,58,1,0.728466920905706,high749,1,0.2 -high75,CHDScenario1DS82,82,1,0.268408905225467,high75,1,0.2 -high750,CHDScenario5DS73,,5,0.870130006907839,high750,5,-0.3429 -high751,CHDScenario15DS40,,15,0.935687055943401,high751,15,-0.16058 -high752,CHDScenario15DS97,,15,0.449854277479489,high752,15,-0.16058 -high753,CHDScenario9DS64,,9,0.288620874251661,high753,9,12.62 -high754,CHDScenario11DS2,,11,0.180462392438315,high754,11,10.77 -high755,CHDScenario1DS52,52,1,0.197454572376847,high755,1,0.2 -high756,CHDScenario4DS47,,4,0.579655182867572,high756,4,2.1 -high757,CHDScenario8DS5,,8,0.565917264428771,high757,8,-1.432 -high758,CHDScenario2DS27,127,2,0.823286630442879,high758,2,0.8 -high759,CHDScenario4DS61,,4,0.0847881832619072,high759,4,2.1 -high76,CHDScenario15DS53,,15,0.336540877609342,high76,15,-0.16058 -high760,CHDScenario7DS4,,7,0.937550064911243,high760,7,0 -high761,CHDScenario7DS92,,7,0.122028400859917,high761,7,0 -high762,CHDScenario14DS6,,14,0.444314286514975,high762,14,61.11 -high763,CHDScenario2DS71,171,2,0.457395331885428,high763,2,0.8 -high764,CHDScenario4DS89,,4,0.354989693484287,high764,4,2.1 -high765,CHDScenario13DS85,,13,0.63464410938023,high765,13,-0.8486 -high766,CHDScenario3DS53,,3,0.255803803517923,high766,3,-0.800000000000001 -high767,CHDScenario9DS13,,9,0.868000944878872,high767,9,12.62 -high768,CHDScenario3DS79,,3,0.919455382292954,high768,3,-0.800000000000001 -high769,CHDScenario1DS27,27,1,0.382806407991808,high769,1,0.2 -high77,CHDScenario12DS3,,12,0.37728905717883,high77,12,-3.159 -high770,CHDScenario16DS91,,16,0.122254174656743,high770,16,1 -high771,CHDScenario3DS99,,3,0.15592444693033,high771,3,-0.800000000000001 -high772,CHDScenario8DS97,,8,0.224847292336106,high772,8,-1.432 -high773,CHDScenario9DS94,,9,0.112019102411632,high773,9,12.62 -high774,CHDScenario15DS89,,15,0.452313115775004,high774,15,-0.16058 -high775,CHDScenario14DS42,,14,0.0503692652375084,high775,14,61.11 -high776,CHDScenario7DS99,,7,0.767562318914684,high776,7,0 -high777,CHDScenario13DS88,,13,0.515319928235432,high777,13,-0.8486 -high778,CHDScenario7DS38,,7,0.206838265111792,high778,7,0 -high779,CHDScenario9DS95,,9,0.736274074254972,high779,9,12.62 -high78,CHDScenario11DS24,,11,0.648507055607204,high78,11,10.77 -high780,CHDScenario4DS52,,4,0.811835165837873,high780,4,2.1 -high781,CHDScenario16DS24,,16,0.310105132364025,high781,16,1 -high782,CHDScenario6DS68,,6,0.505241342526009,high782,6,-1.1039 -high783,CHDScenario14DS61,,14,0.54413295044566,high783,14,61.11 -high784,CHDScenario2DS45,145,2,0.278752700263391,high784,2,0.8 -high785,CHDScenario15DS91,,15,0.244298032963612,high785,15,-0.16058 -high786,CHDScenario16DS76,,16,0.302533900659771,high786,16,1 -high787,CHDScenario14DS21,,14,0.112993454927324,high787,14,61.11 -high788,CHDScenario3DS60,,3,0.634066797399059,high788,3,-0.800000000000001 -high789,CHDScenario6DS83,,6,0.803363055412584,high789,6,-1.1039 -high79,CHDScenario6DS70,,6,0.677013765441512,high79,6,-1.1039 -high790,CHDScenario3DS74,,3,0.314452766606684,high790,3,-0.800000000000001 -high791,CHDScenario13DS6,,13,0.100965349262648,high791,13,-0.8486 -high792,CHDScenario11DS14,,11,0.104821611709607,high792,11,10.77 -high793,CHDScenario8DS74,,8,0.938095779682046,high793,8,-1.432 -high794,CHDScenario16DS54,,16,0.445299351021155,high794,16,1 -high795,CHDScenario5DS37,,5,0.928119959639692,high795,5,-0.3429 -high796,CHDScenario9DS76,,9,0.954393378463995,high796,9,12.62 -high797,CHDScenario16DS63,,16,0.385442638928641,high797,16,1 -high798,CHDScenario3DS36,,3,0.445919499825526,high798,3,-0.800000000000001 -high799,CHDScenario3DS26,,3,0.350297597246707,high799,3,-0.800000000000001 -high8,CHDScenario1DS81,81,1,0.0512980462931635,high8,1,0.2 -high80,CHDScenario9DS2,,9,0.347894451453485,high80,9,12.62 -high800,CHDScenario1DS35,35,1,0.147718001385815,high800,1,0.2 -high801,CHDScenario5DS72,,5,0.719125469186497,high801,5,-0.3429 -high802,CHDScenario7DS22,,7,0.10414392416151,high802,7,0 -high803,CHDScenario3DS22,,3,0.885069696331921,high803,3,-0.800000000000001 -high804,CHDScenario11DS79,,11,0.670200468330855,high804,11,10.77 -high805,CHDScenario9DS55,,9,0.202731243575516,high805,9,12.62 -high806,CHDScenario11DS43,,11,0.549706816986918,high806,11,10.77 -high807,CHDScenario12DS88,,12,0.338014265921844,high807,12,-3.159 -high808,CHDScenario14DS66,,14,0.0234736073406148,high808,14,61.11 -high809,CHDScenario9DS8,,9,0.973248185412315,high809,9,12.62 -high81,CHDScenario15DS98,,15,0.854492868479733,high81,15,-0.16058 -high810,CHDScenario12DS100,,12,0.896491515427229,high810,12,-3.159 -high811,CHDScenario16DS74,,16,0.0267311562433121,high811,16,1 -high812,CHDScenario2DS69,169,2,0.913078882391551,high812,2,0.8 -high813,CHDScenario10DS40,,10,0.678416191456558,high813,10,9.134 -high814,CHDScenario10DS63,,10,0.211125443697878,high814,10,9.134 -high815,CHDScenario1DS66,66,1,0.0408603930149198,high815,1,0.2 -high816,CHDScenario12DS23,,12,0.935369306692285,high816,12,-3.159 -high817,CHDScenario8DS46,,8,0.638894038873403,high817,8,-1.432 -high818,CHDScenario5DS46,,5,0.787078560107706,high818,5,-0.3429 -high819,CHDScenario10DS44,,10,0.964009089000141,high819,10,9.134 -high82,CHDScenario8DS37,,8,0.688888730738202,high82,8,-1.432 -high820,CHDScenario5DS26,,5,0.326105699108475,high820,5,-0.3429 -high821,CHDScenario5DS52,,5,0.530789659585418,high821,5,-0.3429 -high822,CHDScenario2DS10,110,2,0.465860776108495,high822,2,0.8 -high823,CHDScenario7DS98,,7,0.563015000208538,high823,7,0 -high824,CHDScenario14DS2,,14,0.431660729066252,high824,14,61.11 -high825,CHDScenario11DS86,,11,0.0156580073435701,high825,11,10.77 -high826,CHDScenario12DS91,,12,0.966921320845873,high826,12,-3.159 -high827,CHDScenario16DS93,,16,0.113658625452351,high827,16,1 -high828,CHDScenario10DS57,,10,0.713716585654825,high828,10,9.134 -high829,CHDScenario16DS100,,16,0.22897036538674,high829,16,1 -high83,CHDScenario6DS46,,6,0.807845916852803,high83,6,-1.1039 -high830,CHDScenario16DS97,,16,0.678847128687209,high830,16,1 -high831,CHDScenario6DS72,,6,0.788048034633308,high831,6,-1.1039 -high832,CHDScenario3DS4,,3,0.955741937884348,high832,3,-0.800000000000001 -high833,CHDScenario2DS68,168,2,0.316107522164689,high833,2,0.8 -high834,CHDScenario5DS23,,5,0.662113109513945,high834,5,-0.3429 -high835,CHDScenario2DS78,178,2,0.385905695222863,high835,2,0.8 -high836,CHDScenario10DS81,,10,0.850684820858813,high836,10,9.134 -high837,CHDScenario8DS62,,8,0.0837777734543935,high837,8,-1.432 -high838,CHDScenario9DS71,,9,0.712451630665435,high838,9,12.62 -high839,CHDScenario13DS32,,13,0.965762753977259,high839,13,-0.8486 -high84,CHDScenario2DS97,,2,0.391556886885224,high84,2,0.8 -high840,CHDScenario9DS87,,9,0.126946012182642,high840,9,12.62 -high841,CHDScenario10DS38,,10,0.782037950309684,high841,10,9.134 -high842,CHDScenario11DS26,,11,0.838658220585638,high842,11,10.77 -high843,CHDScenario14DS62,,14,0.878357355507151,high843,14,61.11 -high844,CHDScenario13DS97,,13,0.672500478754116,high844,13,-0.8486 -high845,CHDScenario7DS7,,7,0.634378857640447,high845,7,0 -high846,CHDScenario15DS76,,15,0.835031375268781,high846,15,-0.16058 -high847,CHDScenario5DS86,,5,0.432795585920936,high847,5,-0.3429 -high848,CHDScenario8DS59,,8,0.186800716070267,high848,8,-1.432 -high849,CHDScenario5DS89,,5,0.950100439302506,high849,5,-0.3429 -high85,CHDScenario16DS35,,16,0.666142992081819,high85,16,1 -high850,CHDScenario7DS72,,7,0.949892110602131,high850,7,0 -high851,CHDScenario8DS28,,8,0.0351634649579916,high851,8,-1.432 -high852,CHDScenario7DS74,,7,0.884662729414812,high852,7,0 -high853,CHDScenario3DS67,,3,0.278880688918355,high853,3,-0.800000000000001 -high854,CHDScenario14DS60,,14,0.913454000058997,high854,14,61.11 -high855,CHDScenario2DS11,111,2,0.437491711965051,high855,2,0.8 -high856,CHDScenario4DS96,,4,0.0688269026668384,high856,4,2.1 -high857,CHDScenario2DS93,193,2,0.584742331346704,high857,2,0.8 -high858,CHDScenario16DS14,,16,0.625871542274197,high858,16,1 -high859,CHDScenario6DS45,,6,0.556153679897265,high859,6,-1.1039 -high86,CHDScenario13DS66,,13,0.959784166681595,high86,13,-0.8486 -high860,CHDScenario3DS43,,3,0.539410684851545,high860,3,-0.800000000000001 -high861,CHDScenario14DS24,,14,0.979008126981468,high861,14,61.11 -high862,CHDScenario13DS54,,13,0.443417250274613,high862,13,-0.8486 -high863,CHDScenario14DS38,,14,0.817125809637646,high863,14,61.11 -high864,CHDScenario2DS31,131,2,0.426939054431085,high864,2,0.8 -high865,CHDScenario2DS84,184,2,0.449888162203684,high865,2,0.8 -high866,CHDScenario7DS11,,7,0.814694722197106,high866,7,0 -high867,CHDScenario6DS16,,6,0.839719877037148,high867,6,-1.1039 -high868,CHDScenario16DS36,,16,0.748605656770252,high868,16,1 -high869,CHDScenario5DS33,,5,0.185932263855089,high869,5,-0.3429 -high87,CHDScenario4DS63,,4,0.0576266220641126,high87,4,2.1 -high870,CHDScenario12DS8,,12,0.0873616984567972,high870,12,-3.159 -high871,CHDScenario2DS3,103,2,0.47456661617587,high871,2,0.8 -high872,CHDScenario15DS78,,15,0.0211953492328103,high872,15,-0.16058 -high873,CHDScenario12DS47,,12,0.086765740206416,high873,12,-3.159 -high874,CHDScenario15DS67,,15,0.456430497021075,high874,15,-0.16058 -high875,CHDScenario6DS79,,6,0.460602796385231,high875,6,-1.1039 -high876,CHDScenario12DS53,,12,0.305263031891324,high876,12,-3.159 -high877,CHDScenario5DS16,,5,0.565811611822713,high877,5,-0.3429 -high878,CHDScenario14DS98,,14,0.602817437664045,high878,14,61.11 -high879,CHDScenario5DS83,,5,0.0266511221801669,high879,5,-0.3429 -high88,CHDScenario10DS89,,10,0.428824082593164,high88,10,9.134 -high880,CHDScenario5DS20,,5,0.426910554586863,high880,5,-0.3429 -high881,CHDScenario14DS76,,14,0.104078214512864,high881,14,61.11 -high882,CHDScenario3DS2,,3,0.573823681619058,high882,3,-0.800000000000001 -high883,CHDScenario16DS88,,16,0.388397497828805,high883,16,1 -high884,CHDScenario16DS79,,16,0.535979622165434,high884,16,1 -high885,CHDScenario14DS7,,14,0.166162543814784,high885,14,61.11 -high886,CHDScenario4DS4,,4,0.485860854219741,high886,4,2.1 -high887,CHDScenario5DS71,,5,0.222142752483032,high887,5,-0.3429 -high888,CHDScenario5DS84,,5,0.612555413931773,high888,5,-0.3429 -high889,CHDScenario4DS14,,4,0.936633949088139,high889,4,2.1 -high89,CHDScenario14DS78,,14,0.314344199064776,high89,14,61.11 -high890,CHDScenario9DS11,,9,0.766447797171323,high890,9,12.62 -high891,CHDScenario13DS41,,13,0.27897183325326,high891,13,-0.8486 -high892,CHDScenario3DS78,,3,0.0586195321327355,high892,3,-0.800000000000001 -high893,CHDScenario9DS68,,9,0.525877987736434,high893,9,12.62 -high894,CHDScenario6DS55,,6,0.168055052648472,high894,6,-1.1039 -high895,CHDScenario12DS13,,12,0.45832333304505,high895,12,-3.159 -high896,CHDScenario14DS92,,14,0.585106341904135,high896,14,61.11 -high897,CHDScenario16DS33,,16,0.21944712479478,high897,16,1 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-high965,CHDScenario16DS95,,16,0.837527470602147,high965,16,1 -high966,CHDScenario7DS93,,7,0.641667326759395,high966,7,0 -high967,CHDScenario4DS38,,4,0.329752723218618,high967,4,2.1 -high968,CHDScenario4DS16,,4,0.136048611191669,high968,4,2.1 -high969,CHDScenario13DS47,,13,0.626922690555545,high969,13,-0.8486 -high97,CHDScenario13DS9,,13,0.656203898913227,high97,13,-0.8486 -high970,CHDScenario11DS76,,11,0.288187471008011,high970,11,10.77 -high971,CHDScenario6DS95,,6,0.340351336061102,high971,6,-1.1039 -high972,CHDScenario1DS9,9,1,0.633249639187283,high972,1,0.2 -high973,CHDScenario11DS22,,11,0.382381797813203,high973,11,10.77 -high974,CHDScenario15DS15,,15,0.556193252604296,high974,15,-0.16058 -high975,CHDScenario5DS22,,5,0.737401653301171,high975,5,-0.3429 -high976,CHDScenario13DS31,,13,0.329194133849397,high976,13,-0.8486 -high977,CHDScenario11DS36,,11,0.655502824271342,high977,11,10.77 -high978,CHDScenario8DS58,,8,0.134094330323829,high978,8,-1.432 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-high992,CHDScenario8DS96,,8,0.0269361464851964,high992,8,-1.432 -high993,CHDScenario2DS23,123,2,0.213920024542569,high993,2,0.8 -high994,CHDScenario10DS37,,10,0.644919600481259,high994,10,9.134 -high995,CHDScenario16DS40,,16,0.661788990167878,high995,16,1 -high996,CHDScenario11DS1,,11,0.332025617041405,high996,11,10.77 -high997,CHDScenario8DS94,,8,0.550907858441263,high997,8,-1.432 -high998,CHDScenario12DS76,,12,0.0569617616789186,high998,12,-3.159 -high999,CHDScenario15DS14,,15,0.715800025389386,high999,15,-0.16058 diff --git a/doc/examples/data/high1.CSV b/doc/examples/data/high1.CSV deleted file mode 100644 index 7ea9b531..00000000 --- a/doc/examples/data/high1.CSV +++ /dev/null @@ -1,1001 +0,0 @@ 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diff --git a/doc/examples/data/high2.CSV b/doc/examples/data/high2.CSV deleted file mode 100644 index 6e2afaa0..00000000 --- a/doc/examples/data/high2.CSV +++ /dev/null @@ -1,2001 +0,0 @@ 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diff --git a/doc/examples/data/high3.CSV b/doc/examples/data/high3.CSV deleted file mode 100644 index b57b1795..00000000 --- a/doc/examples/data/high3.CSV +++ /dev/null @@ -1,1001 +0,0 @@ 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diff --git a/doc/examples/py_double_ml_abtest_no_split_linreg.ipynb b/doc/examples/py_double_ml_abtest_no_split_linreg.ipynb deleted file mode 100644 index bf2be0c9..00000000 --- a/doc/examples/py_double_ml_abtest_no_split_linreg.ipynb +++ /dev/null @@ -1,4059 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "consecutive-cabinet", - "metadata": {}, - "source": [ - "# Python: A/B Testing with DoubleML" - ] - }, - { - "cell_type": "markdown", - "id": "opponent-indonesian", - "metadata": {}, - "source": [ - "\"An\n", - "\n", - "Image Source Freepik http://www.freepik.com, Designed by macrovector\n" - ] - }, - { - "cell_type": "markdown", - "id": "c7c96f88", - "metadata": {}, - "source": [ - "In this notebook, we demontrate exemplarily how the [DoubleML](https://docs.doubleml.org/stable/index.html) package can be used to estimate the causal effect of seeing a new ad design on customers' purchases in a webshop. The [DoubleML](https://docs.doubleml.org/stable/index.html) package for Python and R provides an implementation of the double / debiased machine learning (DML) framework of [Chernozhukov et al. (2018)](https://arxiv.org/abs/1608.00060) and can be used to estimate causal effects based on machine learning (ML) methods.\n", - "\n", - "## A/B Testing\n", - "\n", - "A/B testing is a frequently used framework to perform causal inference in practice. For example, a manager of a webshop might want to optimally adapt the webshop design according to users' preferences. For examle, she might want to estimate the effect of a new ad design, which is displayed on the starting page, on a customer's purchases (in $100\\$$). A/B tests refer to an experimental design in which a certain treatment, for example a new ad design (called \"Version $A$\"), is randomly assigned to groups of individuals, like website visitors or app users. If a user is not \"treated\", i.e., he is not exposed to Version $A$, he sees an alternative design \"Version $B$\" like the old design of the ad. The assignment of the treatment might either be unconditionally random, i.e., randomly assigned to all visitors of the online shop or directed towards specific groups of them. In the latter case, the treatment assignment would be conditional on their characteristics, like their shopping history. For example, a discount might only be granted to customers who already made some purchases in the past.\n", - "\n", - "In general, the goal of the A/B test is to assess whether the treatment has an effect on the outcome variable of interest. In our example, the manager wants to evaluate whether the new ad design changed the monetary value of products purchased (in $100\\$$). Alternative settings of A/B tests refer to improvement of a user experience on a website or estimation of price elasticities. Websites and apps are ideal for running A/B tests because they make it very easy to precisely direct the treatment to visitors and users (or to specific subgroups of them) as well as to collect the data required for evaluation of the intervention.\n", - "\n", - "## Scenario\n", - "\n", - "Let's consider the following stylized scenario. The manager of a webshop is performing an A/B test to estimate the effect a new ad design $A$ has on customers' purchases, $Y$, on average. This effect is called the **A**verage **T**reatment **E**ffect (**ATE**). The treatment is assigned randomly conditional on the visitors' characteristics, which we call $V$. Such characteristics could be collected from a customer's shoppers account, for example. These might include the number of previous purchases, time since the last purchase, length of stay on a page as well as whether a customer has a rewards card, among other characteristics.
\n", - "\n", - "In the following, we use a **D**irected **A**cyclical **G**raph (DAG) to illustrate our assumptions on the causal structure of the scenario. As not only the outcome, but also the treatment is dependent on the individuals characteristics, there are arrows going from $V$ to both $A$ and $Y$. In our example, we also assume that the treatment $A$ is a direct cause of the customers' purchases $Y$.\n", - "\n", - "\n", - "![Scenario illustration with a DAG](figures/DAG.svg)\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "id": "220997c6", - "metadata": {}, - "source": [ - "Let's assume the conditional randomization has been conducted properly, such that a tidy data set has been collected. Now, a data scientist wants to evaluate whether the new ad design causally affected the sales, by using the [DoubleML](https://docs.doubleml.org/stable/index.html) package.\n", - "\n", - "### Why control for individual characteristics?\n", - "\n", - "Before we start the case study, let us briefly address the question why we need to include individual characteristics in our analysis at all. There are mainly two reasons why we want to control for observable characteristics. First, so-called confounders, i.e., variables that have a causal effect on both the treatment variable and the outcome variable, possibly create a bias in our estimate. In order to uncover the true causal effect of the treatment, it is necessary that our causal framework takes all confounding variables into account. Otherwise, the average causal effect of the treatment on the outcome is not identified. A second reason to include individual characteristics is efficiency. The more variation can be explained within our causal framework, the more precise will be the resulting estimate. In practical terms, greater efficiency leads to tighter confidence intervals and smaller standard errors and p-values. This might help to improve the power of A/B tests even if the treatment variable is unconditionally assigned to individuals.\n", - "\n", - "### Why use machine learning to analyze A/B tests?\n", - "\n", - "ML methods have turned out to be very flexible in terms of modeling complex relationships of explanatory variables and dependent variables and, thus, have exhibited a great predictive performance in many applications. In the double machine learning approach ([Chernozhukov et al. (2018)](https://arxiv.org/abs/1608.00060)), ML methods are used for modelling so-called nuisance functions. In terms of the A/B case study considered here, ML tools can be used to flexibly control for confounding variables. For example, a linear parametric specification as in a standard linear regression model might not be correct and, hence, not sufficient to account for the underlying confounding. Moreover, by using powerful ML techniques, the causal model will likely be able to explain a greater share of the total variation and, hence, lead to more precise estimation." - ] - }, - { - "cell_type": "markdown", - "id": "0ec5b0cf", - "metadata": {}, - "source": [ - "## Data \n", - "\n", - "As an illustrative example we use a data set from the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge). In this challenge, a great number of data sets have been generated in a way that they mimic distributional relationships that are found in many economic real data applications. Although the data have not been generated explicitly to address an A/B testing case study, they are well-suited for demonstration purposes. We will focus on one of the many different data genereting processes (DGP) that we picked at random, in this particualar case a data set called `high42`. An advantage of using the synthetic [ACIC 2019 data](https://sites.google.com/view/acic2019datachallenge/data-challenge) is that we know the true average treatment effect which is 0.8 in our data set.\n", - "\n", - "First we load the data." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "e39d4dd0", - "metadata": {}, - "outputs": [], - "source": [ - "import pandas as pd\n", - "\n", - "#fetch_ACIChigh42 needs to be defined\n", - "#df = fetch_ACIChigh42(return_type='DataFrame')\n", - "\n", - "#load code locally\n", - "df = pd.read_csv('data/high42.csv', sep=',', na_values=\".\")\n", - "\n", - "#code can also be loaded using a URL of the data\n", - "#url = 'https://raw.githubusercontent.com/DoubleML/doubleml-hiwi-sandbox/master/case_studies/AB_testing/data/high42.CSV?token=AQWGKQRE57BBRGOCBPSNBJTBD57ZQ'\n", - "#df = pd.read_csv(url)" - ] - }, - { - "cell_type": "markdown", - "id": "11525056-cdec-4916-9cb4-aa4268e99175", - "metadata": {}, - "source": [ - "We see that the data set consists of 1000 observations (= website visitors) and 202 variables. The $Y$ column represents the customers' purchases (in $100\\$$). The treatment variable $A$ is binary with a value 1 indicating that a customer has been exposed to the new ad design (and value 0 otherwise). The remaining 200 columns $V$ represent individual characteristics of the customers." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "10edc74d", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(1000, 202)\n" - ] - } - ], - "source": [ - "print(df.shape)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "6760c009", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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YAV1V2V3V4V5V6V7V8...V191V192V193V194V195V196V197V198V199V200
07.358185110007192.79376923.67695080.185443...1.46283711627.274196004.6839560.565667030.024338
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" - ], - "text/plain": [ - " Y A V1 V2 V3 V4 V5 V6 V7 V8 ... \\\n", - "0 7.358185 1 10 0 0 7 192.793769 23.676950 8 0.185443 ... \n", - "1 8.333672 1 12 0 1 4 199.653596 19.281270 7 0.514842 ... \n", - "2 7.472758 0 14 1 1 2 194.207792 24.589331 5 0.309199 ... \n", - "3 6.502319 1 0 1 0 9 201.838024 25.513918 4 0.160160 ... \n", - "4 7.043758 1 12 0 0 9 201.360443 31.160641 6 0.291976 ... \n", - "\n", - " V191 V192 V193 V194 V195 V196 V197 V198 V199 \\\n", - "0 1.462837 1 1627.274196 0 0 4.683956 0.565667 0 3 \n", - "1 1.330522 1 1661.484439 1 0 6.766661 -0.395402 0 4 \n", - "2 1.384151 1 1658.939293 0 0 5.647794 1.112766 0 0 \n", - "3 1.220303 1 1650.801625 0 0 5.370363 -0.305842 0 4 \n", - "4 1.170094 1 1676.818876 0 0 3.446532 2.440661 0 1 \n", - "\n", - " V200 \n", - "0 0.024338 \n", - "1 0.056518 \n", - "2 0.013442 \n", - "3 0.034632 \n", - "4 0.017514 \n", - "\n", - "[5 rows x 202 columns]" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df.head()" - ] - }, - { - "cell_type": "markdown", - "id": "c6e32feb", - "metadata": {}, - "source": [ - "### Descriptive Statistics\n" - ] - }, - { - "cell_type": "markdown", - "id": "horizontal-hanging", - "metadata": {}, - "source": [ - "Once we loaded the data, we find that the outcome variable, $Y$, is continuous with mean around $7.33$. The treatment variable $A$ is binary with a value of $1$ indicating that a visitor was exposed to the new ad design $A$ as opposed to design $B$ (corresponding to a value of $A$ equal to $1$). The control variables $V$ are a collection of mixed data types, including continuous, discrete and binary variables." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "d14f929c-178b-47fc-8293-29a634194f21", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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YAV1V2V3V4V5V6V7V8...V191V192V193V194V195V196V197V198V199V200
count1000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.000000...1000.0000001000.000001000.0000001000.0000001000.0000001000.0000001000.0000001000.000001000.0000001000.000000
mean7.3312390.4430009.2900000.3770000.6160006.477000200.08875828.0660286.0310000.294206...1.3182090.942001667.4545610.2540000.1740005.804205-0.0769210.294001.6290000.037936
std1.3798520.4969893.8896050.4848770.4866012.8701416.1054089.9209412.4803610.119454...0.2701780.2338644.1919130.4355150.3792992.6558351.0027540.455821.3889880.021688
min3.4350520.0000000.0000000.0000000.0000000.000000183.12306712.0206300.0000000.047160...0.6680930.000001524.2916750.0000000.0000001.097708-3.6446520.000000.0000000.001478
25%6.4055830.0000007.0000000.0000000.0000005.000000195.94156921.2062304.0000000.204260...1.1193691.000001637.6995140.0000000.0000004.065465-0.7513550.000001.0000000.021711
50%7.3352480.00000010.0000000.0000001.0000007.000000199.87611726.2025826.0000000.282867...1.2937901.000001667.7634800.0000000.0000005.236465-0.0910560.000001.0000000.034009
75%8.2718811.00000012.0000001.0000001.0000008.000000204.39806733.0711898.0000000.374078...1.4768281.000001695.9726311.0000000.0000006.8982400.5946471.000002.0000000.049100
max13.1972601.00000020.0000001.0000001.00000015.000000220.58441095.41002014.0000000.706249...2.4486611.000001825.6970961.0000001.00000038.4279742.8326731.000009.0000000.139716
\n", - "

8 rows × 202 columns

\n", - "
" - ], - "text/plain": [ - " Y A V1 V2 V3 \\\n", - "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 \n", - "mean 7.331239 0.443000 9.290000 0.377000 0.616000 \n", - "std 1.379852 0.496989 3.889605 0.484877 0.486601 \n", - "min 3.435052 0.000000 0.000000 0.000000 0.000000 \n", - "25% 6.405583 0.000000 7.000000 0.000000 0.000000 \n", - "50% 7.335248 0.000000 10.000000 0.000000 1.000000 \n", - "75% 8.271881 1.000000 12.000000 1.000000 1.000000 \n", - "max 13.197260 1.000000 20.000000 1.000000 1.000000 \n", - "\n", - " V4 V5 V6 V7 V8 ... \\\n", - "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 ... \n", - "mean 6.477000 200.088758 28.066028 6.031000 0.294206 ... \n", - "std 2.870141 6.105408 9.920941 2.480361 0.119454 ... \n", - "min 0.000000 183.123067 12.020630 0.000000 0.047160 ... \n", - "25% 5.000000 195.941569 21.206230 4.000000 0.204260 ... \n", - "50% 7.000000 199.876117 26.202582 6.000000 0.282867 ... \n", - "75% 8.000000 204.398067 33.071189 8.000000 0.374078 ... \n", - "max 15.000000 220.584410 95.410020 14.000000 0.706249 ... \n", - "\n", - " V191 V192 V193 V194 V195 \\\n", - "count 1000.000000 1000.00000 1000.000000 1000.000000 1000.000000 \n", - "mean 1.318209 0.94200 1667.454561 0.254000 0.174000 \n", - "std 0.270178 0.23386 44.191913 0.435515 0.379299 \n", - "min 0.668093 0.00000 1524.291675 0.000000 0.000000 \n", - "25% 1.119369 1.00000 1637.699514 0.000000 0.000000 \n", - "50% 1.293790 1.00000 1667.763480 0.000000 0.000000 \n", - "75% 1.476828 1.00000 1695.972631 1.000000 0.000000 \n", - "max 2.448661 1.00000 1825.697096 1.000000 1.000000 \n", - "\n", - " V196 V197 V198 V199 V200 \n", - "count 1000.000000 1000.000000 1000.00000 1000.000000 1000.000000 \n", - "mean 5.804205 -0.076921 0.29400 1.629000 0.037936 \n", - "std 2.655835 1.002754 0.45582 1.388988 0.021688 \n", - "min 1.097708 -3.644652 0.00000 0.000000 0.001478 \n", - "25% 4.065465 -0.751355 0.00000 1.000000 0.021711 \n", - "50% 5.236465 -0.091056 0.00000 1.000000 0.034009 \n", - "75% 6.898240 0.594647 1.00000 2.000000 0.049100 \n", - "max 38.427974 2.832673 1.00000 9.000000 0.139716 \n", - "\n", - "[8 rows x 202 columns]" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df.describe()" - ] - }, - { - "cell_type": "markdown", - "id": "d7e45649", - "metadata": {}, - "source": [ - "From the explanatory variables $V1$ to $V200$, 107 variables are continuous, while 95 are integers. From the integer-variables 59 are binary variables. " - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "bde50bfe", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "float64 107\n", - "int64 95\n", - "dtype: int64\n", - "Number of binary variables: 59\n" - ] - } - ], - "source": [ - "print(df.dtypes.value_counts())\n", - "print(\"Number of binary variables:\", len(df[df.columns[df.isin([0,1]).all()]].columns))" - ] - }, - { - "cell_type": "markdown", - "id": "0ce90b4b", - "metadata": {}, - "source": [ - "Let's continue with some visual inspection." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "b4d2dfb4", - "metadata": {}, - "outputs": [], - "source": [ - "# Define the settings for the graphs first\n", - "import seaborn as sns\n", - "sns.set()\n", - "colors = sns.color_palette()\n", - "\n", - "import matplotlib.pyplot as plt\n", - "\n", - "plt.rcParams['figure.figsize'] = 5., 3.75\n", - "sns.set(font_scale=1.5)\n", - "sns.set_style('whitegrid', {'axes.spines.top': False,\n", - " 'axes.spines.bottom': False,\n", - " 'axes.spines.left': False,\n", - " 'axes.spines.right': False})" - ] - }, - { - "cell_type": "markdown", - "id": "11045894", - "metadata": {}, - "source": [ - "The first figure shows that 443 out of the 1000 customers have been exposed to the new ad design." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "2b5037d3", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "df['A'].value_counts().plot(kind='bar', color=colors)\n", - "\n", - "plt.title('Treatment')\n", - "plt.xlabel('A')\n", - "_ = plt.ylabel('count')" - ] - }, - { - "cell_type": "markdown", - "id": "8c2dc825", - "metadata": {}, - "source": [ - "### Unconditional Estimate of ATE" - ] - }, - { - "cell_type": "markdown", - "id": "8da84d00", - "metadata": {}, - "source": [ - "As a first naive estimate, we could calculate the unconditional average treatment effect. In other words, we simply take the difference between $Y$ observed for the customers who have been exposed to the treatment $(A=1)$ and those who haven't been exposed $(A=0)$. As a visualization, we plot the density of the outcome variable conditional on the treatment status to get a first impression on the descriptive relationship of $A$ and $Y$." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "57392f09", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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" - ], - "text/plain": [ - " Y\n", - "A \n", - "0 NaN\n", - "1 1.117603" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df[['A', 'Y']].groupby('A').mean().diff()" - ] - }, - { - "cell_type": "markdown", - "id": "e6f3fa75-a5d4-480c-b627-4b99c6f6afe3", - "metadata": {}, - "source": [ - "The uncoditional effect is around $1.118$. Because we use a simulated data set in this example, we know that the true effect is $0.8$. Therefore the unconditional ATE overestimates the true effect, because it does not account for individual characteristics. In order to get an estimation on the ATE that explicitly takes the confounding variables $V$ into account, we apply the [DoubleML](https://docs.doubleml.org/stable/index.html) package in the next section." - ] - }, - { - "cell_type": "markdown", - "id": "9e21e9bb", - "metadata": {}, - "source": [ - "## Estimate ATE with the `DoubleML` package" - ] - }, - { - "cell_type": "markdown", - "id": "19830a0a", - "metadata": {}, - "source": [ - "Let’s use the package [DoubleML](https://docs.doubleml.org/stable/index.html) to estimate the average treatment effect of the new ad design on the value of customers' purchases. First, the required packages are imported." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "afaf4106", - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import pandas as pd\n", - "import doubleml as dml\n", - "\n", - "from sklearn.linear_model import LinearRegression\n", - "from sklearn.linear_model import LogisticRegression\n", - "from sklearn.linear_model import LassoCV, LogisticRegressionCV\n", - "from sklearn.ensemble import RandomForestClassifier, RandomForestRegressor\n", - "from sklearn.preprocessing import StandardScaler\n", - "from sklearn.pipeline import make_pipeline\n", - "from sklearn.metrics import mean_squared_error\n", - "from sklearn.metrics import log_loss\n", - "from xgboost import XGBClassifier, XGBRegressor\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import scipy.stats as stats" - ] - }, - { - "cell_type": "markdown", - "id": "49242003", - "metadata": {}, - "source": [ - "### The Data Backend: `DoubleMLData`" - ] - }, - { - "cell_type": "markdown", - "id": "3653b53a", - "metadata": {}, - "source": [ - "To start our analysis, we initialize the data backend from the previously loaded data set, i.e., we create a new instance of a [DoubleMLData](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLData.html#doubleml.DoubleMLData) object. During initialization, we specify the roles of the variables in the data set, i.e., in our example the outcome variable $Y$ via the parameter `y_col`, the treatment variable $A$ via `d_cols` and the confounding variables $V$ via `x_cols`." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "abdd10b7", - "metadata": {}, - "outputs": [], - "source": [ - "# Specify explanatory variables for data-backend\n", - "features_base = list(df.columns.values)[2:]\n", - "\n", - "# Initialize DoubleMLData (data-backend of DoubleML)\n", - "data_dml = dml.DoubleMLData(df,\n", - " y_col='Y',\n", - " d_cols='A',\n", - " x_cols=features_base)" - ] - }, - { - "cell_type": "markdown", - "id": "5800ca50-c293-4266-8dd7-00fadcea8d51", - "metadata": {}, - "source": [ - "We can print the data-backend to see the variables, which we have assigned as outcome, treatment and controls." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "37b9bd8a", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "================== DoubleMLData Object ==================\n", - "\n", - "------------------ Data summary ------------------\n", - "Outcome variable: Y\n", - "Treatment variable(s): ['A']\n", - "Covariates: ['V1', 'V2', 'V3', 'V4', 'V5', 'V6', 'V7', 'V8', 'V9', 'V10', 'V11', 'V12', 'V13', 'V14', 'V15', 'V16', 'V17', 'V18', 'V19', 'V20', 'V21', 'V22', 'V23', 'V24', 'V25', 'V26', 'V27', 'V28', 'V29', 'V30', 'V31', 'V32', 'V33', 'V34', 'V35', 'V36', 'V37', 'V38', 'V39', 'V40', 'V41', 'V42', 'V43', 'V44', 'V45', 'V46', 'V47', 'V48', 'V49', 'V50', 'V51', 'V52', 'V53', 'V54', 'V55', 'V56', 'V57', 'V58', 'V59', 'V60', 'V61', 'V62', 'V63', 'V64', 'V65', 'V66', 'V67', 'V68', 'V69', 'V70', 'V71', 'V72', 'V73', 'V74', 'V75', 'V76', 'V77', 'V78', 'V79', 'V80', 'V81', 'V82', 'V83', 'V84', 'V85', 'V86', 'V87', 'V88', 'V89', 'V90', 'V91', 'V92', 'V93', 'V94', 'V95', 'V96', 'V97', 'V98', 'V99', 'V100', 'V101', 'V102', 'V103', 'V104', 'V105', 'V106', 'V107', 'V108', 'V109', 'V110', 'V111', 'V112', 'V113', 'V114', 'V115', 'V116', 'V117', 'V118', 'V119', 'V120', 'V121', 'V122', 'V123', 'V124', 'V125', 'V126', 'V127', 'V128', 'V129', 'V130', 'V131', 'V132', 'V133', 'V134', 'V135', 'V136', 'V137', 'V138', 'V139', 'V140', 'V141', 'V142', 'V143', 'V144', 'V145', 'V146', 'V147', 'V148', 'V149', 'V150', 'V151', 'V152', 'V153', 'V154', 'V155', 'V156', 'V157', 'V158', 'V159', 'V160', 'V161', 'V162', 'V163', 'V164', 'V165', 'V166', 'V167', 'V168', 'V169', 'V170', 'V171', 'V172', 'V173', 'V174', 'V175', 'V176', 'V177', 'V178', 'V179', 'V180', 'V181', 'V182', 'V183', 'V184', 'V185', 'V186', 'V187', 'V188', 'V189', 'V190', 'V191', 'V192', 'V193', 'V194', 'V195', 'V196', 'V197', 'V198', 'V199', 'V200']\n", - "Instrument variable(s): None\n", - "No. Observations: 1000\n", - "\n", - "------------------ DataFrame info ------------------\n", - "\n", - "RangeIndex: 1000 entries, 0 to 999\n", - "Columns: 202 entries, Y to V200\n", - "dtypes: float64(107), int64(95)\n", - "memory usage: 1.5 MB\n", - "\n" - ] - } - ], - "source": [ - "print(data_dml)" - ] - }, - { - "cell_type": "markdown", - "id": "714346b8-90dd-4f15-b880-d71f4f60b04e", - "metadata": {}, - "source": [ - "## The Inference Problem and Choosing an Appropriate Model\n", - "\n", - "The inference problem is to determine the causal effect of seeing the new ad design $A$ on a customer's purchases $Y$ once we control for individual characteristics $V$. In our example, we are interested in the average treatment effect. Basically, there are two causal models available in [DoubleMLData](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLData.html#doubleml.DoubleMLData) that can be used to estimate the ATE.\n", - "\n", - "The so-called interactive regression model (IRM) called by [DoubleMLIRM](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLIRM.html) is a flexible (nonparametric) model to estimate this causal quantity. The model does not impose functional form restrictions on the underlying regression relationships, for example, linearity or additivity as in a standard linear regression model. This means that the model hosts heterogeneous treatment effects, i.e., account for variation in the effect of the new ad design across customers. Moreover, it is possible to also estimate other causal parameters with the IRM, for example, the average treatment effect on the treated (= those customers who have been exposed to the new ad), which might be of interest too.\n", - "\n", - "The second causal model that can be used here is the partially linear regression model (PLR). The PLR incorporates stronger assumptions, for example, that the treatment effect is additive and constant, i.e., in the model it is assumed that the effect does not very across individuals. We will start with the IRM and include the PLR estimates at the end of the notebook." - ] - }, - { - "cell_type": "markdown", - "id": "9e798e44-8fc8-4c93-9cfb-2d3ad7486dc0", - "metadata": {}, - "source": [ - "## 1. Interactive Regression Model (IRM)\n", - "\n", - "We briefly introduce the [Interactive Regression Model](https://docs.doubleml.org/stable/guide/models.html#interactive-regression-model-irm) (IRM) where the main regression relationship of interest is provided by\n", - "\n", - "$$Y = g_0(D, X) + U, \\quad E(U | X, D) = 0,$$\n", - "\n", - "where the treatment variable is binary, $D \\in \\lbrace 0,1 \\rbrace$. We consider estimation of the average treatment effect (ATE):\n", - "\n", - "$$\\theta_0 = \\mathbb{E}[g_0(1, X) - g_0(0,X)],$$\n", - "\n", - "when treatment effects are fully heterogeneous. In order to be able to use ML methods, the estimation framework generally requires a property called \"double robustness\" or \"Neyman orthogonality\". In the IRM, double robustness can be achieved by including the first-stage estimation\n", - "\n", - "$$D = m_0(X) + V, \\quad E(V | X) = 0,$$\n", - "\n", - "which amounts to estimation of the propensity score, i.e., the probability that a customer is exposed to the treatment provided her observed characteristics. Both predictions are then combined in [the doubly robust score for the average treatment effect](https://docs.doubleml.org/stable/guide/scores.html#interactive-regression-model-irm) which is given by\n", - "\n", - "$$\\psi(W; \\theta, \\eta) := g(1,X) - g(0,X) + \\frac{D (Y - g(1,X))}{m(X)} - \\frac{(1 - D)(Y - g(0,X))}{1 - m(x)} - \\theta.$$" - ] - }, - { - "cell_type": "markdown", - "id": "13a5f6f7-64c5-499b-b68a-16ca98943cd6", - "metadata": {}, - "source": [ - "Because the data set was simulated we are aware of the true ATE, $\\theta_0=0.8$. The interpretation of this is that exposure to the new ad increases sales (in $100\\$$) by around $0.8$ on average. In the following, we try to estimate this causal effect using the [DoubleML](https://docs.doubleml.org/stable/index.html) package and assess whether the estimated effect is significantly different from zero." - ] - }, - { - "cell_type": "markdown", - "id": "69f0731d", - "metadata": {}, - "source": [ - "### Assess predictive performance in the IRM" - ] - }, - { - "cell_type": "markdown", - "id": "6d494c68", - "metadata": {}, - "source": [ - "In the following, we will compare the estimate of the ATE based on different learners. Moreover, we will also have a look how well the learners can predict the nuisance components of the causal model. \n", - "\n", - "To evaluate the predictive performance, we'll first define a helper function that uses a DoubleML model object and returns a summary for a predictive measure. We'll use the root mean squared error (RMSE) for the main regression and the log loss measure $L_{log}$ for the propensity score estimation.\n", - "\n", - "Estimation of the IRM delivers two arrays for the prediction function $g_0(D, X)$: `ml_g0` for $g_0(0, X)$ and `ml_g1` for $g_0(1, X)$. If we want to get the correct prediction for each observation based on the treatment realization, we pick the corresponding value of either `ml_g0` (for $D=0$) or `ml_g1` (for $D=1$). As we apply random sample splitting repeatedly in every model, the RMSE and the log loss can be calculated for each repetition. We are interested in mean and standard deviation across all repetitions." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "aa2a8f81", - "metadata": {}, - "outputs": [], - "source": [ - "def pred_acc_irm(DoubleML, prop):\n", - " \"\"\"\n", - " A function to calculate prediction accuracy values for every repetition\n", - " of a Double Machine Learning model using IRM, DoubleMLIRM\n", - " \n", - " ...\n", - " \n", - " Parameters\n", - " ----------\n", - " DoubleML : doubleml.double_ml_irm.DoubleMLIRM\n", - " The IRM Double Machine Learning model\n", - " prop : bool\n", - " Indication if RMSE values have to be computed for main regression or\n", - " log loss values for propensity score\n", - " \"\"\"\n", - " \n", - " # export data and predictions of the DoubleML model\n", - " y = DoubleML._dml_data.y\n", - " d = DoubleML._dml_data.d\n", - " g0 = DoubleML.predictions.get('ml_g0')\n", - " g1 = DoubleML.predictions.get('ml_g1') \n", - " m = DoubleML.predictions.get('ml_m')\n", - " \n", - " # dimensions of prediction array\n", - " h = g0.shape[0]\n", - " w = DoubleML.n_rep\n", - " \n", - " # check whether treatment is binary \n", - " if np.isin(d, [0,1]).all() == False:\n", - " raise ValueError(\"Treatment must be a binary variable.\")\n", - " \n", - " # prepare array to store prediction accuracy measure values\n", - " pred_acc_array = np.zeros((w,))\n", - " \n", - " # check whether to assess main regression or propensity score accuracy: \n", - " if prop == False:\n", - " \n", - " # evaluate main regression accuracy\n", - " # export an array with correctly picked prediction values \n", - " export_pred_array = np.zeros((h, w)) \n", - " for i in range(w):\n", - " for j in range(h):\n", - " if d[j] == 0:\n", - " export_pred_array[j,i] = g0[j,i]\n", - " else:\n", - " export_pred_array[j,i] = g1[j,i]\n", - " \n", - " # fill array that contains rmse of each repetition\n", - " for i in range(w):\n", - " pred_acc_array[i] = mean_squared_error(y, export_pred_array[:,i], squared=False) \n", - " else:\n", - " \n", - " # evaluate propensity score accuracy\n", - " # fill array that contains log loss of each repetition\n", - " for i in range(w):\n", - " pred_acc_array[i] = log_loss(d, m[:,i], eps=0.025)\n", - " \n", - " return pred_acc_array" - ] - }, - { - "cell_type": "markdown", - "id": "suburban-infrastructure", - "metadata": {}, - "source": [ - "### Benchmark: Model based on Linear and Logistic Regression" - ] - }, - { - "cell_type": "markdown", - "id": "93f3af17-bcf9-429b-af9a-b90ea1153937", - "metadata": {}, - "source": [ - "Let us first start with a benchmark model that is based on linear and logistic regression. Hence, we estimate the functions $g_0(D,X)$ using a linear regression model and $m_0(X)$ by using an (unpenalized) logistic regression. In both cases, we include all available characteristics $V$. Later we will assess whether we can find a \"better\" estimator based on ML methods like lasso, random forests and boosting. Because we have 200 variables and 1000 observations, this is approaching a high dimentional setting, therefore the linear and the logistic regression may not estimate the parameters well." - ] - }, - { - "cell_type": "markdown", - "id": "authorized-school", - "metadata": {}, - "source": [ - "We start by initializing the learners for linear regression and logistic regression. Then, we initialize a causal model object, here of the class [DoubleMLIRM](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLIRM.html). The latter is based on the data-backend we have specified above. To reduce the disproportionate impact of extreme propensity score weights in the interactive model we trim the propensity score from below and above at thresholds of 0.025 and 0.975." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "76037798", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.795384 0.086909 9.151966 5.590671e-20 0.625047 0.965722" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize Linear and Logistic Regression learners\n", - "linreg = make_pipeline(StandardScaler(), LinearRegression())\n", - "logreg_class = make_pipeline(StandardScaler(), LogisticRegression(penalty=\"none\"))\n", - "\n", - "# Initialize DoubleMLIRM model\n", - "np.random.seed(1234)\n", - "dml_irm_regression = dml.DoubleMLIRM(data_dml,\n", - " ml_g = linreg,\n", - " ml_m = logreg_class,\n", - " trimming_threshold = 0.025,\n", - " n_folds = 1,\n", - " apply_cross_fitting = False,\n", - " n_rep=1)\n", - "\n", - "dml_irm_regression.fit(store_predictions=True)\n", - "\n", - "reg_summary = dml_irm_regression.summary\n", - "reg_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "controlling-collapse", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [-0.00461562]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_irm_regression.coef - 0.8)" - ] - }, - { - "cell_type": "markdown", - "id": "emerging-highlight", - "metadata": {}, - "source": [ - "We see that the causal estimate suffers from a substantial bias and is quite noisy: The ATE is overestimated by around 0.26 and the standard error is around 0.62. The corresponding 95%-confidence interval is relatively wide. It even covers the value of zero. Hence, we cannot reject the null hypothesis that the average treatment effect is different from zero at the 5% significance level.\n", - "\n", - "Next, we'll calculate the RMSE and the log loss for the nuisance functions in order to find out how the benchmark compares to other ML models." - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "7ad39856", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_linlog_irm = pred_acc_irm(dml_irm_regression, prop=False)\n", - "rmse_main_linlog_irm_mean = np.mean(rmse_main_linlog_irm)\n", - "rmse_main_linlog_irm_std = np.std(rmse_main_linlog_irm)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_linlog_irm = pred_acc_irm(dml_irm_regression, prop=True)\n", - "logloss_prop_linlog_irm_mean = np.mean(logloss_prop_linlog_irm)\n", - "logloss_prop_linlog_irm_std = np.std(logloss_prop_linlog_irm)" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "dd39c325", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 0.812050411691478\n", - "Standard deviation of the RMSE is 0.0\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_linlog_irm_mean)\n", - "print(\"Standard deviation of the RMSE is\", rmse_main_linlog_irm_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "e21456ef", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 0.5343917954144319\n", - "Standard deviation of log loss is 0.0\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_linlog_irm_mean)\n", - "print(\"Standard deviation of log loss is\", logloss_prop_linlog_irm_std)" - ] - }, - { - "cell_type": "markdown", - "id": "neutral-converter", - "metadata": {}, - "source": [ - "Next, let us find out if we are able to use ML methods to find estimators that have a lower bias and a smaller standard error than the benchmark." - ] - }, - { - "cell_type": "markdown", - "id": "723b8e6c", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Lasso\n", - "\n", - "We estimate the nuisance components $g_0$ and $m_0$ using lasso as provided by [scikit-learn](https://scikit-learn.org). We load the learner by initializing instances from the classes [LassoCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html) and [LogisticRegressionCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegressionCV.html). Here we specify that the lasso should use the value of $\\lambda$ that minimizes the cross-validated mean squared error, which is based on 5-fold cross validation. We initialize the [DoubleMLIRM](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLIRM.html) object and use the newly defined learners." - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "73cbfd4b", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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A0.8555590.07092812.0624171.668137e-330.7165440.994575
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.855559 0.070928 12.062417 1.668137e-33 0.716544 0.994575" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize Lasso learners\n", - "lasso = make_pipeline(StandardScaler(), LassoCV(cv=5, max_iter=20000)) \n", - "lasso_class = make_pipeline(StandardScaler(),\n", - " LogisticRegressionCV(cv=5, penalty='l1', solver='liblinear', \n", - " Cs = 4, max_iter=1000)) \n", - "\n", - "# Initialize DoubleMLIRM model\n", - "np.random.seed(1234)\n", - "dml_irm_lasso = dml.DoubleMLIRM(data_dml,\n", - " ml_g = lasso,\n", - " ml_m = lasso_class,\n", - " trimming_threshold = 0.025, \n", - " n_folds = 3,\n", - " n_rep = 3)\n", - "\n", - "dml_irm_lasso.fit(store_predictions=True)\n", - "\n", - "lasso_summary = dml_irm_lasso.summary\n", - "lasso_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "stock-bookmark", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [0.05555945]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_irm_lasso.coef - 0.8)" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "id": "85c6e74e", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_lasso_irm = pred_acc_irm(dml_irm_lasso, prop=False)\n", - "rmse_main_lasso_irm_mean = np.mean(rmse_main_lasso_irm)\n", - "rmse_main_lasso_irm_std = np.std(rmse_main_lasso_irm)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_lasso_irm = pred_acc_irm(dml_irm_lasso, prop=True)\n", - "logloss_prop_lasso_irm_mean = np.mean(logloss_prop_lasso_irm)\n", - "logloss_prop_lasso_irm_std = np.std(logloss_prop_lasso_irm)" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "id": "c659681b", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 1.1143405452234652\n", - "Standard deviation of RMSE is 0.005869688113839954\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_lasso_irm_mean)\n", - "print(\"Standard deviation of RMSE is\", rmse_main_lasso_irm_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "id": "388cdfcf", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 0.6686766530020503\n", - "Standard deviation of log loss is 0.0032543941531603953\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_lasso_irm_mean)\n", - "print(\"Standard deviation of log loss is\", logloss_prop_lasso_irm_std)" - ] - }, - { - "cell_type": "markdown", - "id": "religious-algebra", - "metadata": {}, - "source": [ - "We see that the lasso-based estimate for the ATE is $0.86$ and, hence, much closer to the true value of $0.8$ than in the benchmark $1.06$. Moreover, we can achieve improvements in terms of estimation precision as can be recognized from the smaller standard error. Also the prediction measures for the nuisance components are much smaller for Lasso than in the linear/logistic benchmark. Using the Lasso learners makes it now possible to conclude that the ATE is significantly different from zero at a significance level of 5%." - ] - }, - { - "cell_type": "markdown", - "id": "33d06b0d", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Random Forest" - ] - }, - { - "cell_type": "markdown", - "id": "4d9d008a-5b6a-4acf-93b9-b26599541653", - "metadata": {}, - "source": [ - "Alternatively, we can repeat this procedure with other machine learning methods, for example a random forest learner as provided by the [RandomForestRegressor](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html) and [RandomForestClassifier](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html) class in [scikit-learn](https://scikit-learn.org)." - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "id": "2092891a", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A0.8931760.07742111.536558.631791e-310.7414331.044919
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.893176 0.077421 11.53655 8.631791e-31 0.741433 1.044919" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize Random Forest learners\n", - "randomForest = RandomForestRegressor()\n", - "randomForest_class = RandomForestClassifier()\n", - "\n", - "# Initialize DoubleMLIRM model\n", - "np.random.seed(1234)\n", - "dml_irm_forest = dml.DoubleMLIRM(data_dml,\n", - " ml_g = randomForest,\n", - " ml_m = randomForest_class,\n", - " trimming_threshold = 0.025,\n", - " n_folds = 3,\n", - " n_rep = 3)\n", - "\n", - "# Set nuisance-part specific parameters\n", - "dml_irm_forest.set_ml_nuisance_params('ml_g0', 'A', {\n", - " 'max_features': 200, 'n_estimators': 250})\n", - "dml_irm_forest.set_ml_nuisance_params('ml_g1', 'A', {\n", - " 'max_features': 200, 'n_estimators': 250})\n", - "dml_irm_forest.set_ml_nuisance_params('ml_m', 'A', {\n", - " 'max_features': 200, 'n_estimators': 250})\n", - "\n", - "dml_irm_forest.fit(store_predictions=True) \n", - "\n", - "forest_summary = dml_irm_forest.summary\n", - "forest_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "id": "vital-insight", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [0.09317591]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_irm_forest.coef - 0.8)" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "id": "14c230b0", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_forest_irm = pred_acc_irm(dml_irm_forest, prop=False)\n", - "rmse_main_forest_irm_mean = np.mean(rmse_main_forest_irm)\n", - "rmse_main_forest_irm_std = np.std(rmse_main_forest_irm)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_forest_irm = pred_acc_irm(dml_irm_forest, prop=True)\n", - "logloss_prop_forest_irm_mean = np.mean(logloss_prop_forest_irm)\n", - "logloss_prop_forest_irm_std = np.std(logloss_prop_forest_irm)" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "id": "1d633282", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 1.1688034544446142\n", - "Standard deviation of RMSE is 0.00826647072034282\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_forest_irm_mean)\n", - "print(\"Standard deviation of RMSE is\", rmse_main_forest_irm_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "id": "16a7a785", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 0.6823242335385794\n", - "Standard deviation of log loss is 0.0026223238604172463\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_forest_irm_mean)\n", - "print(\"Standard deviation of log loss is\", logloss_prop_forest_irm_std)" - ] - }, - { - "cell_type": "markdown", - "id": "d4b6e16b-6cb9-40d8-a4fa-c438f23b49f3", - "metadata": {}, - "source": [ - "The results are relatively similar to the one obtained by lasso with a bias and standard errors that are slightly greater than before. The predictive accuracy of the random forest learners is also slightly worse than that of Lasso." - ] - }, - { - "cell_type": "markdown", - "id": "9ac68b60", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Extreme Gradient Boosting" - ] - }, - { - "cell_type": "markdown", - "id": "cc71c762-8497-43e5-a151-a5239641d510", - "metadata": {}, - "source": [ - "Next, we estimate the ATE using extreme gradient boosting as provided by [xgboost](https://docs.getml.com/latest/api_reference/predictors.html)." - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "id": "90b9ef4e", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A0.7909060.1043067.5825883.387302e-140.5864710.995341
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.790906 0.104306 7.582588 3.387302e-14 0.586471 0.995341" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize Extreme Gradient Boosting learners\n", - "boost = XGBRegressor(n_jobs=1, objective = \"reg:squarederror\")\n", - "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", - " objective = \"binary:logistic\", eval_metric = \"logloss\")\n", - "\n", - "# Initialize DoubleMLIRM model\n", - "np.random.seed(1234)\n", - "dml_irm_boost = dml.DoubleMLIRM(data_dml,\n", - " ml_g = boost,\n", - " ml_m = boost_class,\n", - " trimming_threshold = 0.025,\n", - " n_folds = 3,\n", - " n_rep = 3)\n", - "\n", - "# Set nuisance-part specific parameters\n", - "dml_irm_boost.set_ml_nuisance_params('ml_g0', 'A', {\n", - " 'n_estimators': 30, 'eta': 0.2})\n", - "dml_irm_boost.set_ml_nuisance_params('ml_g1', 'A', {\n", - " 'n_estimators': 30, 'eta': 0.2})\n", - "dml_irm_boost.set_ml_nuisance_params('ml_m', 'A', {\n", - " 'n_estimators': 15, 'eta': 0.2})\n", - "\n", - "dml_irm_boost.fit(store_predictions=True)\n", - "\n", - "boost_summary = dml_irm_boost.summary\n", - "boost_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "id": "traditional-ribbon", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [-0.0090944]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_irm_boost.coef - 0.8)" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "id": "efd04e78", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_boost_irm = pred_acc_irm(dml_irm_boost, prop=False)\n", - "rmse_main_boost_irm_mean = np.mean(rmse_main_boost_irm)\n", - "rmse_main_boost_irm_std = np.std(rmse_main_boost_irm)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_boost_irm = pred_acc_irm(dml_irm_boost, prop=True)\n", - "logloss_prop_boost_irm_mean = np.mean(logloss_prop_boost_irm)\n", - "logloss_prop_boost_irm_std = np.std(logloss_prop_boost_irm)" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "id": "114aa5cf", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 1.2287566646120192\n", - "Standard deviation of RMSE is 0.010275338353331828\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_boost_irm_mean)\n", - "print(\"Standard deviation of RMSE is\", rmse_main_boost_irm_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "id": "c1ebde27", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 0.7204831015081563\n", - "Standard deviation of log loss is 0.01297502257820836\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_boost_irm_mean)\n", - "print(\"Standard deviation of log loss is\", logloss_prop_boost_irm_std)" - ] - }, - { - "cell_type": "markdown", - "id": "9ee7f068-1ac4-4d7d-99a7-5c68c91e8b51", - "metadata": {}, - "source": [ - "The estimated coefficient is very close to the true ATE of $0.8$ but has a small negative bias. The interpretation of the results obtained with lasso, random forests and boosting are very similar. In all cases we are able to reject the null hypothesis that the ad has no effect on the sales." - ] - }, - { - "cell_type": "markdown", - "id": "fba54a14-c685-4948-819d-94a99d88e94a", - "metadata": {}, - "source": [ - "#### IRM - Summary of coefficient estimates\n", - "\n", - "We save the estimates, bias and confidence intervals for later peresentation and comparision." - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "id": "5e16a294", - "metadata": { - "scrolled": false, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefBias2.5 %97.5 %
regression0.795-0.0050.6250.966
lasso0.8560.0560.7170.995
forest0.8930.0930.7411.045
xgboost0.791-0.0090.5860.995
\n", - "
" - ], - "text/plain": [ - " coef Bias 2.5 % 97.5 %\n", - "regression 0.795 -0.005 0.625 0.966\n", - "lasso 0.856 0.056 0.717 0.995\n", - "forest 0.893 0.093 0.741 1.045\n", - "xgboost 0.791 -0.009 0.586 0.995" - ] - }, - "execution_count": 35, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "irm_summary = pd.concat((reg_summary, lasso_summary, forest_summary, boost_summary))\n", - "irm_summary.index = ['regression','lasso', 'forest', 'xgboost']\n", - "irm_summary = irm_summary[['coef', '2.5 %', '97.5 %']]\n", - "irm_summary.insert(1, \"Bias\", [irm_summary.loc['regression','coef'] - 0.8, \n", - " irm_summary.loc['lasso','coef'] - 0.8, \n", - " irm_summary.loc['forest','coef'] - 0.8, \n", - " irm_summary.loc['xgboost','coef'] - 0.8])\n", - "irm_summary.round(3)" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "id": "4b478603", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "errors = np.full((2, irm_summary.shape[0]), np.nan)\n", - "errors[0, :] = irm_summary['coef'] - irm_summary['2.5 %']\n", - "errors[1, :] = irm_summary['97.5 %'] - irm_summary['coef']\n", - "plt.errorbar(irm_summary.index, irm_summary.coef, fmt='o', yerr=errors)\n", - "plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", - "\n", - "plt.title('Interactive Regression Model (IRM)')\n", - "plt.xlabel('ML method')\n", - "_ = plt.ylabel('Coefficients and 95%-CI')" - ] - }, - { - "cell_type": "markdown", - "id": "8c891e02", - "metadata": {}, - "source": [ - "#### IRM - Summary of prediction assessment metric's mean values" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "id": "6790aad8", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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main RMSEmain RMSE (sd)prop log lossprop log loss (sd)
regression0.8120.0000.5340.000
lasso1.1140.0060.6690.003
forest1.1690.0080.6820.003
xgboost1.2290.0100.7200.013
\n", - "
" - ], - "text/plain": [ - " main RMSE main RMSE (sd) prop log loss prop log loss (sd)\n", - "regression 0.812 0.000 0.534 0.000\n", - "lasso 1.114 0.006 0.669 0.003\n", - "forest 1.169 0.008 0.682 0.003\n", - "xgboost 1.229 0.010 0.720 0.013" - ] - }, - "execution_count": 37, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "irm_rmse_index = ['regression','lasso', 'forest', 'xgboost']\n", - "irm_rmse = pd.DataFrame([[rmse_main_linlog_irm_mean, rmse_main_linlog_irm_std, \n", - " logloss_prop_linlog_irm_mean, logloss_prop_linlog_irm_std],\n", - " [rmse_main_lasso_irm_mean, rmse_main_lasso_irm_std,\n", - " logloss_prop_lasso_irm_mean, logloss_prop_lasso_irm_std],\n", - " [rmse_main_forest_irm_mean, rmse_main_forest_irm_std,\n", - " logloss_prop_forest_irm_mean, logloss_prop_forest_irm_std],\n", - " [rmse_main_boost_irm_mean, rmse_main_boost_irm_std,\n", - " logloss_prop_boost_irm_mean, logloss_prop_boost_irm_std]],\n", - " index=irm_rmse_index,\n", - " columns=['main RMSE', 'main RMSE (sd)',\n", - " 'prop log loss', 'prop log loss (sd)'])\n", - "irm_rmse.round(3)" - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "id": "a5be2641", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 40, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# graphical illustration of RMSE for main regression\n", - "errors_irm_rmse = np.full((2, irm_rmse.shape[0]), np.nan)\n", - "errors_irm_rmse[0, :] = irm_rmse['main RMSE'] - irm_rmse['main RMSE (sd)']\n", - "errors_irm_rmse[1, :] = irm_rmse['main RMSE'] + irm_rmse['main RMSE (sd)']\n", - "plt.errorbar(x=irm_rmse.index, y=irm_rmse['main RMSE'], fmt='x',\n", - " yerr=errors_irm_rmse, c='darkslategray')" - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "id": "d42b8ca8", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "regression 0.812050\n", - "lasso 1.108471\n", - "forest 1.160537\n", - "xgboost 1.218481\n", - "dtype: float64" - ] - }, - "execution_count": 45, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "irm_rmse['main RMSE'] - irm_rmse['main RMSE (sd)']" - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "id": "9255bc0a", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 39, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# graphical illustration of log loss for main regression\n", - "errors_irm_logloss = np.full((2, irm_rmse.shape[0]), np.nan)\n", - "errors_irm_logloss[0, :] = irm_rmse['prop log loss'] - irm_rmse['prop log loss (sd)']\n", - "errors_irm_logloss[1, :] = irm_rmse['prop log loss'] + irm_rmse['prop log loss (sd)']\n", - "plt.errorbar(x=irm_rmse.index, y=irm_rmse['prop log loss'], fmt='x',\n", - " yerr=errors_irm_logloss, c='darkslategray')" - ] - }, - { - "cell_type": "markdown", - "id": "27c6157d", - "metadata": {}, - "source": [ - "### Inspection of the benchmark model\n", - "\n", - "It is natural to investigate why the the benchmark model performs so much worse as compared to the ML models. First of all, we can conclude that the predictive performance of the linear and logistic regression for the nuisance functions is considerably worse and more variable than for lasso, random forest and xgboost. Moreover, we can also inspect the propensity score estimates of the logistic regression which appear to be very close to zero and one for many observations.\n", - "\n", - "We first define a helper function that plots the propensity scores for each of the cross-fitting repetitions." - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "id": "78afa7eb", - "metadata": {}, - "outputs": [], - "source": [ - "def rep_propscore_plot(DoubleML):\n", - " \"\"\"\n", - " A function to create histograms as sublots for every repetition's propensity score density \n", - " of a Double Machine Learning model\n", - " \n", - " ...\n", - " \n", - " Parameters\n", - " ----------\n", - " DoubleML : doubleml\n", - " The Double Machine Learning model\n", - " \"\"\"\n", - " \n", - " \n", - " #export nuisance part from the DoubleML model\n", - " m = DoubleML.predictions.get('ml_m')\n", - " \n", - " # dimensions of nuisance array\n", - " h = m.shape[0]\n", - " rep = DoubleML.n_rep\n", - " \n", - " # create histograms as subplots covering the propensity score densities of all repetitions\n", - " fig, ax = plt.subplots(1, rep, figsize=[20,4.8])\n", - " for i in range(rep):\n", - " ax[i].hist(np.reshape(m[:,i], h), bins=25)\n", - " ax[i].set_title('repetition ' + str(i+1))\n", - " ax[i].set_xlabel(\"prop_score\")\n", - " ax[i].set_ylabel(\"density\")\n", - " \n", - " plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "id": "53d9d81d", - "metadata": {}, - "outputs": [ - { - "ename": "TypeError", - "evalue": "'AxesSubplot' object is not subscriptable", - "output_type": "error", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[1;31mTypeError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_19728/494899183.py\u001b[0m in \u001b[0;36m\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "rep_propscore_plot(dml_irm_regression)" - ] - }, - { - "cell_type": "markdown", - "id": "4f8d0f9f", - "metadata": {}, - "source": [ - "Let's compare this to the corresponding plot for the lasso-based model." - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "id": "e67ebd28", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "rep_propscore_plot(dml_irm_lasso)" - ] - }, - { - "cell_type": "markdown", - "id": "b282c8d9", - "metadata": {}, - "source": [ - "We observe that the propensity score estimates of the lasso-based model are more centered and only close to zero and one for very few observations." - ] - }, - { - "cell_type": "markdown", - "id": "b29e412d-d86f-46b4-840f-cbbe082faf0b", - "metadata": {}, - "source": [ - "### Conclusion\n", - "\n", - "We can conclude that the interactive regression model (IRM) estimates are close to the true coefficient value, if the nuisance components are estimated with machine learning methods. The performance of Lasso and the tree-based methods random forests and extreme gradient boosting are comparable. All of the ML-based estimators have exhibited a superior performance to the benchmark based on linear and logistic regression, which seems to be rather unstable in the data example considered.\n" - ] - }, - { - "cell_type": "markdown", - "id": "f50297c5", - "metadata": {}, - "source": [ - "## 2. Partially Linear Regression Model (PLR)\n", - "\n", - "The [DoubleML](https://docs.doubleml.org/stable/index.html) package also includes the [Partial Linear Regression (PLR)](https://docs.doubleml.org/stable/guide/models.html#partially-linear-regression-model-plr) model, which assumes the population regression has a linear and additive structure. Although in reality, we never know if this structure really holds for the underlying data generating process, we can apply this model and see how the estimates compare to those from the IRM." - ] - }, - { - "cell_type": "markdown", - "id": "fa24e6e1-b878-401f-b38a-c29cc0620c2c", - "metadata": {}, - "source": [ - "We estimate the function $g_0$ and $m_0$ in the following PLR model:\n", - "\n", - "\\begin{eqnarray}\n", - "& Y = D\\theta_0 + g_0(X) + \\zeta, &\\quad E[\\zeta \\mid D,X]= 0,\\\\\n", - "& D = m_0(X) + V, &\\quad E[V \\mid X] = 0.\n", - "\\end{eqnarray}\n", - "\n", - "To estimate the causal parameter $\\theta_0$, we use double machine learning with 3-fold cross-fitting again. The steps of our analysis are very similar to the IRM cases with the difference being that we use a model class [DoubleMLPLR](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLPLR.html) for estimation." - ] - }, - { - "cell_type": "markdown", - "id": "8e7ad0b5", - "metadata": {}, - "source": [ - "### Assess predictive performance in the PLR" - ] - }, - { - "cell_type": "markdown", - "id": "73c26a84", - "metadata": {}, - "source": [ - "As in the IRM, we want to calculate mean and standard deviation of the RMSE / log loss values across all repetitions to evaluate the prediction performance. Once again, a helper function is used as follows:" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "id": "54a843e3", - "metadata": {}, - "outputs": [], - "source": [ - "def pred_acc_plr(DoubleML, prop):\n", - " \"\"\"\n", - " A function to calculate prediction accuracy values for every repetition\n", - " of a Double Machine Learning model using PLR, DoubleMLPLR\n", - " \n", - " ...\n", - " \n", - " Parameters\n", - " ----------\n", - " DoubleML : doubleml.double_ml_plr.DoubleMLPLR\n", - " The PLR Double Machine Learning model\n", - " prop : bool\n", - " Indication if RMSE values have to be computed for main regression or log loss values for propensity score\n", - " \"\"\"\n", - " \n", - " \n", - " # export data, fitted coefficient and predictions of the DoubleML model\n", - " y = DoubleML._dml_data.y\n", - " d = DoubleML._dml_data.d\n", - " theta = DoubleML.coef\n", - " g0 = DoubleML.predictions.get('ml_g')\n", - " m = DoubleML.predictions.get('ml_m')\n", - " \n", - " # dimensions of prediction array\n", - " h = g0.shape[0]\n", - " w = DoubleML.n_rep\n", - " \n", - " # check whether treatment is binary \n", - " if np.isin(d, [0,1]).all() == False:\n", - " raise ValueError(\"Treatment must be a binary variable.\")\n", - " \n", - " # prepare array to store prediction accuracy values\n", - " pred_acc_array = np.zeros((w,))\n", - " \n", - " # check whether to assess main regression or propensity score accuracy: \n", - " if prop == False:\n", - " \n", - " # evaluate main regression accuracy\n", - " # export array with prediction values\n", - " export_pred_array = np.zeros((h, w)) \n", - " for i in range(w):\n", - " for j in range(h):\n", - " export_pred_array[j,i] = theta*d[j] + g0[j,i]\n", - " \n", - " # fill array that contains rmse of each repetition\n", - " for i in range(w):\n", - " pred_acc_array[i] = mean_squared_error(y, export_pred_array[:,i], squared=False)\n", - " \n", - " else:\n", - " \n", - " # evaluate propensity score accuracy\n", - " # fill array that contains log loss of each repetition\n", - " for i in range(w):\n", - " pred_acc_array[i] = log_loss(d, m[:,i], eps=0.025)\n", - " \n", - " return pred_acc_array" - ] - }, - { - "cell_type": "markdown", - "id": "331a36d6", - "metadata": {}, - "source": [ - "### Benchmark: Model based on Linear and Logistic Regression" - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "id": "1432e567-d221-490d-9361-39b9072cb6d4", - "metadata": { - "scrolled": true, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A0.7849990.06712711.6941911.364815e-310.6534320.916565
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.784999 0.067127 11.694191 1.364815e-31 0.653432 0.916565" - ] - }, - "execution_count": 44, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize Linear and Logistic Regression learners\n", - "linreg = make_pipeline(StandardScaler(), LinearRegression())\n", - "logreg_class = make_pipeline(StandardScaler(), LogisticRegression(penalty=\"none\"))\n", - "\n", - "# Initialize DoubleMLPLR model\n", - "np.random.seed(1234)\n", - "dml_plr_regression = dml.DoubleMLPLR(data_dml,\n", - " ml_g = linreg,\n", - " ml_m = logreg_class,\n", - " n_folds = 3,\n", - " n_rep = 3)\n", - "\n", - "dml_plr_regression.fit(store_predictions=True)\n", - "\n", - "reg_summary = dml_plr_regression.summary\n", - "reg_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "id": "ff708453", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [-0.01500149]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_plr_regression.coef - 0.8)" - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "id": "88392566", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_linlog_plr = pred_acc_plr(dml_plr_regression, prop=False)\n", - "rmse_main_linlog_plr_mean = np.mean(rmse_main_linlog_plr)\n", - "rmse_main_linlog_plr_std = np.std(rmse_main_linlog_plr)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_linlog_plr = pred_acc_plr(dml_plr_regression, prop=True)\n", - "logloss_prop_linlog_plr_mean = np.mean(logloss_prop_linlog_plr)\n", - "logloss_prop_linlog_plr_std = np.std(logloss_prop_linlog_plr)" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "id": "08227dfc", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 1.3418428467276253\n", - "Standard deviation of RMSE is 0.009847706467828324\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_linlog_plr_mean)\n", - "print(\"Standard deviation of RMSE is\", rmse_main_linlog_plr_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "id": "c91ed6e8", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 1.0228568161263911\n", - "Standard deviation of log loss is 0.027536454508812133\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_linlog_plr_mean)\n", - "print(\"Standard deviation of log loss is\", logloss_prop_linlog_plr_std)" - ] - }, - { - "cell_type": "markdown", - "id": "4dd8948f", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Lasso" - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "id": "0bbbc3ce", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A0.8047950.07027111.4528072.276523e-300.6670670.942522
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.804795 0.070271 11.452807 2.276523e-30 0.667067 0.942522" - ] - }, - "execution_count": 49, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize DoubleMLPLR model\n", - "np.random.seed(1234)\n", - "dml_plr_lasso = dml.DoubleMLPLR(data_dml,\n", - " ml_g = lasso,\n", - " ml_m = lasso_class,\n", - " n_folds = 3,\n", - " n_rep = 3)\n", - "\n", - "dml_plr_lasso.fit(store_predictions=True)\n", - "\n", - "lasso_summary=dml_plr_lasso.summary\n", - "lasso_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "id": "30aef0c8", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [0.00479477]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_plr_lasso.coef - 0.8)" - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "id": "96383f94", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_lasso_plr = pred_acc_plr(dml_plr_lasso, prop=False)\n", - "rmse_main_lasso_plr_mean = np.mean(rmse_main_lasso_plr)\n", - "rmse_main_lasso_plr_std = np.std(rmse_main_lasso_plr)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_lasso_plr = pred_acc_plr(dml_plr_lasso, prop=True)\n", - "logloss_prop_lasso_plr_mean = np.mean(logloss_prop_lasso_plr)\n", - "logloss_prop_lasso_plr_std = np.std(logloss_prop_lasso_plr)" - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "id": "10a66c25", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 1.1394799633725696\n", - "Standard deviation of RMSE is 0.003190385536736178\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_lasso_plr_mean)\n", - "print(\"Standard deviation of RMSE is\", rmse_main_lasso_plr_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 53, - "id": "afe3b2b9", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 0.6686763881131824\n", - "Standard deviation of log loss 0.003254281706002184\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_lasso_plr_mean)\n", - "print(\"Standard deviation of log loss\", logloss_prop_lasso_plr_std)" - ] - }, - { - "cell_type": "markdown", - "id": "a4ed2694", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Random Forests" - ] - }, - { - "cell_type": "code", - "execution_count": 54, - "id": "e5f3ac90", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A0.7993070.07329710.9050281.090595e-270.6556470.942967
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.799307 0.073297 10.905028 1.090595e-27 0.655647 0.942967" - ] - }, - "execution_count": 54, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize Random Forest learners\n", - "randomForest = RandomForestRegressor()\n", - "randomForest_class = RandomForestClassifier()\n", - "\n", - "# Initialize DoubleMLPLR model\n", - "np.random.seed(1234)\n", - "dml_plr_forest = dml.DoubleMLPLR(data_dml,\n", - " ml_g = randomForest,\n", - " ml_m = randomForest_class,\n", - " n_folds = 3,\n", - " n_rep = 3)\n", - "\n", - "dml_plr_forest.fit(store_predictions=True)\n", - "\n", - "forest_summary = dml_plr_forest.summary\n", - "forest_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "id": "4c40246d", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [-0.00069288]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_plr_forest.coef - 0.8)" - ] - }, - { - "cell_type": "code", - "execution_count": 56, - "id": "a977c34b", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_forest_plr = pred_acc_plr(dml_plr_forest, prop=False)\n", - "rmse_main_forest_plr_mean = np.mean(rmse_main_forest_plr)\n", - "rmse_main_forest_plr_std = np.std(rmse_main_forest_plr)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_forest_plr = pred_acc_plr(dml_plr_forest, prop=True)\n", - "logloss_prop_forest_plr_mean = np.mean(logloss_prop_forest_plr)\n", - "logloss_prop_forest_plr_std = np.std(logloss_prop_forest_plr)" - ] - }, - { - "cell_type": "code", - "execution_count": 57, - "id": "1f54fed6", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 1.1886867050333019\n", - "Standard deviation of RMSE is 0.006048072563384578\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_forest_plr_mean)\n", - "print(\"Standard deviation of RMSE is\", rmse_main_forest_plr_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 58, - "id": "8101acf6", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 0.6836880652313276\n", - "Standard deviation of log loss is 0.005321479254441978\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_forest_plr_mean)\n", - "print(\"Standard deviation of log loss is\", logloss_prop_forest_plr_std)" - ] - }, - { - "cell_type": "markdown", - "id": "6aa9af04", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Extreme Gradient Boosting" - ] - }, - { - "cell_type": "code", - "execution_count": 59, - "id": "6fab5d3a", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A0.823840.07167611.4939881.414286e-300.6833580.964321
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.82384 0.071676 11.493988 1.414286e-30 0.683358 0.964321" - ] - }, - "execution_count": 59, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize Extreme Gradient Boosting learners\n", - "boost = XGBRegressor(n_jobs = 1, objective = \"reg:squarederror\", \n", - " eta = 0.1, n_estimators = 57, max_depth = 2)\n", - "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", - " objective = \"binary:logistic\",\n", - " eval_metric = \"logloss\",\n", - " eta = 0.1, n_estimators = 10,\n", - " max_depth = 3)\n", - "\n", - "# Initialize DoubleMLPLR model\n", - "np.random.seed(1234)\n", - "dml_plr_boost = dml.DoubleMLPLR(data_dml,\n", - " ml_g = boost,\n", - " ml_m = boost_class,\n", - " n_folds = 3,\n", - " n_rep = 3)\n", - "\n", - "dml_plr_boost.fit(store_predictions=True)\n", - "\n", - "boost_summary = dml_plr_boost.summary\n", - "boost_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 60, - "id": "6e3252f8", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [0.02383965]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_plr_boost.coef - 0.8)" - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "id": "e90a61cc", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_boost_plr = pred_acc_plr(dml_plr_boost, prop=False)\n", - "rmse_main_boost_plr_mean = np.mean(rmse_main_boost_plr)\n", - "rmse_main_boost_plr_std = np.std(rmse_main_boost_plr)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_boost_plr = pred_acc_plr(dml_plr_boost, prop=True)\n", - "logloss_prop_boost_plr_mean = np.mean(logloss_prop_boost_plr)\n", - "logloss_prop_boost_plr_std = np.std(logloss_prop_boost_plr)" - ] - }, - { - "cell_type": "code", - "execution_count": 62, - "id": "72121d00", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 1.1560362080432272\n", - "Standard deviation of RMSE is 0.0027129250049691073\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_boost_plr_mean)\n", - "print(\"Standard deviation of RMSE is\", rmse_main_boost_plr_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 63, - "id": "8513cd4e", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 0.677578683851663\n", - "Standard deviation of log loss is 0.005774390874769318\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_boost_plr_mean)\n", - "print(\"Standard deviation of log loss is\", logloss_prop_boost_plr_std)" - ] - }, - { - "cell_type": "markdown", - "id": "a979a78b", - "metadata": {}, - "source": [ - "#### PLR - Summary of coefficient estimates" - ] - }, - { - "cell_type": "code", - "execution_count": 64, - "id": "dba8d33c", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefBias2.5 %97.5 %
regression0.785-0.0150.6530.917
lasso0.8050.0050.6670.943
forest0.799-0.0010.6560.943
xgboost0.8240.0240.6830.964
\n", - "
" - ], - "text/plain": [ - " coef Bias 2.5 % 97.5 %\n", - "regression 0.785 -0.015 0.653 0.917\n", - "lasso 0.805 0.005 0.667 0.943\n", - "forest 0.799 -0.001 0.656 0.943\n", - "xgboost 0.824 0.024 0.683 0.964" - ] - }, - "execution_count": 64, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "plr_summary = pd.concat((reg_summary, lasso_summary, forest_summary, boost_summary))\n", - "plr_summary.index = ['regression','lasso', 'forest', 'xgboost']\n", - "plr_summary = plr_summary[['coef', '2.5 %', '97.5 %']]\n", - "plr_summary.insert(1, \"Bias\", [plr_summary.loc['regression','coef'] - 0.8, \n", - " plr_summary.loc['lasso','coef'] - 0.8, \n", - " plr_summary.loc['forest','coef'] - 0.8, \n", - " plr_summary.loc['xgboost','coef'] - 0.8])\n", - "plr_summary.round(3) " - ] - }, - { - "cell_type": "code", - "execution_count": 65, - "id": "86fe5d87", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "errors = np.full((2, plr_summary.shape[0]), np.nan)\n", - "errors[0, :] = plr_summary['coef'] - plr_summary['2.5 %']\n", - "errors[1, :] = plr_summary['97.5 %'] - plr_summary['coef']\n", - "plt.errorbar(plr_summary.index, plr_summary.coef, fmt='o', yerr=errors)\n", - "plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", - "\n", - "plt.title('Partially Linear Regression Model (PLR)')\n", - "plt.xlabel('ML method')\n", - "_ = plt.ylabel('Coefficients and 95%-CI')" - ] - }, - { - "cell_type": "markdown", - "id": "19fc42af", - "metadata": {}, - "source": [ - "#### PLR - Summary of prediction accuracy metric's mean values" - ] - }, - { - "cell_type": "code", - "execution_count": 66, - "id": "b8937548", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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main RMSEmain RMSE (sd)prop log lossprop log loss (sd)
regression1.3420.0101.0230.028
lasso1.1390.0030.6690.003
forest1.1890.0060.6840.005
xgboost1.1560.0030.6780.006
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" - ], - "text/plain": [ - " main RMSE main RMSE (sd) prop log loss prop log loss (sd)\n", - "regression 1.342 0.010 1.023 0.028\n", - "lasso 1.139 0.003 0.669 0.003\n", - "forest 1.189 0.006 0.684 0.005\n", - "xgboost 1.156 0.003 0.678 0.006" - ] - }, - "execution_count": 66, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "plr_rmse_index = ['regression','lasso', 'forest', 'xgboost']\n", - "plr_rmse = pd.DataFrame([[rmse_main_linlog_plr_mean, rmse_main_linlog_plr_std, \n", - " logloss_prop_linlog_plr_mean, logloss_prop_linlog_plr_std],\n", - " [rmse_main_lasso_plr_mean, rmse_main_lasso_plr_std,\n", - " logloss_prop_lasso_plr_mean, logloss_prop_lasso_plr_std],\n", - " [rmse_main_forest_plr_mean, rmse_main_forest_plr_std,\n", - " logloss_prop_forest_plr_mean, logloss_prop_forest_plr_std],\n", - " [rmse_main_boost_plr_mean, rmse_main_boost_plr_std,\n", - " logloss_prop_boost_plr_mean, logloss_prop_boost_plr_std]],\n", - " index=plr_rmse_index,\n", - " columns=['main RMSE', 'main RMSE (sd)',\n", - " 'prop log loss', 'prop log loss (sd)'])\n", - "plr_rmse.round(3)" - ] - }, - { - "cell_type": "code", - "execution_count": 67, - "id": "79fe38ed", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 67, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# graphical illustration of RMSE for main regression\n", - "errors_plr_rmse = np.full((2, plr_rmse.shape[0]), np.nan)\n", - "errors_plr_rmse[0, :] = plr_rmse['main RMSE'] - plr_rmse['main RMSE (sd)']\n", - "errors_plr_rmse[1, :] = plr_rmse['main RMSE'] + plr_rmse['main RMSE (sd)']\n", - "plt.errorbar(x=plr_rmse.index, y=plr_rmse['main RMSE'], fmt='x',\n", - " yerr=errors_plr_rmse, c='darkslategray')" - ] - }, - { - "cell_type": "code", - "execution_count": 68, - "id": "bb40406b", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 68, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# graphical illustration of log loss for main regression\n", - "errors_plr_logloss = np.full((2, plr_rmse.shape[0]), np.nan)\n", - "errors_plr_logloss[0, :] = plr_rmse['prop log loss'] - plr_rmse['prop log loss (sd)']\n", - "errors_plr_logloss[1, :] = plr_rmse['prop log loss'] + plr_rmse['prop log loss (sd)']\n", - "plt.errorbar(x=plr_rmse.index, y=plr_rmse['prop log loss'], fmt='x',\n", - " yerr=errors_plr_logloss, c='darkslategray')" - ] - }, - { - "cell_type": "markdown", - "id": "27d1d2a9-beed-493d-ae92-8d4e92cde8ae", - "metadata": {}, - "source": [ - "### Summary of IRM and PLR Results" - ] - }, - { - "cell_type": "code", - "execution_count": 69, - "id": "1b4ddf50-50de-4bab-a110-767b8d50df21", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefBias2.5 %97.5 %
ModelML
IRMregression1.0580.258-0.1672.282
lasso0.8560.0560.7170.995
forest0.8930.0930.7411.045
xgboost0.791-0.0090.5860.995
PLRregression0.785-0.0150.6530.917
lasso0.8050.0050.6670.943
forest0.799-0.0010.6560.943
xgboost0.8240.0240.6830.964
\n", - "
" - ], - "text/plain": [ - " coef Bias 2.5 % 97.5 %\n", - "Model ML \n", - "IRM regression 1.058 0.258 -0.167 2.282\n", - " lasso 0.856 0.056 0.717 0.995\n", - " forest 0.893 0.093 0.741 1.045\n", - " xgboost 0.791 -0.009 0.586 0.995\n", - "PLR regression 0.785 -0.015 0.653 0.917\n", - " lasso 0.805 0.005 0.667 0.943\n", - " forest 0.799 -0.001 0.656 0.943\n", - " xgboost 0.824 0.024 0.683 0.964" - ] - }, - "execution_count": 69, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df_summary = pd.concat((irm_summary,plr_summary)).reset_index().rename(columns={'index': 'ML'})\n", - "df_summary['Model'] = np.concatenate((np.repeat('IRM', 4), np.repeat('PLR', 4)))\n", - "df_summary.set_index(['Model', 'ML']).round(3)" - ] - }, - { - "cell_type": "markdown", - "id": "64aa3065-da5c-49b9-88f2-5c08c1b7e617", - "metadata": {}, - "source": [ - "### Conclusion\n", - "\n", - "As in the IRM model, the ML-based PLR models are associated with a smaller bias as compared to the model that is based on linear and logistic regression. It seems that the estimates obtained from the PLR are slightly closer to the true ATE than those from the IRM analysis. This might suggest, that the parametric assumptions (i.e., an additive and homogeneous causal effect) that are incorporated in the PLR turn out to be **not restrictive** in our example data set. However, if both models are based on appropriate ML learners, the conclusions are very similar. In all cases, the ML-based estimates were very close to the true ATE and we were always able to reject the null hypothesis of a zero effect at all common significance levels. In terms of the A/B testing example, it can be concluded that the new ad increases customers purchases (in $100\\$$) by around 0.8 on average and that this effect is significantly different from zero at the 5% significance level. The results are summarized in the graphic below." - ] - }, - { - "cell_type": "code", - "execution_count": 70, - "id": "c80cadcc", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize=(8, 9))\n", - "colors = sns.color_palette()\n", - "for ind, model in enumerate(['IRM', 'PLR']):\n", - " sns.set(font_scale=1.15)\n", - " plt.subplot(3, 1, ind+1)\n", - " this_df = df_summary.query('Model == @model')\n", - " errors = np.full((2, this_df.shape[0]), np.nan)\n", - " errors[0, :] = this_df['coef'] - this_df['2.5 %']\n", - " errors[1, :] = this_df['97.5 %'] - this_df['coef']\n", - " plt.errorbar(this_df.ML, this_df.coef, fmt='o', yerr=errors,\n", - " color=colors[ind], ecolor=colors[ind])\n", - " plt.ylim([0.5, 1.2])\n", - " plt.title(model)\n", - " plt.ylabel('Coeff. and 95%-CI')\n", - " plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", - " plt.legend(bbox_to_anchor=(1.04,0.5), loc=\"best\", borderaxespad=0)\n", - "\n", - "_ = plt.xlabel('ML method')" - ] - }, - { - "cell_type": "markdown", - "id": "90109d08", - "metadata": {}, - "source": [ - "## Appendix" - ] - }, - { - "cell_type": "markdown", - "id": "e42903ad", - "metadata": {}, - "source": [ - "### Propensity score estimates" - ] - }, - { - "cell_type": "markdown", - "id": "157d7295", - "metadata": {}, - "source": [ - "For both the IRM and the PLR model, we want to compare the propensity score estimates of all learners. Since repeated sample splitting is used for every learner, we first want to check whether the repetitions provide similare propensity score estimates. If that is the case, it should be legitimate to pick any of the repetitions for the comparision across all learners." - ] - }, - { - "cell_type": "markdown", - "id": "bb614dd1", - "metadata": {}, - "source": [ - "#### IRM - Repetitions of the Linear and Logistic regression model" - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "id": "a2a753a7", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "rep_propscore_plot(dml_irm_lasso)" - ] - }, - { - "cell_type": "markdown", - "id": "6ae81d8d", - "metadata": {}, - "source": [ - "#### IRM - Repetitions of the Random Forest model" - ] - }, - { - "cell_type": "code", - "execution_count": 73, - "id": "2775a78e", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "h = dml_irm_regression.predictions.get('ml_m').shape[0]\n", - "fig, ax = plt.subplots(1, 4, figsize=(20,4.8))\n", - "\n", - "#regression histogram\n", - "ax[0].hist(np.reshape(dml_irm_regression.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[0].set_title('regression')\n", - "ax[0].set_xlabel(\"prop_score\")\n", - "ax[0].set_ylabel(\"density\")\n", - "\n", - "#lasso histogram\n", - "ax[1].hist(np.reshape(dml_irm_lasso.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[1].set_title('lasso')\n", - "ax[1].set_xlabel(\"prop_score\")\n", - "ax[1].set_ylabel(\"density\")\n", - "\n", - "#random forest histogram\n", - "ax[2].hist(np.reshape(dml_irm_forest.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[2].set_title('random forest')\n", - "ax[2].set_xlabel(\"prop_score\")\n", - "ax[2].set_ylabel(\"density\")\n", - "\n", - "#boosting histogram\n", - "ax[3].hist(np.reshape(dml_irm_boost.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[3].set_title('xgboost')\n", - "ax[3].set_xlabel(\"prop_score\")\n", - "ax[3].set_ylabel(\"density\")\n", - " \n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "7a9a161d", - "metadata": {}, - "source": [ - "#### PLR - Repetitions of the Linear and Logistic regression model" - ] - }, - { - "cell_type": "code", - "execution_count": 76, - "id": "c4da298e", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "rep_propscore_plot(dml_plr_lasso)" - ] - }, - { - "cell_type": "markdown", - "id": "768dabe2", - "metadata": {}, - "source": [ - "#### PLR - Repetitions of the Random Forest model" - ] - }, - { - "cell_type": "code", - "execution_count": 78, - "id": "7639ef46", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "rep_propscore_plot(dml_plr_boost)" - ] - }, - { - "cell_type": "markdown", - "id": "70375158", - "metadata": {}, - "source": [ - "#### PLR - Propensity score estimates across learners" - ] - }, - { - "cell_type": "code", - "execution_count": 80, - "id": "1aeded78", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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fPjmdTi1YsEB1dXW64oorNHz4cEnSokWL5HQ6VVZWpkcffVSDBw9W9+7dGz2POl4/jk8SDmvjSia0qOuuu06HDx/WjBkztGfPHkVFRWnKlCkaPXq0JOnRRx/13HGgW7duGjFihKch1ZDf//73kqRJkyaprKxMMTExevTRRzVo0CBJ0oMPPqiHHnpIP/74oyIjI3Xrrbfq2muvVVBQkEpKSpSRkaEDBw7o7LPP1v33369f/OIX+vTTTz3779Gjh/7rv/5LixYt0l/+8hdFREQoNTVVU6dObbXXCIB1DRkyRLfccotuvfVW1dXVqUePHrr11lv1xBNPaP/+/Ro/frz27t2rm2++WVVVVerRo4f+8pe/6JxzztG0adP08MMP69e//rVqamoUHx+vJUuWKDw8XNdee62qqqr08MMPa8+ePTrnnHM0c+ZMjRo1KtBPGcBpmDVrlh588EENGjRInTp10uWXX65f/vKX+uabb5r8f0NCQpSbm6sHH3xQQ4YM0dlnn60rr7xS69atk+Tfc5PTOdaCBQu0YMECpaSk6MiRI+rdu7eef/55RUZGNlojjTEaOXKkxo4dq1mzZunGG29s8ecDwDtPPvmkKioqNGPGDEnSI488otTUVL333nt64okn9Nhjj2n27Nnq16+fBg8eXO9KppEjRyo3N1dTp07V+eefr+eff94zrPaxxx7TggULNHr0aB05ckSXXnqpVqxYoTPPPFOS9OKLL2r+/PmehtNVV12le++9V5IaPY9KSEhQv379lJycrMWLFys5OdmPrxaaK8gcn2gC8IOPP/5Y/fv3V3h4uKRjVwU8+OCD2rBhQ4CTAQAAAED79f333+vgwYPq3bu3Z9nx6Uj++Mc/BjAZ7IThcvCrefPm6bnnnpPb7daBAwe0bNkyXX755YGOBQAAAADtWnl5uX7zm99o+/btkqQtW7Zow4YNGjZsWICTwU64kgl+tX37ds2ZM0fbt29Xhw4ddPXVV2vGjBmeiS8BAAAAAIHxyiuv6MUXX1R5ebnOOecc3X777Z6pTwBv0GQCAAAAAACAzxguBwAAAAAAAJ/RZAIAAAAAAIDPOgQ6QGs6cOCw6uqaHg0YFdVZ5eVVfkjUMsjb+uyWua3mDQ4OUpcu9p+vy9ta1Fx2+LmTsWWQsWWcbsbWqkWrV6/WSy+9pJUrV0qSCgoKlJ2dreLiYiUkJGjevHmKi4trcp23Dhw4rC5dOln+59QQO7y/GkJu/2rruTkvanl2e8/YLa9EZn/xZ+amalGbbjLV1RmvC5hVCp23yNv67JaZvNbVnFp0Ovu2OjK2DDK2DCtkdLvdWr58uRYtWqSLL75YklRTU6PMzExNmzZNKSkpys3NVVZWlvLy8hpd1xzHn7sVXoPTQW7/Ird/2TX36WjN86LTYaUs3rBbXonM/mKVzAyXAwAA8KMFCxZo/fr1mjRpkmfZpk2b1KlTJ6WnpyssLEwZGRnatWuXCgsLG10HAABgJTSZAAAA/GjChAl65ZVX1KNHD8+y4uJixcfHex6HhIQoNjZWRUVFja4DAACwkjY9XA4AAMBqunbtetKyI0eOyOFw1FvmcDjkdDobXdccUVGdJUnR0ZHNTGwN5PYvcvuXXXMDwE/RZAIAAAiwhppG1dXV6tixY6PrmqO8vEpRUZ1VVlbpc15/i46OJLcfkdu/vM0dHBzkaRYDgFUxXA4AACDA4uLiVFJS4nnsdrtVWlqquLi4RtcBAABYCU0mAACAAEtKSlJFRYXy8/Plcrm0ZMkSxcTEqFevXo2uAwAAsBKaTAAAAAEWERGhpUuXauXKlUpKStLGjRuVk5OjoKCgRtcBAABYCXMyAQAABEB6errS09M9jxMTE5Wfn9/gto2tAwAAsAquZAIAAAAAAIDPaDIBAAAAAADAZwyXk+Q66lZ0dGSj2zhralV5qNpPiQAAbV3kGQ5FhDf+a7jG5VZ4WIgkNfh7it9NABrjTZ2hjgBoTFN1hBqCn6LJJCksNESp099udJtVC0ep0k95AABtX0R4B69+9zS2Db+bADTG2zpDHQFwKk3VEWoIfoomEwAAAOBHXBkAAGiraDIBAAAAfsSVAQCAtoqJvwEAAAAAAOAzrmQCAAAALISb0gAA7IomEwAAAGAh3JQGAGBXDJcDAAAAAACAz2gyAQAAAAAAwGd+bTKtXr1at9xyi+fxhx9+qFGjRqlfv3667rrrtG7dOs+6goICpaWlqW/fvho7dqx27tzpz6gAAAAAAABoBr80mdxut1544QXde++9MsZIksrKyjR16lTdfffd2rJli+6//37NmDFDu3btUk1NjTIzMzVu3Dht3rxZycnJysrK8kdUAAAAAAAAnAa/NJkWLFig9evXa9KkSZ5l33//vVJSUjRixAgFBwdr6NChOu+88/TFF19o06ZN6tSpk9LT0xUWFqaMjAzt2rVLhYWF/ogLAAAAAACAZvLL3eUmTJigrl276s033/Qsu+SSS3TJJZd4Hu/evVs7duxQQkKCNmzYoPj4eM+6kJAQxcbGqqioSAkJCf6IDAAAAAAAgGbwS5Opa9euja7ft2+fJk+erJtuuknx8fFau3atHA5HvW0cDoecTmezjhsV1bnZWRsTHR3ZovvzhZWyeMNueSX7ZSYv4LvIMxyKCG/8V6OzplaVh6r9lAgAAACwD780mRrzzTff6Pbbb1dycrLuv/9+SQ03lKqrq9WxY8dm7bu8vEp1dabJ7bz9sltWVtms47eW6OhIy2Txht3ySvbL3FbzBgcHtXizGGhMRHgHpU5/u9FtVi0cJft82gAAAAD/8evd5X5qy5YtuvXWW3XzzTdr9uzZCgoKkiTFxcWppKTEs53b7VZpaani4uIClBQAAAAAAACNCViT6YcfflBmZqbuvffeehOCS1JSUpIqKiqUn58vl8ulJUuWKCYmRr169QpQWgAAAABoe1avXq1bbrnF87igoEBpaWnq27evxo4dq507d3q1DgCkADaZ3njjDR08eFBz587VpZde6vn31ltvKSIiQkuXLtXKlSuVlJSkjRs3Kicnx3OlEwAAAADg9Lndbr3wwgu69957ZcyxKUZqamqUmZmpcePGafPmzUpOTlZWVlaT6wDgOL/OyZSenq709HRJ0p133qk777zzlNsmJiYqPz/fX9EAAAAAoN1YsGCBCgoKNGnSJH3yySeSpE2bNqlTp06e72wZGRlavny5CgsL9cMPP5xyHXcAB3BcQOdkAgAAAAD434QJE/TKK6+oR48enmXFxcWKj4/3PA4JCVFsbKyKiooaXQcAxwX87nIAAAAAAP/q2rXrScuOHDkih8NRb9nxO383tq45rHbnYG/vNG4VVszbVCYrZm4KmU8fTSYAAAAAQINNo+rqanXs2LHRdc1RXl6lujrjc9aWEB0dqbKyykDH8Fog8nrTuGgsk91eY4nMTQkODmq0WcxwOQAAAACA4uLiVFJS4nnsdrtVWlqquLi4RtcBwHE0mQAAAAAASkpKUkVFhfLz8+VyubRkyRLFxMSoV69eja4DgONoMgEAAAAAFBERoaVLl2rlypVKSkrSxo0blZOTo6CgoEbXAcBxzMkEAAAAAO1Uenq60tPTPY8TExOVn5/f4LaNrQMAiSuZAAAAAAAA0AJoMgEAAAAAAMBnNJkAAAAAAADgM5pMAAAAAAAA8BlNJgAAAAAAAPiMJhMAAAAAAAB8RpMJAAAAAAAAPusQ6AAAAACAHUSe4VBEeOOnz86aWlUeqvZTIgAArIUmEwAAAOCFiPAOSp3+dqPbrFo4SpV+ygMAgNUwXA4AJG3ZskWjR49Wv379lJqaqg0bNkiSCgoKlJaWpr59+2rs2LHauXNngJMCAAAAgDXRZALQ7tXW1uqOO+7Q9OnTtXXrVt11112aMmWKnE6nMjMzNW7cOG3evFnJycnKysoKdFwAAAAAsCSaTADavQMHDqiiokJHjx6VMUZBQUGKiIjQp59+qk6dOik9PV1hYWHKyMjQrl27VFhYGOjIAAAAAGA5zMkEoN2Ljo7WmDFjlJGRoZCQEAUHB2vx4sUqLi5WfHy8Z7uQkBDFxsaqqKhICQkJAUwMAAAAANZDkwlAu1dbWyuHw6Gnn35aw4YN05o1azRjxgyNHz9eDoej3rYOh0NOp7NZ+4+K6tySceuJjo5stX23lLaY0UrPiSzNY/WMW7Zs0Zw5c1RaWqru3bsrKytLycnJKigoUHZ2toqLi5WQkKB58+YpLi4u0HEBAADqockEoN1bt26dioqKNGvWLEnS9ddfr7y8PEk6qaFUXV2tjh07Nmv/5eVVqqszLRP2BNHRkSors/Y9jOyW0dsGREs8p5Zqdljl9bXbz7o5goODWrVZfNzx+eEWLFig5ORkvffee5oyZYo+/fRTZWZmatq0aUpJSVFubq6ysrI8dQoAAMAqaDIBaPf27t2r2traestCQ0PVpUsXlZSUeJa53W6VlpZy9QCAVuHN/HCSlJGRoeXLl6uwsJChuwCAgHIddTf5h7PIMxyqPFTtp0QINJpMANq9IUOG6IknntC7776ra6+9Vv/4xz/02Wef6eGHH9Yzzzyj/Px8paamKjc3VzExMerVq1egI8PiIs9wKCKcX7FoHuaHAwDYTVhoiFKnv93oNqsWjpK1r3VGS+IMGEC7l5CQoEWLFunJJ5/UAw88oHPPPVfPPPOMunfvrqVLlyo7O1tz5sxR7969lZOTo6CgoEBHhsVFhHfw6oQLOJG/5oez+rxUp2Kn3Cdmbc3cLbXvhvZjp9f7ROQGgMCiyQQAkkaOHKmRI0eetDwxMVH5+fkBSASr8uaycH/xJouzppZL1G3CH/PDRUV1tvzcWQ2xypxfzZ237VS5/TUn2+nOM2eV17u52npuf80PBwC+oMkEAEAzeHtZuJWy2O8rV/vE/HAAAMDuggMdAAAAAMfmh/v888/17rvvyhij9evX67PPPtPll1+uiooK5efny+VyacmSJcwPBwAALIkmEwAAgAUcnx9uyZIlGjBggJ5++ul688OtXLlSSUlJ2rhxI/PDAQAAS/LrcLnVq1frpZde0sqVKyVJBQUFys7OVnFxsRISEjRv3jzPpd+NrQMAAGiLmB8OANDWMIdk++KXJpPb7dby5cu1aNEiXXzxxZKkmpoaZWZmatq0aUpJSVFubq6ysrKUl5fX6DoAAAAAAGAPzCHZvvhluNyCBQu0fv16TZo0ybNs06ZN6tSpk9LT0xUWFqaMjAzt2rVLhYWFja4DAAAAAACA9fjlSqYJEyaoa9euevPNNz3LiouLFR8f73kcEhKi2NhYFRUV6ccffzzluoSEBH9EBgAAACAp8gyHIsIb/9rAUBcAgOSnJlPXrl1PWnbkyBE5HI56yxwOh5xOZ6PrAAAAAPhPRHgHhroAALzi14m/T9RQ06i6ulodO3ZsdF1zREV19jnniZqarMyfrJTFG3bLK9kvM3kBAAAAAIEUsCZTXFxcvYm83W63SktLFRcXJ4fDccp1zVFeXqW6OtPkdt5+2S0rs8bfZ6KjIy2TxRt2yyvZL3NbzRscHNTizWIAAAAAQOvwy8TfDUlKSlJFRYXy8/Plcrm0ZMkSxcTEqFevXo2uAwAAAAAAgPUErMkUERGhpUuXauXKlUpKStLGjRuVk5OjoKCgRtcBAAAAaBmuo25FR0fW+yfppMcAAHjDr8Pl0tPTlZ6e7nmcmJio/Pz8BrdtbB0AAPDO8S+QjeGuUED7FRYa4tWk3gAAeCNgczIBAIDW5+0XSPvM6gYAAACroskEAAAAAEAbEnmGQxHhjX/d50pmtAaaTAAAAAAAtCER4R24khkBEbCJvwEAAAAAANB20GQCAAAAAHhs2bJFo0ePVr9+/ZSamqoNGzZIkgoKCpSWlqa+fftq7Nix2rlzZ4CTArAamkwAgHYh8gzHSbfp/umtugEAaO9qa2t1xx13aPr06dq6davuuusuTZkyRU6nU5mZmRo3bpw2b96s5ORkZWVlBTouAIthTiYAQLvg7dwEANonbybJBdqDAwcOqKKiQkePHpUxRkFBQYqIiNCnn36qTp06KT09XZKUkZGh5cuXq7CwUAkJCQFODcAq+E0KAACAdo9GNHBMdHS0xowZo4yMDIWEhCg4OFiLFy9WcXGx4uPjPduFhIQoNjZWRUVFNJkAeNBkAgAAAABIOjZczuFw6Omnn9awYcO0Zs0azZgxQ+PHj5fD4ai3rcPhkNPpbNb+o6I6t2Rcn9ltuHxL57XS8yeLb6ySmSYTAAAAAECStG7dOhUVFWnWrFmSpOuvv155eXmSdFJDqbq6Wh07dmzW/svLq1RXZ1omrI+ioyNVVlYZ6Bhea05ebxsOTe3Pn40Lq/ws7Pa+kPybOTg4qNFmMRN/AwAAAAAkSXv37lVtbW29ZaGhoerSpYtKSko8y9xut0pLSxUXF+fnhACsjCYTAAAAAECSNGTIEH3++ed69913ZYzR+vXr9dlnn+nyyy9XRUWF8vPz5XK5tGTJEsXExKhXr16BjgzAQhguBwBAO+c66m7ycnhnTa0qD1X7KREAIFASEhK0aNEiPfnkk3rggQd07rnn6plnnlH37t21dOlSZWdna86cOerdu7dycnIUFBQU6MgALIQmEwAA7VxYaIhXd9Wy1+wEAIDTNXLkSI0cOfKk5YmJicrPzw9AIgB2wXA5AAAAAAAA+IwrmQAAAAAAsInIMxyKCPf9q7w3w+WB5qLJBAAAAACATUSEd/BqmHtTvB0uDzQHw+UAAAAAAADgM5pMAAAAAAAA8BnD5QAAAIAW8tM5TpjvBADQntBkAgAAAFoIc5wAANozhssBAAAAAADAZ1zJBAAAAAAAAuanQ40b4qypVeWhaj8lwumiyQQAAAAAAALG26HGlX7Kg9PHcDkAAAAAAAD4jCYTAAAAAAAAfEaTCQAAAAAAAD6jyQQAAAAAAACf0WQCAAAAAACAzwLeZNqyZYtGjx6tfv36KTU1VRs2bJAkFRQUKC0tTX379tXYsWO1c+fOACcF0Jbt3btXGRkZSkpK0ogRI/T228fubkEtAgAAAADvBLTJVFtbqzvuuEPTp0/X1q1bddddd2nKlClyOp3KzMzUuHHjtHnzZiUnJysrKyuQUQG0YcYYTZw4URdccIE2btyohQsXKjs7W0VFRdQiAAAAAPBSQJtMBw4cUEVFhY4ePSpjjIKCghQREaFPP/1UnTp1Unp6usLCwpSRkaFdu3apsLAwkHEBtFFbt27V4cOHdffdd6tDhw669NJLlZeXp127dlGLAAAAAMBLAW0yRUdHa8yYMcrIyFCfPn00depUzZ8/X8XFxYqPj/dsFxISotjYWBUVFQUwLYC26quvvtL555+vOXPmaPDgwUpJSVFpaalKS0upRQD8iqG7AADAzjoE8uC1tbVyOBx6+umnNWzYMK1Zs0YzZszQ+PHj5XA46m3rcDjkdDoDlBRAW3bo0CF99NFHuu+++/TBBx/o008/1V133aWJEye2SC2KiurcknHriY6ObLV9txQ7ZIR3mvpZ2uFnbeWMx4fujhgxQosXL9a//vUvTZgwQYmJicrMzNS0adOUkpKi3NxcZWVlKS8vL9CRAQAA6glok2ndunUqKirSrFmzJEnXX3+954Tpp1/iqqur1bFjx2btv6W/2FnpxNRKWbxht7yS/TKT9/SFhYWpa9euGj9+vCQpOTlZ/fv3lzGmRWpReXmV6upMi+U9Ljo6UmVllS2+35ZkpYxWes/ZVWM/Syv9rE/ldDMGBwe1arP4uBOH7gYHBzc4dFeSMjIytHz5chUWFiohIaHVcwEAAHgroE2mvXv3qra2tt6y0NBQdenSRSUlJZ5lbrdbpaWliouLa9b+vf1i5+0XD6ucPNvhRP5Edssr2S9zW83rry92PXv21OHDhz1zw0lSXV2dIiMjW6QWAYA3Thy6u3r1akVFRWnatGmNDt2lyQQAAKwkoHMyDRkyRJ9//rneffddGWO0fv16ffbZZ7r88stVUVGh/Px8uVwuLVmyRDExMerVq1cg4wJoo4YOHarw8HAtXrxYbrdbH3zwgbZt26aRI0dSiwD4zfGhuz179tQHH3ygGTNmaPr06Tp8+DDTCAAAAFsI6JVMCQkJWrRokZ588kk98MADOvfcc/XMM8+oe/fuWrp0qbKzszVnzhz17t1bOTk5nisMAKAlORwOrVixQg8//LCSkpIUFRWlBQsWUIsA+FVrD909fmWoXYeO2jV3a7Laa2KFPFbIcDrsmhsAfiqgTSZJGjlypEaOHHnS8sTEROXn5wcgEYD2KC4uTsuWLTtpObUIgL+09tDd8vIqRUV1ttXw6uP8MSzcjl/ym3pN/P2cAv3estv0AcdZbRoBAPBFQIfLAQAA4BiG7gIAALvzqsn0X//1X9q3b19rZwHQBkSe4VB0dGSj/1xH3S1+XOoUAH9prXpzfOju1q1blZSUpLlz59Yburty5UolJSVp48aNDN0FwLkPAEvyarjcBx98oL/85S8aOnSo0tPTNWLECIWGhrZ2NgA2FBHeQanT3250m1ULR7X4calTAPylNesNQ3cBeItzHwBW5NWVTC+99JLWrl2rX/ziF3riiSf0y1/+Uo888oi++OKL1s4HAF6hTgHwF+oNACugFgGwIq/nZOrevbsyMzO1Zs0aPfPMM9q2bZvGjBmj66+/Xn/9619VV1fXmjkBoEnUKQD+Qr0BYAXUIgBW4/Xd5dxutzZs2KC//e1v+t///V/FxsZqxowZ6t69u5599ll9/PHH+stf/tKKUQGgcdQpAP5CvQFgBdQiAFbjVZPp4Ycf1po1a+R2u5WSkqKXX35Zffr08ayPjY3VzTff3GohAaAp1CkA/kK9AWAF1CIAVuRVk6m0tFQPPPCArrzySoWFhZ20vlu3blq8eHGLhwMAb1GnAPgL9QaAFVCLAFiRV3MyxcfH69prrz2peM2cOVOS1KVLFyUnJ7d8OgDwEnUKgL9QbwBYAbUIgBWd8kqmvXv36pNPPpEkvfbaa7rwwgvrra+srNSaNWs0b9681k0IAKdAnQLgL9QbAFZALQJgdadsMnXp0kUvv/yy9u/fL5fLpZycnHrrw8LCdMcdd7R6QAA4FeoUAH+h3gCNcx11Kzo68pTrnTW1qjxU7cdEbZO/atHevXv10EMPaevWrerUqZPuvvtujRo1SgUFBcrOzlZxcbESEhI0b948xcXF+Xw8AG3HKZtMYWFhysvLkyT9/ve/1/PPP++3UADgDeoUAH+h3gCNCwsNUer0t0+5ftXCUar0Y562yh+1yBijiRMnasSIEVq8eLH+9a9/acKECUpMTFRmZqamTZumlJQU5ebmKisry5MHAKQmJv7+4YcfdM455+iRRx7Rnj17GtwmJiamVYJZTVN/nZH4Cw0QCNQpAP5CvQFgBa1di7Zu3arDhw/r7rvvVnBwsC699FLl5eVp165d6tSpk9LT0yVJGRkZWr58uQoLC5WQkHDaxwPQtjTaZLruuuu0detWjRgxQkFBQTLG1FsfFBSkr776qlUDWkVTf52R+AsNEAjUKQD+Qr0BYAWtXYu++uornX/++ZozZ45Wr16tqKgoTZs2TaWlpYqPj/dsFxISotjYWBUVFdFkAuDRaJPp73//uyRp/fr1fgkDAM1FnQLgL9QbAFbQ2rXo0KFD+uijj3Tffffpgw8+0Keffqq77rpLEydOlMPhqLetw+GQ0+lslRwA7KnRJtPPf/5zSVL37t1VXl6uqKgouVwu5eXl6ayzztI111zjl5AAcCrUKQD+Qr0BYAWtXYvCwsLUtWtXjR8/XpKUnJys/v37yxhzUkOpurpaHTt2bNb+o6I6+5SvpTU1JYq/uY66FRYacsr1Vsvrb/56/nZ8na2SudEm03H//d//rdmzZ2vbtm16/PHH9e677yooKEglJSWaPHlya2cEgCZRpwD4C/UGVuDNfKFo21qrFvXs2VOHDx+WMUZBQUGSpLq6OkVGRqqkpMSzndvtVmlpabPvLldeXqW6OtP0hn4QHR2psjJrTXgSHR3p1TQt7ZU/fl5WfF80xZ+Zg4ODGm0We9VkWrZsmZ566im53W69+eabys3NVdeuXTVu3DhOpgBYAnUKgL9Qb2AF3s4XirartWrR0KFDFR4ersWLF+uOO+7QRx99pG3btumRRx5Rbm6u8vPzlZqaqtzcXMXExKhXr14t+KwA2J1XTaY9e/Zo6NCh2rp1q0JCQtSvXz8FBQXp0KFDrZ0PALxCnQLgL9QbAFbQWrXI4XBoxYoVevjhh5WUlKSoqCgtWLBA3bt319KlS5Wdna05c+aod+/eysnJ8VztBACSl02mn/3sZyouLtbq1as1cOBABQUFadOmTYqOjm7tfADgFeoUAH+h3gCwgtasRXFxcVq2bNlJyxMTE5Wfn+/z/gG0XV41mSZMmKCUlBQFBwdr+fLl+uc//6nbb79d2dnZrZ0PALxCnQLgL9QbAFZALQJgRV41mW655RYlJyerQ4cO+vnPf679+/frlVdeUWJiYmvnAwCvUKcA+Av1BoAVUIuAk0We4VBE+KnbHM6aWlUeqvZjovbHqyaTJHXr1k379+/Xnj17JElnnXWW9uzZo5iYmFYLBwDNQZ0C4C/UGwBWQC0C6osI79DoTRFWLRwle903zn68ajKtXr1a2dnZqqz8vx/H8VtafvXVV60WDgC8RZ0C4C/UGwBWQC0CYEVeNZkWL16sW265RWlpaerQweuLnwDAb6hTAPyFegPACqhFAKzIq2r0/fffa8qUKRQvAJZFnQLgL9QbAFZALQJgRcHebHTRRRdpx44drZ0FAE4bdQqAv1BvAFgBtQiAFXnV9u7fv79++9vf6pprrtHZZ59db92UKVNaJRgANAd1CoC/UG8AWAG1CIAVedVk2rZtm3r16qWioiIVFRV5lgcFBbVaMABoDuoUAH+h3gCwAmoRACvyqsn00ksvtXYOAPAJdQqAv1BvAFgBtQiAFXk1J5N0rFM+Y8YMjR8/Xvv379czzzwjY4zPAfbu3auMjAwlJSVpxIgRevvttyVJBQUFSktLU9++fTV27Fjt3LnT52MBaNtaq04BwE9RbwBYAbUI7YnrqFvR0ZGN/kPgeXUl07p16zRr1iylpqbqiy++0NGjR5WXlyeXy6WpU6ee9sGNMZo4caJGjBihxYsX61//+pcmTJigxMREZWZmatq0aUpJSVFubq6ysrKUl5d32scC0La1Vp0CcMzxE7vGRJ7hUOWhaj8lChzqDQAroBahvQkLDVHq9Lcb3WbVwlF+SoNT8arJ9NRTT+npp5/WwIED9be//U3dunVTbm6uJk6c6FMB27p1qw4fPqy7775bwcHBuvTSS5WXl6ddu3apU6dOSk9PlyRlZGRo+fLlKiwsVEJCwmkfr7V5cwLurKltFyfggL+1Vp0CcIy3J3aVfsoTSNQbAFZALQJgRV41mfbs2aMBAwZI+r+J5M4//3xVVVX5dPCvvvpK559/vubMmaPVq1crKipK06ZNU2lpqeLj4z3bhYSEKDY2VkVFRZZuMnECDgROa9UpAPgp6g0AK6AWAbAir5pM5557rt5//31dccUVnmWbNm3Sf/zHf/h08EOHDumjjz7Sfffdpw8++ECffvqp7rrrLk2cOFEOh6Petg6HQ06ns1n7j4rq7FO+1tISY0XtNt7Ubnkl+2Vu73lbq04BwE9RbwBYAbUIgBV51WSaOnWq7rzzTl155ZVyOp2aPXu2Vq1apccff9yng4eFhalr164aP368JCk5OVn9+/eXMeakhlJ1dbU6duzYrP2Xl1eprq7pie/8/eW8rMy3a5mioyN93oc/2S2vZL/MVsrr7efJm7zBwUFeN4tbq04BwE9RbwBYAbUIgBV5dXe55ORkvfbaazrjjDN02WWXye126/nnn6/XNT8dPXv21OHDh+vdAaGurk6RkZEqKSnxLHO73SotLVVcXJxPxwPQdrVWnQKAn6LeALACahEAK2r0SqZx48Z5xvceZ4xRSUmJFi5cKElasWLFaR986NChCg8P1+LFi3XHHXfoo48+0rZt2/TII48oNzdX+fn5Sk1NVW5urmJiYtSrV6/TPhaAtqm16xQAHEe9AWAF1CIAVtbolUxJSUkaNGiQYmJi9OWXX+rCCy/UNddco1/84hcqLCzUeeed59PBHQ6HVqxYoa1btyopKUlz587VggUL1L17dy1dulQrV65UUlKSNm7cqJycnJOKKQC0dp0CgOOoNwCsgFoEwMoavZJpypQpkqRbbrlFubm56tevn2fdVVddpezsbJ8DxMXFadmyZSctT0xMVH5+vs/7B9C2+aNOwR4iz3AoItyrqQaB00K9AVqXN3XcWVOrykPVfkpkTdQiAFbm1dn4V199pV/84hf1ll144YX15k0CgECiTiEivINSp799yvWrFo7yYxq0ZdQboHU0VcelY7XcGrc6CTxqkf3wBzG0B169w+Pj47VixQpNmDDBs+zZZ59V7969Wy0YADQHdQqAv1Bv7IcvdmiLqEX2420jFbAzr37b/ulPf9LkyZO1YsUKdevWTXv27FFdXZ2ef/751s4HAF5pqTq1Y8cOpaWl6Z133tG5556rgoICZWdnq7i4WAkJCZo3bx53ugTaOc6L7IcvdmiLqEUArMirJlO/fv20bt06vf/++9q7d6+6deumK6+8UpGRka2dDwC80hJ1qra2VjNnzpTL5ZIk1dTUKDMzU9OmTVNKSopyc3OVlZWlvLy81noaAGyA8yIAVkAtAmBFXl83fOaZZ2r06NGtGAUAfONrnVq6dKn69++vgoICSdKmTZvUqVMnpaenS5IyMjK0fPlyFRYWKiEhoSUiA7ApzosAWAG1CIDVBAc6AABYwfbt27V69WpNnTrVs6y4uFjx8fGexyEhIYqNjVVRUVEAEgJoT3bs2KGLL75Yu3btkiQVFBQoLS1Nffv21dixY7Vz584AJwQAADgZTSYA7Z7L5dLMmTM1e/ZsRUREeJYfOXJEDoej3rYOh0NOp9PfEQG0I6caujtu3Dht3rxZycnJysrKCnBKAACAk3GbDQDt3tNPP61Bgwapf//+9ZY31FCqrq5Wx44dm7X/qKjOPmc8leho68+7YIeMaDlW/3lbPZ/E0F0AAGBfNJkAtHtr165VWVmZ8vPzPcvS0tI0e/ZslZSUeJa53W6VlpY2++5y5eVVqqszLRXXIzo6UmVllS2+35bkz4x2aB60B1Z+T57u+zE4OKhVm8UnOj50Ny8vTy+++KKkxofu0mQCAABWQpMJQLu3Zs2aeo8TEhL01ltvqVu3bpo/f77y8/OVmpqq3NxcxcTEqFevXgFKCqAta+2hu8cbZXZtyNo1N/5PS/0MG9uPXd8nds0NAD9FkwkATiEiIkJLly5Vdna25syZo969eysnJ0dBQUGBjgagDWrtobvl5VWKiups6avNTsXXqyL5Am8NTf0Mvf05nWo/drjCtyHe5vbnVZUAcLpoMgHATxQWFnr+OzExsd4wOgBoLa09dBcAAKC1cXc5AAAAC1izZo3++c9/asuWLdqyZYsk6a233tJVV12liooK5efny+VyacmSJQzdBQAAlkSTCQAAwMKOD91duXKlkpKStHHjRobuAgAAS2K4HAAAgAUxdBcAANgNVzIBAAAAAADAZzSZAAAAAAAn2bFjhy6++GLt2rVLklRQUKC0tDT17dtXY8eO1c6dOwOcEIDV0GQC4LXIMxyKjo5s9B8AAADsr7a2VjNnzpTL5ZIk1dTUKDMzU+PGjdPmzZuVnJysrKysAKcEYDXMyQTAaxHhHZQ6/e1Gt1m1cJSf0gAAAKC1LF26VP3791dBQYEkadOmTerUqZPS09MlSRkZGVq+fLkKCwuVkJAQyKgALIQrmQAAAAAAHtu3b9fq1as1depUz7Li4mLFx8d7HoeEhCg2NlZFRUUBSAjAqriSCQAAAAAgSXK5XJo5c6Zmz56tiIgIz/IjR47I4XDU29bhcMjpdDZr/1FRnVskZ0vxdroH11G3wkJDfN4GgefNz9yO04BYJTNNJgAAAACAJOnpp5/WoEGD1L9//3rLG2ooVVdXq2PHjs3af3l5lerqjM85W0J0dKTKyiq93tabaSMa259VmgDtXVM/8+a8L6zCn5mDg4MabRbTZAIAAAAASJLWrl2rsrIy5efne5alpaVp9uzZKikp8Sxzu90qLS1VXFxcAFJak+uom0YS2j2aTH7WVOFx1tSq8lC1HxMBAAAAwDFr1qyp9zghIUFvvfWWunXrpvnz5ys/P1+pqanKzc1VTEyMevXqFaCk1hMWGtLo1U7cIAftAU0mP/Om8NjrwjwAAAAAbV1ERISWLl2q7OxszZkzR71791ZOTo6CgoICHQ2AhdBkAgAAAAA0qLCw0PPfiYmJ9YbRAcBPBQc6AAAAAAAAAOyPJhMAAAAAAAB8xnA5AIDlRZ7hUEQ4v7IAAAAAK7PMGfuOHTuUlpamd955R+eee64KCgqUnZ2t4uJiJSQkaN68edweEwDaqYjwDo3eNEHiji0AAABAoFliuFxtba1mzpwpl8slSaqpqVFmZqbGjRunzZs3Kzk5WVlZWQFOCQBoDZFnOBQdHdnoPwAAAADWZ4krmZYuXar+/furoKBAkrRp0yZ16tRJ6enpkqSMjAwtX75chYWFSkhICGRUAEAL4yolAAAAoG0I+JVM27dv1+rVqzV16lTPsuLiYsXHx3seh4SEKDY2VkVFRQFICAAAAAAAgKYE9Eoml8ulmTNnavbs2YqIiPAsP3LkiBwOR71tHQ6HnE5ns/YfFdW5RXL6mzdDQ+w2fMRueSX7ZSYvAAAAACCQAtpkevrppzVo0CD179+/3vKGGkrV1dXq2LFjs/ZfXl6lujrT5HZW+7JbVlbZ6Pro6Mgmt7ESu+WV7JfZX3lb8rPiTd7g4CDbNosBAP7B3ScBALCOgP5GXrt2rcrKypSfn+9ZlpaWptmzZ6ukpMSzzO12q7S0lLv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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "h = dml_plr_regression.predictions.get('ml_m').shape[0]\n", - "fig, ax = plt.subplots(1, 4, figsize=(20,4.8))\n", - "\n", - "#regression histogram\n", - "ax[0].hist(np.reshape(dml_plr_regression.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[0].set_title('regression')\n", - "ax[0].set_xlabel(\"prop_score\")\n", - "ax[0].set_ylabel(\"density\")\n", - "\n", - "#lasso histogram\n", - "ax[1].hist(np.reshape(dml_plr_lasso.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[1].set_title('lasso')\n", - "ax[1].set_xlabel(\"prop_score\")\n", - "ax[1].set_ylabel(\"density\")\n", - "\n", - "#random forest histogram\n", - "ax[2].hist(np.reshape(dml_plr_forest.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[2].set_title('random forest')\n", - "ax[2].set_xlabel(\"prop_score\")\n", - "ax[2].set_ylabel(\"density\")\n", - "\n", - "#boosting histogram\n", - "ax[3].hist(np.reshape(dml_plr_boost.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[3].set_title('xgboost')\n", - "ax[3].set_xlabel(\"prop_score\")\n", - "ax[3].set_ylabel(\"density\")\n", - " \n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "3aa8d603-0df5-48c6-ad62-ac5ffe3e8ada", - "metadata": {}, - "source": [ - "______\n", - "\n", - "**Notes and Acknowledgement**\n", - "\n", - "We would like to thank the organizers of the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge) for setting up this data challenge and making the numerous synthetic data examples publicly available. Although the data examples in the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge) do not explicitly adress A/B testing, we put the data example here in this context to give a tractable example on the use of causal machine learning in practice. The parameters for the random forests and extreme gradient boosting learners have been tuned externally. The corresponding tuning notebook will be uploaded in the examples gallery in the future." - ] - }, - { - "cell_type": "markdown", - "id": "egyptian-platform", - "metadata": {}, - "source": [ - "## References\n", - "\n", - "Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W. and Robins, J. (2018), Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21: C1-C68. doi:10.1111/ectj.12097." - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.12" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/doc/examples/py_double_ml_abtest_tuning.ipynb b/doc/examples/py_double_ml_abtest_tuning.ipynb deleted file mode 100644 index 332ba090..00000000 --- a/doc/examples/py_double_ml_abtest_tuning.ipynb +++ /dev/null @@ -1,1931 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "copyrighted-berry", - "metadata": { - "papermill": { - "duration": 0.02998, - "end_time": "2021-05-26T10:02:06.433929", - "exception": false, - "start_time": "2021-05-26T10:02:06.403949", - "status": "completed" - }, - "tags": [] - }, - "source": [ - "## Tuning Parameters for Python A/B Testing with DoubleML" - ] - }, - { - "cell_type": "markdown", - "id": "exciting-march", - "metadata": { - "papermill": { - "duration": 0.028056, - "end_time": "2021-05-26T10:02:06.564012", - "exception": false, - "start_time": "2021-05-26T10:02:06.535956", - "status": "completed" - }, - "tags": [] - }, - "source": [ - "Here, we illustrate how to tune the parameters of lasso, random forest and gradient boosting. The results are the same as in the A/B Test Main notebook [TODO: Insert link]. The baseline learner linear regression requires no tuning and is therefore not included in this notebook.\n", - "\n", - "Tuning in [DoubleML](https://docs.doubleml.org/stable/index.html) builds upon the functionalities of the Python package scikit learn. The hyperparameter-tuning is performed using either an exhaustive search over specified parameter values implemented in [sklearn.model_selection.GridSearchCV](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.RandomizedSearchCV.html) or via a randomized search implemented in [sklearn.model_selection.RandomizedSearchCV](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html).\n", - "\n", - "We will perform parameter tuning in the A/B Case Study example based on the models:\n", - "\n", - "* Partially linear regression (PLR)\n", - "* Interactive regression model (IRM)\n", - "\n", - "for\n", - "* logistic regression ([LogisticRegressionCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegressionCV.html)),\n", - "* lasso ([LassoCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html)),\n", - "* random forests ([RandomForestRegressor](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html)),\n", - "* extreme gradient boosting ([XGBRegressor/XGBClassifier](https://xgboost.readthedocs.io/en/latest/python/python_api.html)). " - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "id": "grave-marking", - "metadata": { - "papermill": { - "duration": 0.546507, - "end_time": "2021-05-26T10:02:07.138982", - "exception": false, - "start_time": "2021-05-26T10:02:06.592475", - "status": "completed" - }, - "tags": [] - }, - "outputs": [], - "source": [ - "import pandas as pd\n", - "df = pd.read_csv('data/high42.csv', sep=',', na_values=\".\")\n", - "\n", - "#code can also be loaded using a URL of the data\n", - "#url = 'https://raw.githubusercontent.com/DoubleML/doubleml-hiwi-sandbox/master/case_studies/AB_testing/data/high42.CSV?token=AQWGKQUK2PJ4ANBW5GFDG2LAY5ZN4'\n", - "#df = pd.read_csv(url)" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "id": "linear-period", - "metadata": { - "papermill": { - "duration": 7.12797, - "end_time": "2021-05-26T10:02:14.295968", - "exception": false, - "start_time": "2021-05-26T10:02:07.167998", - "status": "completed" - }, - "tags": [] - }, - "outputs": [], - "source": [ - "#pip install -U DoubleML" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "id": "sonic-disclaimer", - "metadata": { - "papermill": { - "duration": 1.50983, - "end_time": "2021-05-26T10:02:15.836637", - "exception": false, - "start_time": "2021-05-26T10:02:14.326807", - "status": "completed" - }, - "tags": [] - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import pandas as pd\n", - "import doubleml as dml\n", - "\n", - "from sklearn.preprocessing import PolynomialFeatures\n", - "\n", - "from sklearn.linear_model import LinearRegression\n", - "from sklearn.linear_model import LogisticRegression\n", - "\n", - "from sklearn.linear_model import LassoCV, LogisticRegressionCV\n", - "from sklearn.ensemble import RandomForestClassifier, RandomForestRegressor\n", - "from sklearn.preprocessing import StandardScaler\n", - "from sklearn.pipeline import make_pipeline\n", - "\n", - "from xgboost import XGBClassifier, XGBRegressor\n", - "\n", - "import matplotlib.pyplot as plt" - ] - }, - { - "cell_type": "markdown", - "id": "9ad48b2f-db15-4002-ade7-4fbd5d3666d0", - "metadata": {}, - "source": [ - "### The Data Backend: `DoubleMLData`" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "id": "economic-chicken", - "metadata": { - "papermill": { - "duration": 0.066803, - "end_time": "2021-05-26T10:02:15.993192", - "exception": false, - "start_time": "2021-05-26T10:02:15.926389", - "status": "completed" - }, - "tags": [] - }, - "outputs": [], - "source": [ - "# Set up basic model: Specify variables for data-backend\n", - "features_base = list(df.columns.values)[2:]\n", - "\n", - "# Initialize DoubleMLData (data-backend of DoubleML)\n", - "data_dml_base = dml.DoubleMLData(df,\n", - " y_col='Y',\n", - " d_cols='A',\n", - " x_cols=features_base)\n", - "\n", - "#print(data_dml_base)" - ] - }, - { - "cell_type": "markdown", - "id": "960d19cb-1db9-4a68-9be1-9b8194f1bbb9", - "metadata": {}, - "source": [ - "## 1. Tuning: Interactive Regression Model (IRM)\n", - "### Lasso\n", - "\n", - "We start our tuning exercise with the interactive regression model with the nuisance parts being estimated by lasso. In a first step we set up our learners based on the [sklearn.linear_model](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.linear_model) package. Here, we don't have to specify parameters. In a second step we initalize our model object, here we use the class [DoubleMLIRM](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLIRM.html). We specify the linear model [LassoCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html#sklearn.linear_model.LassoCV) in a pipeline with a standard scaler applied. \n", - "\n", - "For the lasso regression we set 5 folds of cross validation and the maximum number of iterations to 10000. [LogisticRegressionCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegressionCV.html) with L1 penalty is a lassso classifier. A liblinear `solver` is chosen, which is specifically good for small datasets. A grid of `Cs`, which control the strength of regularization, is created that ranges from 0 to 1. The best `C` is selected by the cross-validation, defined by the `cv` parameter. Note that if we don't specify any parameters for the learners, default values are used.\n", - "\n", - "Using the assigned learners, we initialize the `DoubleMLIRM` model." - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "id": "c383b584-7011-4469-87fa-3eb2fd742850", - "metadata": { - "papermill": { - "duration": 8.853437, - "end_time": "2021-05-26T10:04:04.449701", - "exception": false, - "start_time": "2021-05-26T10:03:55.596264", - "status": "completed" - }, - "tags": [] - }, - "outputs": [], - "source": [ - "# Lasso\n", - "Cs = 0.0001*np.logspace(0, 4, 10) \n", - "lasso = make_pipeline(StandardScaler(), LassoCV(cv=5, max_iter=10000)) \n", - "\n", - "lasso_class = make_pipeline(StandardScaler(), LogisticRegressionCV(cv=5, penalty='l1', solver='liblinear', \n", - " Cs = Cs, max_iter=1000)) \n", - "\n", - "\n", - "# Initialize DoubleMLIRM model\n", - "np.random.seed(123)\n", - "\n", - "dml_irm_lasso = dml.DoubleMLIRM(data_dml_base,\n", - " ml_g = lasso,\n", - " ml_m = lasso_class,\n", - " trimming_threshold = 0.025, \n", - " n_folds = 3)" - ] - }, - { - "cell_type": "markdown", - "id": "21b99548-3e20-47fb-98f5-4edf174a64f3", - "metadata": { - "papermill": { - "duration": 0.031063, - "end_time": "2021-05-26T10:02:16.524653", - "exception": false, - "start_time": "2021-05-26T10:02:16.493590", - "status": "completed" - }, - "tags": [] - }, - "source": [ - "When one doesn't know, which hyperparameters to set when assigning the learner, trying different parameters or tuning is necessery.\n", - "\n", - "### 1. Parameters to Tune\n", - "\n", - "All parameters of a learner can be accessed via a the field [.get_params()](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLPLR.html#doubleml.DoubleMLPLR.get_params). For example in the case of the [LassoCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html#sklearn.linear_model.LassoCV) the parameters that can tuned are:" - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "id": "bd39548f-3c2a-4763-bad7-f6096ddbc7e0", - "metadata": { - "papermill": { - "duration": 0.041091, - "end_time": "2021-05-26T10:02:16.597951", - "exception": false, - "start_time": "2021-05-26T10:02:16.556860", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "dict_keys(['memory', 'steps', 'verbose', 'standardscaler', 'lassocv', 'standardscaler__copy', 'standardscaler__with_mean', 'standardscaler__with_std', 'lassocv__alphas', 'lassocv__copy_X', 'lassocv__cv', 'lassocv__eps', 'lassocv__fit_intercept', 'lassocv__max_iter', 'lassocv__n_alphas', 'lassocv__n_jobs', 'lassocv__normalize', 'lassocv__positive', 'lassocv__precompute', 'lassocv__random_state', 'lassocv__selection', 'lassocv__tol', 'lassocv__verbose'])\n" - ] - } - ], - "source": [ - "print(lasso.get_params().keys())" - ] - }, - { - "cell_type": "markdown", - "id": "5fa3a099-fe24-487b-bfaf-0385439d6214", - "metadata": { - "papermill": { - "duration": 0.03054, - "end_time": "2021-05-26T10:02:16.659995", - "exception": false, - "start_time": "2021-05-26T10:02:16.629455", - "status": "completed" - }, - "tags": [] - }, - "source": [ - "### 2. Tuning Space" - ] - }, - { - "cell_type": "markdown", - "id": "0e583d7d-3683-47f0-9e78-23bb56956eb5", - "metadata": { - "papermill": { - "duration": 0.030255, - "end_time": "2021-05-26T10:02:16.721040", - "exception": false, - "start_time": "2021-05-26T10:02:16.690785", - "status": "completed" - }, - "tags": [] - }, - "source": [ - "Now, we have to specify at least\n", - "\n", - "1. which parameters we would like to tune\n", - "2. the tuning space, i.e., a grid of values for these parameters, \n", - "\n", - "To specify the exact tuning set up in our example, we have to create objects that address points 1. and 2. These are then passed as arguments to the method [tune()](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLPLR.html#doubleml.DoubleMLPLR.tune). To pass the tuning space to the model object, we collect the tuning spaces for all nuisance parts in a named list. The names of the arguments must match the names of the nuisance components. Since tuning takes time the `tune()` method has been commented out. If you uncomment it, it will yield a `C` of $4$ to be the best regularization parameter. A random state of $0$ is assigned for replication." - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "id": "19f95dae-0623-41eb-8787-ce0c532526e5", - "metadata": { - "papermill": { - "duration": 8.853437, - "end_time": "2021-05-26T10:04:04.449701", - "exception": false, - "start_time": "2021-05-26T10:03:55.596264", - "status": "completed" - }, - "tags": [] - }, - "outputs": [], - "source": [ - "tuning_space_ml_g = {} #no tuning here (empty grid)\n", - "tuning_space_ml_m = {\n", - " 'logisticregressioncv__Cs' : np.logspace(0.001, 1, 20, dtype =int),\n", - " 'logisticregressioncv__random_state' : [0]\n", - " }\n", - "\n", - "tuning_spaces = ({\"ml_g\" : tuning_space_ml_g, \n", - " \"ml_m\" : tuning_space_ml_m})\n", - "\n", - "#to tune lasso, uncomment next two lines\n", - "#dml_irm_lasso.tune(tuning_spaces, search_mode = 'randomized_search', tune_on_folds = True,\n", - "# n_folds_tune=3, n_iter_randomized_search = 50, set_as_params = True, n_jobs_cv = -1)" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "id": "dff114cc-6bbd-4ee4-9f9a-88c8f77cd36f", - "metadata": { - "papermill": { - "duration": 8.853437, - "end_time": "2021-05-26T10:04:04.449701", - "exception": false, - "start_time": "2021-05-26T10:03:55.596264", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'A': [None]}\n", - "{'A': [None]}\n", - "{'A': [None]}\n" - ] - } - ], - "source": [ - "print(dml_irm_lasso.get_params('ml_g0'))\n", - "print(dml_irm_lasso.get_params('ml_g1'))\n", - "print(dml_irm_lasso.get_params('ml_m'))" - ] - }, - { - "cell_type": "markdown", - "id": "56e8c8fb-dc94-413c-bc43-7f016cf10e28", - "metadata": {}, - "source": [ - "Next, the best paramter of C is assigned using [.set_ml_nuisance_params](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLPLR.html#doubleml.DoubleMLPLR.set_ml_nuisance_params) method and the model is fit. If you notice only the parameter `C=4` is set for the nuisance fuctnion `ml_m`, while the parameters of the other functions (`mlg0` and `ml_g1`) are left to their defaults. The result of the estimate is the same as in the main notebook." - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "id": "9681a76b-1e3a-42ee-9b0e-f9e87762589e", - "metadata": { - "papermill": { - "duration": 8.853437, - "end_time": "2021-05-26T10:04:04.449701", - "exception": false, - "start_time": "2021-05-26T10:03:55.596264", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.834276 0.070511 11.831913 2.669875e-32 0.696078 0.972475" - ] - }, - "execution_count": 48, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Set nuisance-part specific parameters\n", - "dml_irm_lasso.set_ml_nuisance_params('ml_g0', 'A', {})\n", - "dml_irm_lasso.set_ml_nuisance_params('ml_g1', 'A', {})\n", - "dml_irm_lasso.set_ml_nuisance_params('ml_m', 'A', {\n", - " 'logisticregressioncv__Cs': 4, 'logisticregressioncv__random_state': 0})\n", - "\n", - "#fit model with above set parameters\n", - "dml_irm_lasso.fit(store_predictions=True) \n", - "lasso_summary = dml_irm_lasso.summary\n", - "\n", - "lasso_summary" - ] - }, - { - "cell_type": "markdown", - "id": "surface-tractor", - "metadata": { - "papermill": { - "duration": 0.046539, - "end_time": "2021-05-26T10:04:04.561414", - "exception": false, - "start_time": "2021-05-26T10:04:04.514875", - "status": "completed" - }, - "tags": [] - }, - "source": [ - "### Random Forest\n", - "\n", - "When the treated and untreated groups are unbalanced it could be hard to find overlap in order to calculate the ATE. To reduce the disproportionate impact of extreme propensity score weights in the interactive model, we trim the propensity scores, which are close to the bounds. The trimming threshold for the propensitiy scores is set to $0.025$ meaning that propensity score below $2.5%$ or abobe $97.5%$ are removed. This will remove some of the variance in the model, but will add bias back.\n", - "\n", - "A random forest regression and classifier are called." - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "id": "downtown-investor", - "metadata": { - "papermill": { - "duration": 0.041146, - "end_time": "2021-05-26T10:04:04.636144", - "exception": false, - "start_time": "2021-05-26T10:04:04.594998", - "status": "completed" - }, - "tags": [] - }, - "outputs": [], - "source": [ - "# Random Forest\n", - "randomForest = RandomForestRegressor()\n", - "randomForest_class = RandomForestClassifier()\n", - "\n", - "np.random.seed(123)\n", - "dml_irm_forest = dml.DoubleMLIRM(data_dml_base,\n", - " ml_g = randomForest,\n", - " ml_m = randomForest_class,\n", - " trimming_threshold = 0.025,\n", - " n_folds = 3)" - ] - }, - { - "cell_type": "markdown", - "id": "9921bb70-a994-4358-9114-c554f736b69c", - "metadata": {}, - "source": [ - "A tuning grid of parameters is created for the two learners. Uncommenting the [`.tune`](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLIRM.html?highlight=tune#doubleml.DoubleMLIRM.tune) method will begin the tuning, which can take more than an hour." - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "id": "automated-watershed", - "metadata": { - "papermill": { - "duration": 152.721269, - "end_time": "2021-05-26T10:06:37.391258", - "exception": false, - "start_time": "2021-05-26T10:04:04.669989", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/plain": [ - "dict" - ] - }, - "execution_count": 50, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "#RF Tuning \n", - "\n", - "tuning_space_ml_g = {\n", - " 'max_depth': [8, 10, 12, 15],\n", - "'max_features': ['auto', 'sqrt'],\n", - " 'min_samples_leaf': [1, 2, 4, 5],\n", - " 'min_samples_split': [4, 5, 6, 10],\n", - " 'n_estimators': [100, 200, 300, ]}\n", - "\n", - "tuning_space_ml_m = {\n", - " 'max_depth': [3, 5, 6, 7, 10],\n", - "'max_features': ['auto', 'sqrt'],\n", - " 'min_samples_leaf': [5, 6, 7, 8],\n", - " 'min_samples_split': [2, 3, 5],\n", - " 'n_estimators': [100, 200]}\n", - "\n", - "tuning_spaces = ({\"ml_g\" : tuning_space_ml_g, \n", - " \"ml_m\" : tuning_space_ml_m})\n", - "\n", - "import warnings\n", - "warnings.filterwarnings(\"ignore\")\n", - "\n", - "type(tuning_spaces)\n", - "#dml_irm_forest.tune(tuning_spaces, search_mode = 'randomized_search', tune_on_folds = True,\n", - "# n_folds_tune=3, n_iter_randomized_search = 50, set_as_params = True, return_tune_res = True, n_jobs_cv = -1)" - ] - }, - { - "cell_type": "markdown", - "id": "05feed3c-abdd-4b19-9ac0-41d9e3b4a56c", - "metadata": {}, - "source": [ - "Using the [.get_params](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLIRM.html?highlight=get_params#doubleml.DoubleMLIRM.get_params) method the tuned parameters are printed, which are then hardcoded into [.set_ml_nuisance_params](https://docs.doubleml.org/dev/api/generated/doubleml.DoubleMLPLR.html#doubleml.DoubleMLPLR.set_ml_nuisance_params) method. This way one does not have to wait for the tuning every time." - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "id": "convinced-effect", - "metadata": { - "papermill": { - "duration": 0.042846, - "end_time": "2021-05-26T10:06:37.468481", - "exception": false, - "start_time": "2021-05-26T10:06:37.425635", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'A': [None]}\n", - "{'A': [None]}\n", - "{'A': [None]}\n" - ] - } - ], - "source": [ - "print(dml_irm_forest.get_params('ml_g0'))\n", - "print(dml_irm_forest.get_params('ml_g1'))\n", - "print(dml_irm_forest.get_params('ml_m'))" - ] - }, - { - "cell_type": "markdown", - "id": "b5d0d2e7-d4be-47e7-925c-ea1b6893d269", - "metadata": {}, - "source": [ - "The results are the same as those in the main notebook." - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "id": "every-stack", - "metadata": { - "papermill": { - "duration": 13.713732, - "end_time": "2021-05-26T10:06:51.217700", - "exception": false, - "start_time": "2021-05-26T10:06:37.503968", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.86203 0.08229 10.475455 1.119983e-25 0.700743 1.023316" - ] - }, - "execution_count": 52, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "#Set nuisance-part specific parameters\n", - "dml_irm_forest.set_ml_nuisance_params('ml_g0', 'A', {\n", - " 'max_features': 200, 'n_estimators': 250})\n", - "dml_irm_forest.set_ml_nuisance_params('ml_g1', 'A', {\n", - " 'max_features': 200, 'n_estimators': 250})\n", - "dml_irm_forest.set_ml_nuisance_params('ml_m', 'A', {\n", - " 'max_features': 200, 'n_estimators': 250})\n", - "\n", - "dml_irm_forest.fit(store_predictions=True) \n", - "forest_summary = dml_irm_forest.summary\n", - "\n", - "forest_summary" - ] - }, - { - "cell_type": "markdown", - "id": "preliminary-ladder", - "metadata": { - "papermill": { - "duration": 0.035057, - "end_time": "2021-05-26T10:06:51.519120", - "exception": false, - "start_time": "2021-05-26T10:06:51.484063", - "status": "completed" - }, - "tags": [] - }, - "source": [ - "### Boosted Trees\n", - "\n", - "First we specify the learning task and the corresponding learning objective. The first nuiscance function is estimated using the `XGBRegressor` with objective option reg:squarederror, is a regression with squared loss. The default evaluation metric is the rmse. The second nuisance function is estimated by classification, hence the objective is binary:lorgistic with an evaluation metric logloss. Eta, which ranges $[0,1]$ is the step size shrinkage is used during update to prevent overfitting. Because our outpuv value is already numeric we set the label encoder to false. For further information see the documentation of [XGBoost](https://xgboost.readthedocs.io/en/latest/parameter.html)." - ] - }, - { - "cell_type": "code", - "execution_count": 53, - "id": "touched-duration", - "metadata": { - "papermill": { - "duration": 0.044223, - "end_time": "2021-05-26T10:06:51.598881", - "exception": false, - "start_time": "2021-05-26T10:06:51.554658", - "status": "completed" - }, - "tags": [] - }, - "outputs": [], - "source": [ - "boost = XGBRegressor(n_jobs=1, objective = \"reg:squarederror\")\n", - "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", - " objective = \"binary:logistic\", eval_metric = \"logloss\")\n", - "\n", - "np.random.seed(123)\n", - "dml_irm_boost = dml.DoubleMLIRM(data_dml_base,\n", - " ml_g = boost,\n", - " ml_m = boost_class,\n", - " trimming_threshold = 0.025,\n", - " n_folds = 3)" - ] - }, - { - "cell_type": "code", - "execution_count": 54, - "id": "domestic-belfast", - "metadata": { - "papermill": { - "duration": 0.042653, - "end_time": "2021-05-26T10:06:51.678474", - "exception": false, - "start_time": "2021-05-26T10:06:51.635821", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "['ml_g0', 'ml_g1', 'ml_m']\n" - ] - } - ], - "source": [ - "print(dml_irm_boost.params_names)\n" - ] - }, - { - "cell_type": "markdown", - "id": "054d8a6d-e58f-444e-a2ce-b6de8590d123", - "metadata": {}, - "source": [ - "### Grid Search" - ] - }, - { - "cell_type": "markdown", - "id": "4dcdf726-db3a-4975-b452-5d383ce80582", - "metadata": {}, - "source": [ - "Similarly to the lasso and random forest the tuning for gradient boosting is done. Due to the smaller parameter grid, it only takes about 2 minutes to tune. The hardcoded parameters can be verified by uncommenting the `.tune` method and letting it run." - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "id": "50cebc31-f53b-45ea-90c3-184c002dfe31", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "text/plain": [ - "dict" - ] - }, - "execution_count": 55, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "#parameter space wide\n", - "\n", - "tuning_space_ml_g = {'n_estimators': [5,8,15,25,30, 40, 50], 'eta': [0.01,0.1,0.2,0,5]}\n", - "\n", - "tuning_space_ml_m = {'n_estimators': [5,8,15,25,30, 40, 50], 'eta': [0.01,0.1,0.2,0,5]}\n", - "\n", - "tuning_spaces = ({\"ml_g\" : tuning_space_ml_g, \n", - " \"ml_m\" : tuning_space_ml_m})\n", - "\n", - "import warnings\n", - "warnings.filterwarnings(\"ignore\")\n", - "\n", - "type(tuning_spaces)\n", - "#dml_irm_boost.tune(tuning_spaces, search_mode = 'randomized_search', tune_on_folds = True,\n", - "# n_folds_tune=5, set_as_params = True, return_tune_res = False)" - ] - }, - { - "cell_type": "code", - "execution_count": 56, - "id": "2d9368b4-af15-4921-82ac-321ea78f56f7", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'A': [None]}\n", - "{'A': [None]}\n", - "{'A': [None]}\n" - ] - } - ], - "source": [ - "print(dml_irm_boost.get_params('ml_g0'))\n", - "print(dml_irm_boost.get_params('ml_g1'))\n", - "print(dml_irm_boost.get_params('ml_m'))" - ] - }, - { - "cell_type": "code", - "execution_count": 57, - "id": "03b67303-08ee-458b-86dc-03b96664bee9", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 57, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "#Set nuisance-part specific parameters\n", - "dml_irm_boost.set_ml_nuisance_params('ml_g0', 'A', {\n", - " 'n_estimators': 30, 'eta': 0.2})\n", - "dml_irm_boost.set_ml_nuisance_params('ml_g1', 'A', {\n", - " 'n_estimators': 30, 'eta': 0.2})\n", - "dml_irm_boost.set_ml_nuisance_params('ml_m', 'A', {\n", - " 'n_estimators': 15, 'eta': 0.2})" - ] - }, - { - "cell_type": "code", - "execution_count": 58, - "id": "published-haiti", - "metadata": { - "papermill": { - "duration": 1.624245, - "end_time": "2021-05-26T10:06:57.845803", - "exception": false, - "start_time": "2021-05-26T10:06:56.221558", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.739225 0.092511 7.990648 1.342310e-15 0.557906 0.920544" - ] - }, - "execution_count": 58, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "dml_irm_boost.fit(store_predictions=True)\n", - "boost_summary = dml_irm_boost.summary\n", - "\n", - "boost_summary" - ] - }, - { - "cell_type": "markdown", - "id": "29edef0d-7e46-4004-8dab-ebebd92d0c6b", - "metadata": {}, - "source": [ - "### Summary Results\n", - "We define a small function which calculates the bias from the true parameter $0.8$." - ] - }, - { - "cell_type": "code", - "execution_count": 59, - "id": "e3486038-6b28-4278-a661-072a528a1602", - "metadata": {}, - "outputs": [], - "source": [ - "def bias(x):\n", - " x=x - 0.8\n", - " x=round(abs(x),3)\n", - " return x" - ] - }, - { - "cell_type": "code", - "execution_count": 60, - "id": "touched-bristol", - "metadata": { - "papermill": { - "duration": 0.054738, - "end_time": "2021-05-26T10:06:57.937711", - "exception": false, - "start_time": "2021-05-26T10:06:57.882973", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefBias2.5 %97.5 %
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forest0.8620.0620.7011.023
xgboost0.7390.0610.5580.921
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" - ], - "text/plain": [ - " coef Bias 2.5 % 97.5 %\n", - "lasso 0.834 0.034 0.696 0.972\n", - "forest 0.862 0.062 0.701 1.023\n", - "xgboost 0.739 0.061 0.558 0.921" - ] - }, - "execution_count": 60, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "irm_summary = pd.concat((lasso_summary, forest_summary, boost_summary))\n", - "irm_summary.index = ['lasso', 'forest', 'xgboost']\n", - "\n", - "irm_summary.insert(1, \"Bias\", [bias(irm_summary.loc['lasso','coef']), \n", - " bias(irm_summary.loc['forest','coef']), \n", - " bias(irm_summary.loc['xgboost','coef'])])\n", - "\n", - "irm_summary[['coef', 'Bias', '2.5 %', '97.5 %']].round(3)" - ] - }, - { - "cell_type": "markdown", - "id": "fc7c0d5e-e824-48c1-8427-60416601e330", - "metadata": { - "papermill": { - "duration": 0.030715, - "end_time": "2021-05-26T10:02:16.264183", - "exception": false, - "start_time": "2021-05-26T10:02:16.233468", - "status": "completed" - }, - "tags": [] - }, - "source": [ - "## 2. Tuning: Partial Linear Regression Model\n", - "\n", - "### Lasso\n", - "\n", - "The lasso tuning from above problem works quite well, therefore it was unchanged." - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "id": "524baf7e-978d-452e-b38f-1e91c6004f74", - "metadata": { - "papermill": { - "duration": 0.044535, - "end_time": "2021-05-26T10:02:16.462934", - "exception": false, - "start_time": "2021-05-26T10:02:16.418399", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 61, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "#PLR\n", - "from sklearn.linear_model import Lasso\n", - "\n", - "#is pipeline bc. there is scaling applied before\n", - "lasso = make_pipeline(StandardScaler(), LassoCV(cv=5, max_iter=10000)) #lasso is only for regression (not for classification)\n", - "\n", - "lasso_class = make_pipeline(StandardScaler(),\n", - " LogisticRegressionCV(cv=5, penalty='l1', solver='liblinear', #logistic reg with l1 penalty is a lassso classifier\n", - " max_iter=1000)) #liblinear solver for small datasets\n", - "\n", - "np.random.seed(123)\n", - "# Initialize DoubleMLPLR model\n", - "dml_plr_lasso = dml.DoubleMLPLR(data_dml_base,\n", - " ml_g = lasso,\n", - " ml_m = lasso_class,\n", - " n_folds = 3)\n", - "\n", - "dml_plr_lasso" - ] - }, - { - "cell_type": "code", - "execution_count": 62, - "id": "5bda9cf2-d2dc-4e9a-a29c-51fec8ada893", - "metadata": { - "papermill": { - "duration": 48.914961, - "end_time": "2021-05-26T10:03:05.666964", - "exception": false, - "start_time": "2021-05-26T10:02:16.752003", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.784574 0.070414 11.14235 7.803312e-29 0.646566 0.922582" - ] - }, - "execution_count": 63, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "dml_plr_lasso.fit(store_predictions=True)\n", - "lasso_summary = dml_plr_lasso.summary\n", - "\n", - "lasso_summary" - ] - }, - { - "cell_type": "markdown", - "id": "c6fef8ee-7283-4ec4-9f75-228c512e713e", - "metadata": { - "papermill": { - "duration": 0.04306, - "end_time": "2021-05-26T10:03:09.220743", - "exception": false, - "start_time": "2021-05-26T10:03:09.177683", - "status": "completed" - }, - "tags": [] - }, - "source": [ - "The coefficient estimated with lasso is the same as in the main notebook [TODO:insert link of main notebook]." - ] - }, - { - "cell_type": "markdown", - "id": "ff1daf63-a0b5-4b25-8401-4240c92b82cf", - "metadata": { - "papermill": { - "duration": 0.032194, - "end_time": "2021-05-26T10:03:09.284890", - "exception": false, - "start_time": "2021-05-26T10:03:09.252696", - "status": "completed" - }, - "tags": [] - }, - "source": [ - "### Random Forest" - ] - }, - { - "cell_type": "markdown", - "id": "5884e36c-3e4d-4cfd-8011-96b3b02612db", - "metadata": {}, - "source": [ - "In this case we use the random forest defaults which perform quite well. Therefore no tuning grid is provided." - ] - }, - { - "cell_type": "code", - "execution_count": 64, - "id": "95c1f2ae-e9dd-4bf4-b1cc-b163b0f1e761", - "metadata": { - "papermill": { - "duration": 0.040901, - "end_time": "2021-05-26T10:03:09.357683", - "exception": false, - "start_time": "2021-05-26T10:03:09.316782", - "status": "completed" - }, - "tags": [] - }, - "outputs": [], - "source": [ - "randomForest = RandomForestRegressor()\n", - "randomForest_class = RandomForestClassifier()\n", - "\n", - "np.random.seed(123)\n", - "dml_plr_forest = dml.DoubleMLPLR(data_dml_base,\n", - " ml_g = randomForest,\n", - " ml_m = randomForest_class,\n", - " n_folds = 3,\n", - " n_rep=3)" - ] - }, - { - "cell_type": "code", - "execution_count": 65, - "id": "82241056-5645-409e-961d-6450cc34e8fe", - "metadata": { - "papermill": { - "duration": 43.429064, - "end_time": "2021-05-26T10:03:53.091617", - "exception": false, - "start_time": "2021-05-26T10:03:09.662553", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.823899 0.073474 11.213529 3.499555e-29 0.679893 0.967904" - ] - }, - "execution_count": 65, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "dml_plr_forest.fit(store_predictions=True)\n", - "forest_summary = dml_plr_forest.summary\n", - "\n", - "forest_summary" - ] - }, - { - "cell_type": "markdown", - "id": "f5dcd940-e798-4e5f-b867-b33f921b1809", - "metadata": { - "papermill": { - "duration": 0.031748, - "end_time": "2021-05-26T10:03:53.155272", - "exception": false, - "start_time": "2021-05-26T10:03:53.123524", - "status": "completed" - }, - "tags": [] - }, - "source": [ - "### Bosting\n", - "\n", - "Hyperparameters are pre-set for the boosting learners. The squared error objective is appropriate for a regression learner and the binary:logistic with a log loss evaluation metric for a classifier." - ] - }, - { - "cell_type": "code", - "execution_count": 66, - "id": "a0504319-cee1-42c3-8a44-c7a5f417d9de", - "metadata": { - "papermill": { - "duration": 0.039558, - "end_time": "2021-05-26T10:03:53.369239", - "exception": false, - "start_time": "2021-05-26T10:03:53.329681", - "status": "completed" - }, - "tags": [] - }, - "outputs": [], - "source": [ - "boost = XGBRegressor(n_jobs=1, objective = \"reg:squarederror\",\n", - " eta=0.1)\n", - "\n", - "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", - " objective = \"binary:logistic\", eval_metric = \"logloss\",\n", - " eta=0.1)\n", - "\n", - "# Boosted Trees\n", - "\n", - "np.random.seed(123)\n", - "dml_plr_boost = dml.DoubleMLPLR(data_dml_base,\n", - " ml_g = boost,\n", - " ml_m = boost_class,\n", - " n_folds = 3)" - ] - }, - { - "cell_type": "markdown", - "id": "f49b5655-7425-46b9-b3c2-7eda01c0e86f", - "metadata": { - "papermill": { - "duration": 0.032229, - "end_time": "2021-05-26T10:03:53.505178", - "exception": false, - "start_time": "2021-05-26T10:03:53.472949", - "status": "completed" - }, - "tags": [] - }, - "source": [ - "Bosting is not very good without tuning, therefore a grid of parameters is provided below. It was found using a randomized search, that `n_estimators` in range $55$ and $65$ provide good results. Therfore in the gird search below this range for `n_estimators` is used. Similarly for the $ml_m$ it was found that `n_estimators` between $1$ and $10$ perform well. This refined our search to a smaller range of hyperparameters. To tune, uncomment `dml_plr_boost.tune`." - ] - }, - { - "cell_type": "code", - "execution_count": 67, - "id": "0e0fbdf2-230c-4b61-ba88-faa1a2ca1fba", - "metadata": { - "papermill": { - "duration": 0.041937, - "end_time": "2021-05-26T10:03:53.579534", - "exception": false, - "start_time": "2021-05-26T10:03:53.537597", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "['ml_g', 'ml_m']\n", - "{'A': [None]}\n", - "{'A': [None]}\n" - ] - } - ], - "source": [ - "#tuning further parameters\n", - "\n", - "tuning_space_ml_g = {'n_estimators': np.linspace(55, 65, 5, dtype = int), 'max_depth': [2,3,4,6]}\n", - "\n", - "tuning_space_ml_m = {'n_estimators': np.linspace(1, 10, 5, dtype = int), 'max_depth': [2,3,4,6]}\n", - "\n", - "tuning_spaces = ({\"ml_g\" : tuning_space_ml_g, \n", - " \"ml_m\" : tuning_space_ml_m})\n", - "\n", - "import warnings\n", - "warnings.filterwarnings(\"ignore\")\n", - "\n", - "type(tuning_spaces)\n", - "#dml_plr_boost.tune(tuning_spaces, search_mode = 'randomized_search')\n", - "\n", - "print(dml_plr_boost.params_names)\n", - "print(dml_plr_boost.get_params('ml_g'))\n", - "print(dml_plr_boost.get_params('ml_m'))" - ] - }, - { - "cell_type": "markdown", - "id": "aab368e4-f997-4764-9d12-c3a1eaf1de04", - "metadata": { - "papermill": { - "duration": 0.03227, - "end_time": "2021-05-26T10:03:53.644151", - "exception": false, - "start_time": "2021-05-26T10:03:53.611881", - "status": "completed" - }, - "tags": [] - }, - "source": [ - "The results of the tuning will show that the best hyperparameters for $ml_g$ are `n_estimators: 57, max_depth: 2` and the best hyperparameters for $ml_m$ are `n_estimators: 10, max_depth: 3`. These parameters are hardcoded using the [`.set_ml_nuisance_params`](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLPLR.html#doubleml.DoubleMLPLR.set_ml_nuisance_params) method. " - ] - }, - { - "cell_type": "code", - "execution_count": 68, - "id": "140830c6-2e1a-4ed5-b008-a9f2d00f4dfa", - "metadata": { - "papermill": { - "duration": 0.039799, - "end_time": "2021-05-26T10:03:53.716377", - "exception": false, - "start_time": "2021-05-26T10:03:53.676578", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 68, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "dml_plr_boost.set_ml_nuisance_params('ml_g', 'A', { \n", - " 'n_estimators': 57, 'max_depth': 2})\n", - "dml_plr_boost.set_ml_nuisance_params('ml_m', 'A', { \n", - " 'n_estimators': 10, 'max_depth': 3}) " - ] - }, - { - "cell_type": "code", - "execution_count": 69, - "id": "3972a161-0583-4b9c-b7cb-3a34129c7394", - "metadata": { - "papermill": { - "duration": 1.529645, - "end_time": "2021-05-26T10:03:55.279584", - "exception": false, - "start_time": "2021-05-26T10:03:53.749939", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.814555 0.071203 11.439929 2.641013e-30 0.675 0.95411" - ] - }, - "execution_count": 69, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "dml_plr_boost.fit(store_predictions=True)\n", - "boost_summary = dml_plr_boost.summary\n", - "\n", - "boost_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 70, - "id": "bab3da63-40f4-430d-8379-552068cd6c35", - "metadata": { - "papermill": { - "duration": 0.04787, - "end_time": "2021-05-26T10:03:55.428273", - "exception": false, - "start_time": "2021-05-26T10:03:55.380403", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefBias2.5 %97.5 %
lasso0.7850.0150.6470.923
forest0.8240.0240.6800.968
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" - ], - "text/plain": [ - " coef Bias 2.5 % 97.5 %\n", - "lasso 0.785 0.015 0.647 0.923\n", - "forest 0.824 0.024 0.680 0.968\n", - "xgboost 0.815 0.015 0.675 0.954" - ] - }, - "execution_count": 70, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "plr_summary = pd.concat((lasso_summary, forest_summary, boost_summary))\n", - "plr_summary.index = ['lasso', 'forest', 'xgboost']\n", - "\n", - "plr_summary.insert(1, \"Bias\", [bias(plr_summary.loc['lasso','coef']), \n", - " bias(plr_summary.loc['forest','coef']), \n", - " bias(plr_summary.loc['xgboost','coef'])])\n", - "\n", - "plr_summary[['coef', 'Bias', '2.5 %', '97.5 %']].round(3)" - ] - }, - { - "cell_type": "markdown", - "id": "agricultural-holder", - "metadata": { - "papermill": { - "duration": 0.038336, - "end_time": "2021-05-26T10:06:58.015999", - "exception": false, - "start_time": "2021-05-26T10:06:57.977663", - "status": "completed" - }, - "tags": [] - }, - "source": [ - "## Summary Results All Models\n", - "Regression results are left out because there is no tuning required." - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "id": "pediatric-subdivision", - "metadata": { - "papermill": { - "duration": 0.065362, - "end_time": "2021-05-26T10:06:58.120049", - "exception": false, - "start_time": "2021-05-26T10:06:58.054687", - "status": "completed" - }, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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ModelML
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forest0.8620.0620.7011.023
xgboost0.7390.0610.5580.921
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forest0.8240.0240.6800.968
xgboost0.8150.0150.6750.954
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" - ], - "text/plain": [ - " coef Bias 2.5 % 97.5 %\n", - "Model ML \n", - "IRM Tune lasso 0.834 0.034 0.696 0.972\n", - " forest 0.862 0.062 0.701 1.023\n", - " xgboost 0.739 0.061 0.558 0.921\n", - "PLR Tune lasso 0.785 0.015 0.647 0.923\n", - " forest 0.824 0.024 0.680 0.968\n", - " xgboost 0.815 0.015 0.675 0.954" - ] - }, - "execution_count": 71, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df_summary = pd.concat((irm_summary, plr_summary)).reset_index().rename(columns={'index': 'ML'})\n", - "df_summary['Model'] = np.concatenate((np.repeat('IRM Tune', 3), np.repeat('PLR Tune', 3)))\n", - "df_summary\n", - "\n", - "df_summary=df_summary[['ML', 'Model','coef', 'Bias', '2.5 %', '97.5 %']]\n", - "df_summary\n", - "df_summary.set_index(['Model', 'ML']).round(3)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.12" - }, - "papermill": { - "default_parameters": {}, - "duration": 299.684742, - "end_time": "2021-05-26T10:06:59.042230", - "environment_variables": {}, - "exception": null, - "input_path": "__notebook__.ipynb", - "output_path": "__notebook__.ipynb", - "parameters": {}, - "start_time": "2021-05-26T10:01:59.357488", - "version": "2.3.3" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} From ba564f695d95ab3b5d53242c77a673835c8bb1d3 Mon Sep 17 00:00:00 2001 From: Philipp Bach Date: Wed, 1 Jun 2022 15:33:48 +0200 Subject: [PATCH 15/20] some final edits to Py version --- doc/examples/py_double_ml_abtest.ipynb | 8060 ++++++++++++------------ 1 file changed, 4037 insertions(+), 4023 deletions(-) diff --git a/doc/examples/py_double_ml_abtest.ipynb b/doc/examples/py_double_ml_abtest.ipynb index bcf32f35..014e07d0 100644 --- a/doc/examples/py_double_ml_abtest.ipynb +++ b/doc/examples/py_double_ml_abtest.ipynb @@ -1,4023 +1,4037 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "consecutive-cabinet", - "metadata": {}, - "source": [ - "# Python: A/B Testing with DoubleML" - ] - }, - { - "cell_type": "markdown", - "id": "opponent-indonesian", - "metadata": {}, - "source": [ - "\"An\n", - "\n", - "Image Source Freepik http://www.freepik.com, Designed by macrovector\n" - ] - }, - { - "cell_type": "markdown", - "id": "c7c96f88", - "metadata": {}, - "source": [ - "In this notebook, we demontrate exemplarily how the [DoubleML](https://docs.doubleml.org/stable/index.html) package can be used to estimate the causal effect of seeing a new ad design on customers' purchases in a webshop. The [DoubleML](https://docs.doubleml.org/stable/index.html) package for Python and R provides an implementation of the double / debiased machine learning (DML) framework of [Chernozhukov et al. (2018)](https://arxiv.org/abs/1608.00060) and can be used to estimate causal effects based on machine learning (ML) methods.\n", - "\n", - "## A/B Testing\n", - "\n", - "A/B testing is a frequently used framework to perform causal inference in practice. For example, a manager of a webshop might want to optimally adapt the webshop design according to users' preferences. For examle, she might want to estimate the effect of a new ad design, which is displayed on the starting page, on a customer's purchases (in $100\\$$). A/B tests refer to an experimental design in which a certain treatment, for example a new ad design (called \"Version $A$\"), is randomly assigned to groups of individuals, like website visitors or app users. If a user is not \"treated\", i.e., he is not exposed to Version $A$, he sees an alternative design \"Version $B$\" like the old design of the ad. The assignment of the treatment might either be unconditionally random, i.e., randomly assigned to all visitors of the online shop or directed towards specific groups of them. In the latter case, the treatment assignment would be conditional on their characteristics, like their shopping history. For example, a discount might only be granted to customers who already made some purchases in the past.\n", - "\n", - "In general, the goal of the A/B test is to assess whether the treatment has an effect on the outcome variable of interest. In our example, the manager wants to evaluate whether the new ad design changed the monetary value of products purchased (in $100\\$$). Alternative settings of A/B tests refer to improvement of a user experience on a website or estimation of price elasticities. Websites and apps are ideal for running A/B tests because they make it very easy to precisely direct the treatment to visitors and users (or to specific subgroups of them) as well as to collect the data required for evaluation of the intervention.\n", - "\n", - "## Scenario\n", - "\n", - "Let's consider the following stylized scenario. The manager of a webshop is performing an A/B test to estimate the effect a new ad design $A$ has on customers' purchases, $Y$, on average. This effect is called the **A**verage **T**reatment **E**ffect (**ATE**). The treatment is assigned randomly conditional on the visitors' characteristics, which we call $V$. Such characteristics could be collected from a customer's shoppers account, for example. These might include the number of previous purchases, time since the last purchase, length of stay on a page as well as whether a customer has a rewards card, among other characteristics.
\n", - "\n", - "In the following, we use a **D**irected **A**cyclical **G**raph (DAG) to illustrate our assumptions on the causal structure of the scenario. As not only the outcome, but also the treatment is dependent on the individuals characteristics, there are arrows going from $V$ to both $A$ and $Y$. In our example, we also assume that the treatment $A$ is a direct cause of the customers' purchases $Y$.\n", - "\n", - "\n", - "![Scenario illustration with a DAG](figures/DAG.svg)\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "id": "220997c6", - "metadata": {}, - "source": [ - "Let's assume the conditional randomization has been conducted properly, such that a tidy data set has been collected. Now, a data scientist wants to evaluate whether the new ad design causally affected the sales, by using the [DoubleML](https://docs.doubleml.org/stable/index.html) package.\n", - "\n", - "### Why control for individual characteristics?\n", - "\n", - "Before we start the case study, let us briefly address the question why we need to include individual characteristics in our analysis at all. There are mainly two reasons why we want to control for observable characteristics. First, so-called confounders, i.e., variables that have a causal effect on both the treatment variable and the outcome variable, possibly create a bias in our estimate. In order to uncover the true causal effect of the treatment, it is necessary that our causal framework takes all confounding variables into account. Otherwise, the average causal effect of the treatment on the outcome is not identified. A second reason to include individual characteristics is efficiency. The more variation can be explained within our causal framework, the more precise will be the resulting estimate. In practical terms, greater efficiency leads to tighter confidence intervals and smaller standard errors and p-values. This might help to improve the power of A/B tests even if the treatment variable is unconditionally assigned to individuals.\n", - "\n", - "### Why use machine learning to analyze A/B tests?\n", - "\n", - "ML methods have turned out to be very flexible in terms of modeling complex relationships of explanatory variables and dependent variables and, thus, have exhibited a great predictive performance in many applications. In the double machine learning approach ([Chernozhukov et al. (2018)](https://arxiv.org/abs/1608.00060)), ML methods are used for modelling so-called nuisance functions. In terms of the A/B case study considered here, ML tools can be used to flexibly control for confounding variables. For example, a linear parametric specification as in a standard linear regression model might not be correct and, hence, not sufficient to account for the underlying confounding. Moreover, by using powerful ML techniques, the causal model will likely be able to explain a greater share of the total variation and, hence, lead to more precise estimation." - ] - }, - { - "cell_type": "markdown", - "id": "0ec5b0cf", - "metadata": {}, - "source": [ - "## Data \n", - "\n", - "As an illustrative example we use a data set from the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge). In this challenge, a great number of data sets have been generated in a way that they mimic distributional relationships that are found in many economic real data applications. Although the data have not been generated explicitly to address an A/B testing case study, they are well-suited for demonstration purposes. We will focus on one of the many different data genereting processes (DGP) that we picked at random, in this particualar case a data set called `high42`. An advantage of using the synthetic [ACIC 2019 data](https://sites.google.com/view/acic2019datachallenge/data-challenge) is that we know the true average treatment effect which is 0.8 in our data set.\n", - "\n", - "First we load the data." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "e39d4dd0", - "metadata": {}, - "outputs": [], - "source": [ - "import pandas as pd\n", - "\n", - "#fetch_ACIChigh42 needs to be defined\n", - "#df = fetch_ACIChigh42(return_type='DataFrame')\n", - "\n", - "#load code locally\n", - "df = pd.read_csv('data/high42.csv', sep=',', na_values=\".\")\n", - "\n", - "#code can also be loaded using a URL of the data\n", - "#url = 'https://raw.githubusercontent.com/DoubleML/doubleml-hiwi-sandbox/master/case_studies/AB_testing/data/high42.CSV?token=AQWGKQRE57BBRGOCBPSNBJTBD57ZQ'\n", - "#df = pd.read_csv(url)" - ] - }, - { - "cell_type": "markdown", - "id": "11525056-cdec-4916-9cb4-aa4268e99175", - "metadata": {}, - "source": [ - "We see that the data set consists of 1000 observations (= website visitors) and 202 variables. The $Y$ column represents the customers' purchases (in $100\\$$). The treatment variable $A$ is binary with a value 1 indicating that a customer has been exposed to the new ad design (and value 0 otherwise). The remaining 200 columns $V$ represent individual characteristics of the customers." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "10edc74d", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(1000, 202)\n" - ] - } - ], - "source": [ - "print(df.shape)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "6760c009", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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" - ], - "text/plain": [ - " Y A V1 V2 V3 V4 V5 V6 V7 V8 ... \\\n", - "0 7.358185 1 10 0 0 7 192.793769 23.676950 8 0.185443 ... \n", - "1 8.333672 1 12 0 1 4 199.653596 19.281270 7 0.514842 ... \n", - "2 7.472758 0 14 1 1 2 194.207792 24.589331 5 0.309199 ... \n", - "3 6.502319 1 0 1 0 9 201.838024 25.513918 4 0.160160 ... \n", - "4 7.043758 1 12 0 0 9 201.360443 31.160641 6 0.291976 ... \n", - "\n", - " V191 V192 V193 V194 V195 V196 V197 V198 V199 \\\n", - "0 1.462837 1 1627.274196 0 0 4.683956 0.565667 0 3 \n", - "1 1.330522 1 1661.484439 1 0 6.766661 -0.395402 0 4 \n", - "2 1.384151 1 1658.939293 0 0 5.647794 1.112766 0 0 \n", - "3 1.220303 1 1650.801625 0 0 5.370363 -0.305842 0 4 \n", - "4 1.170094 1 1676.818876 0 0 3.446532 2.440661 0 1 \n", - "\n", - " V200 \n", - "0 0.024338 \n", - "1 0.056518 \n", - "2 0.013442 \n", - "3 0.034632 \n", - "4 0.017514 \n", - "\n", - "[5 rows x 202 columns]" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df.head()" - ] - }, - { - "cell_type": "markdown", - "id": "c6e32feb", - "metadata": {}, - "source": [ - "### Descriptive Statistics\n" - ] - }, - { - "cell_type": "markdown", - "id": "horizontal-hanging", - "metadata": {}, - "source": [ - "Once we loaded the data, we find that the outcome variable, $Y$, is continuous with mean around $7.33$. The treatment variable $A$ is binary with a value of $1$ indicating that a visitor was exposed to the new ad design $A$ as opposed to design $B$ (corresponding to a value of $A$ equal to $1$). The control variables $V$ are a collection of mixed data types, including continuous, discrete and binary variables." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "d14f929c-178b-47fc-8293-29a634194f21", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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YAV1V2V3V4V5V6V7V8...V191V192V193V194V195V196V197V198V199V200
count1000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.0000001000.000000...1000.0000001000.000001000.0000001000.0000001000.0000001000.0000001000.0000001000.000001000.0000001000.000000
mean7.3312390.4430009.2900000.3770000.6160006.477000200.08875828.0660286.0310000.294206...1.3182090.942001667.4545610.2540000.1740005.804205-0.0769210.294001.6290000.037936
std1.3798520.4969893.8896050.4848770.4866012.8701416.1054089.9209412.4803610.119454...0.2701780.2338644.1919130.4355150.3792992.6558351.0027540.455821.3889880.021688
min3.4350520.0000000.0000000.0000000.0000000.000000183.12306712.0206300.0000000.047160...0.6680930.000001524.2916750.0000000.0000001.097708-3.6446520.000000.0000000.001478
25%6.4055830.0000007.0000000.0000000.0000005.000000195.94156921.2062304.0000000.204260...1.1193691.000001637.6995140.0000000.0000004.065465-0.7513550.000001.0000000.021711
50%7.3352480.00000010.0000000.0000001.0000007.000000199.87611726.2025826.0000000.282867...1.2937901.000001667.7634800.0000000.0000005.236465-0.0910560.000001.0000000.034009
75%8.2718811.00000012.0000001.0000001.0000008.000000204.39806733.0711898.0000000.374078...1.4768281.000001695.9726311.0000000.0000006.8982400.5946471.000002.0000000.049100
max13.1972601.00000020.0000001.0000001.00000015.000000220.58441095.41002014.0000000.706249...2.4486611.000001825.6970961.0000001.00000038.4279742.8326731.000009.0000000.139716
\n", - "

8 rows × 202 columns

\n", - "
" - ], - "text/plain": [ - " Y A V1 V2 V3 \\\n", - "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 \n", - "mean 7.331239 0.443000 9.290000 0.377000 0.616000 \n", - "std 1.379852 0.496989 3.889605 0.484877 0.486601 \n", - "min 3.435052 0.000000 0.000000 0.000000 0.000000 \n", - "25% 6.405583 0.000000 7.000000 0.000000 0.000000 \n", - "50% 7.335248 0.000000 10.000000 0.000000 1.000000 \n", - "75% 8.271881 1.000000 12.000000 1.000000 1.000000 \n", - "max 13.197260 1.000000 20.000000 1.000000 1.000000 \n", - "\n", - " V4 V5 V6 V7 V8 ... \\\n", - "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 ... \n", - "mean 6.477000 200.088758 28.066028 6.031000 0.294206 ... \n", - "std 2.870141 6.105408 9.920941 2.480361 0.119454 ... \n", - "min 0.000000 183.123067 12.020630 0.000000 0.047160 ... \n", - "25% 5.000000 195.941569 21.206230 4.000000 0.204260 ... \n", - "50% 7.000000 199.876117 26.202582 6.000000 0.282867 ... \n", - "75% 8.000000 204.398067 33.071189 8.000000 0.374078 ... \n", - "max 15.000000 220.584410 95.410020 14.000000 0.706249 ... \n", - "\n", - " V191 V192 V193 V194 V195 \\\n", - "count 1000.000000 1000.00000 1000.000000 1000.000000 1000.000000 \n", - "mean 1.318209 0.94200 1667.454561 0.254000 0.174000 \n", - "std 0.270178 0.23386 44.191913 0.435515 0.379299 \n", - "min 0.668093 0.00000 1524.291675 0.000000 0.000000 \n", - "25% 1.119369 1.00000 1637.699514 0.000000 0.000000 \n", - "50% 1.293790 1.00000 1667.763480 0.000000 0.000000 \n", - "75% 1.476828 1.00000 1695.972631 1.000000 0.000000 \n", - "max 2.448661 1.00000 1825.697096 1.000000 1.000000 \n", - "\n", - " V196 V197 V198 V199 V200 \n", - "count 1000.000000 1000.000000 1000.00000 1000.000000 1000.000000 \n", - "mean 5.804205 -0.076921 0.29400 1.629000 0.037936 \n", - "std 2.655835 1.002754 0.45582 1.388988 0.021688 \n", - "min 1.097708 -3.644652 0.00000 0.000000 0.001478 \n", - "25% 4.065465 -0.751355 0.00000 1.000000 0.021711 \n", - "50% 5.236465 -0.091056 0.00000 1.000000 0.034009 \n", - "75% 6.898240 0.594647 1.00000 2.000000 0.049100 \n", - "max 38.427974 2.832673 1.00000 9.000000 0.139716 \n", - "\n", - "[8 rows x 202 columns]" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df.describe()" - ] - }, - { - "cell_type": "markdown", - "id": "d7e45649", - "metadata": {}, - "source": [ - "From the explanatory variables $V1$ to $V200$, 107 variables are continuous, while 95 are integers. From the integer-variables 59 are binary variables. " - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "bde50bfe", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "float64 107\n", - "int64 95\n", - "dtype: int64\n", - "Number of binary variables: 59\n" - ] - } - ], - "source": [ - "print(df.dtypes.value_counts())\n", - "print(\"Number of binary variables:\", len(df[df.columns[df.isin([0,1]).all()]].columns))" - ] - }, - { - "cell_type": "markdown", - "id": "0ce90b4b", - "metadata": {}, - "source": [ - "Let's continue with some visual inspection." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "b4d2dfb4", - "metadata": {}, - "outputs": [], - "source": [ - "# Define the settings for the graphs first\n", - "import seaborn as sns\n", - "sns.set()\n", - "colors = sns.color_palette()\n", - "\n", - "import matplotlib.pyplot as plt\n", - "\n", - "plt.rcParams['figure.figsize'] = 5., 3.75\n", - "sns.set(font_scale=1.5)\n", - "sns.set_style('whitegrid', {'axes.spines.top': False,\n", - " 'axes.spines.bottom': False,\n", - " 'axes.spines.left': False,\n", - " 'axes.spines.right': False})" - ] - }, - { - "cell_type": "markdown", - "id": "11045894", - "metadata": {}, - "source": [ - "The first figure shows that 443 out of the 1000 customers have been exposed to the new ad design." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "2b5037d3", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "df['A'].value_counts().plot(kind='bar', color=colors)\n", - "\n", - "plt.title('Treatment')\n", - "plt.xlabel('A')\n", - "_ = plt.ylabel('count')" - ] - }, - { - "cell_type": "markdown", - "id": "8c2dc825", - "metadata": {}, - "source": [ - "### Unconditional Estimate of ATE" - ] - }, - { - "cell_type": "markdown", - "id": "8da84d00", - "metadata": {}, - "source": [ - "As a first naive estimate, we could calculate the unconditional average treatment effect. In other words, we simply take the difference between $Y$ observed for the customers who have been exposed to the treatment $(A=1)$ and those who haven't been exposed $(A=0)$. As a visualization, we plot the density of the outcome variable conditional on the treatment status to get a first impression on the descriptive relationship of $A$ and $Y$." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "57392f09", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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" - ], - "text/plain": [ - " Y\n", - "A \n", - "0 NaN\n", - "1 1.117603" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df[['A', 'Y']].groupby('A').mean().diff()" - ] - }, - { - "cell_type": "markdown", - "id": "e6f3fa75-a5d4-480c-b627-4b99c6f6afe3", - "metadata": {}, - "source": [ - "The uncoditional effect is around $1.118$. Because we use a simulated data set in this example, we know that the true effect is $0.8$. Therefore the unconditional ATE overestimates the true effect, because it does not account for individual characteristics. In order to get an estimation on the ATE that explicitly takes the confounding variables $V$ into account, we apply the [DoubleML](https://docs.doubleml.org/stable/index.html) package in the next section." - ] - }, - { - "cell_type": "markdown", - "id": "9e21e9bb", - "metadata": {}, - "source": [ - "## Estimate ATE with the `DoubleML` package" - ] - }, - { - "cell_type": "markdown", - "id": "19830a0a", - "metadata": {}, - "source": [ - "Let’s use the package [DoubleML](https://docs.doubleml.org/stable/index.html) to estimate the average treatment effect of the new ad design on the value of customers' purchases. First, the required packages are imported." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "afaf4106", - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import pandas as pd\n", - "import doubleml as dml\n", - "\n", - "from sklearn.linear_model import LinearRegression\n", - "from sklearn.linear_model import LogisticRegression\n", - "from sklearn.linear_model import LassoCV, LogisticRegressionCV\n", - "from sklearn.ensemble import RandomForestClassifier, RandomForestRegressor\n", - "from sklearn.preprocessing import StandardScaler\n", - "from sklearn.pipeline import make_pipeline\n", - "from sklearn.metrics import mean_squared_error\n", - "from sklearn.metrics import log_loss\n", - "from xgboost import XGBClassifier, XGBRegressor\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import scipy.stats as stats" - ] - }, - { - "cell_type": "markdown", - "id": "49242003", - "metadata": {}, - "source": [ - "### The Data Backend: `DoubleMLData`" - ] - }, - { - "cell_type": "markdown", - "id": "3653b53a", - "metadata": {}, - "source": [ - "To start our analysis, we initialize the data backend from the previously loaded data set, i.e., we create a new instance of a [DoubleMLData](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLData.html#doubleml.DoubleMLData) object. During initialization, we specify the roles of the variables in the data set, i.e., in our example the outcome variable $Y$ via the parameter `y_col`, the treatment variable $A$ via `d_cols` and the confounding variables $V$ via `x_cols`." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "abdd10b7", - "metadata": {}, - "outputs": [], - "source": [ - "# Specify explanatory variables for data-backend\n", - "features_base = list(df.columns.values)[2:]\n", - "\n", - "# Initialize DoubleMLData (data-backend of DoubleML)\n", - "data_dml = dml.DoubleMLData(df,\n", - " y_col='Y',\n", - " d_cols='A',\n", - " x_cols=features_base)" - ] - }, - { - "cell_type": "markdown", - "id": "5800ca50-c293-4266-8dd7-00fadcea8d51", - "metadata": {}, - "source": [ - "We can print the data-backend to see the variables, which we have assigned as outcome, treatment and controls." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "37b9bd8a", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "================== DoubleMLData Object ==================\n", - "\n", - "------------------ Data summary ------------------\n", - "Outcome variable: Y\n", - "Treatment variable(s): ['A']\n", - "Covariates: ['V1', 'V2', 'V3', 'V4', 'V5', 'V6', 'V7', 'V8', 'V9', 'V10', 'V11', 'V12', 'V13', 'V14', 'V15', 'V16', 'V17', 'V18', 'V19', 'V20', 'V21', 'V22', 'V23', 'V24', 'V25', 'V26', 'V27', 'V28', 'V29', 'V30', 'V31', 'V32', 'V33', 'V34', 'V35', 'V36', 'V37', 'V38', 'V39', 'V40', 'V41', 'V42', 'V43', 'V44', 'V45', 'V46', 'V47', 'V48', 'V49', 'V50', 'V51', 'V52', 'V53', 'V54', 'V55', 'V56', 'V57', 'V58', 'V59', 'V60', 'V61', 'V62', 'V63', 'V64', 'V65', 'V66', 'V67', 'V68', 'V69', 'V70', 'V71', 'V72', 'V73', 'V74', 'V75', 'V76', 'V77', 'V78', 'V79', 'V80', 'V81', 'V82', 'V83', 'V84', 'V85', 'V86', 'V87', 'V88', 'V89', 'V90', 'V91', 'V92', 'V93', 'V94', 'V95', 'V96', 'V97', 'V98', 'V99', 'V100', 'V101', 'V102', 'V103', 'V104', 'V105', 'V106', 'V107', 'V108', 'V109', 'V110', 'V111', 'V112', 'V113', 'V114', 'V115', 'V116', 'V117', 'V118', 'V119', 'V120', 'V121', 'V122', 'V123', 'V124', 'V125', 'V126', 'V127', 'V128', 'V129', 'V130', 'V131', 'V132', 'V133', 'V134', 'V135', 'V136', 'V137', 'V138', 'V139', 'V140', 'V141', 'V142', 'V143', 'V144', 'V145', 'V146', 'V147', 'V148', 'V149', 'V150', 'V151', 'V152', 'V153', 'V154', 'V155', 'V156', 'V157', 'V158', 'V159', 'V160', 'V161', 'V162', 'V163', 'V164', 'V165', 'V166', 'V167', 'V168', 'V169', 'V170', 'V171', 'V172', 'V173', 'V174', 'V175', 'V176', 'V177', 'V178', 'V179', 'V180', 'V181', 'V182', 'V183', 'V184', 'V185', 'V186', 'V187', 'V188', 'V189', 'V190', 'V191', 'V192', 'V193', 'V194', 'V195', 'V196', 'V197', 'V198', 'V199', 'V200']\n", - "Instrument variable(s): None\n", - "No. Observations: 1000\n", - "\n", - "------------------ DataFrame info ------------------\n", - "\n", - "RangeIndex: 1000 entries, 0 to 999\n", - "Columns: 202 entries, Y to V200\n", - "dtypes: float64(107), int64(95)\n", - "memory usage: 1.5 MB\n", - "\n" - ] - } - ], - "source": [ - "print(data_dml)" - ] - }, - { - "cell_type": "markdown", - "id": "714346b8-90dd-4f15-b880-d71f4f60b04e", - "metadata": {}, - "source": [ - "## The Inference Problem and Choosing an Appropriate Model\n", - "\n", - "The inference problem is to determine the causal effect of seeing the new ad design $A$ on a customer's purchases $Y$ once we control for individual characteristics $V$. In our example, we are interested in the average treatment effect. Basically, there are two causal models available in [DoubleMLData](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLData.html#doubleml.DoubleMLData) that can be used to estimate the ATE.\n", - "\n", - "The so-called interactive regression model (IRM) called by [DoubleMLIRM](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLIRM.html) is a flexible (nonparametric) model to estimate this causal quantity. The model does not impose functional form restrictions on the underlying regression relationships, for example, linearity or additivity as in a standard linear regression model. This means that the model hosts heterogeneous treatment effects, i.e., account for variation in the effect of the new ad design across customers. Moreover, it is possible to also estimate other causal parameters with the IRM, for example, the average treatment effect on the treated (= those customers who have been exposed to the new ad), which might be of interest too.\n", - "\n", - "The second causal model that can be used here is the partially linear regression model (PLR). The PLR incorporates stronger assumptions, for example, that the treatment effect is additive and constant, i.e., in the model it is assumed that the effect does not very across individuals. We will start with the IRM and include the PLR estimates at the end of the notebook." - ] - }, - { - "cell_type": "markdown", - "id": "9e798e44-8fc8-4c93-9cfb-2d3ad7486dc0", - "metadata": {}, - "source": [ - "## 1. Interactive Regression Model (IRM)\n", - "\n", - "We briefly introduce the [Interactive Regression Model](https://docs.doubleml.org/stable/guide/models.html#interactive-regression-model-irm) (IRM) where the main regression relationship of interest is provided by\n", - "\n", - "$$Y = g_0(D, X) + U, \\quad E(U | X, D) = 0,$$\n", - "\n", - "where the treatment variable is binary, $D \\in \\lbrace 0,1 \\rbrace$. We consider estimation of the average treatment effect (ATE):\n", - "\n", - "$$\\theta_0 = \\mathbb{E}[g_0(1, X) - g_0(0,X)],$$\n", - "\n", - "when treatment effects are fully heterogeneous. In order to be able to use ML methods, the estimation framework generally requires a property called \"double robustness\" or \"Neyman orthogonality\". In the IRM, double robustness can be achieved by including the first-stage estimation\n", - "\n", - "$$D = m_0(X) + V, \\quad E(V | X) = 0,$$\n", - "\n", - "which amounts to estimation of the propensity score, i.e., the probability that a customer is exposed to the treatment provided her observed characteristics. Both predictions are then combined in [the doubly robust score for the average treatment effect](https://docs.doubleml.org/stable/guide/scores.html#interactive-regression-model-irm) which is given by\n", - "\n", - "$$\\psi(W; \\theta, \\eta) := g(1,X) - g(0,X) + \\frac{D (Y - g(1,X))}{m(X)} - \\frac{(1 - D)(Y - g(0,X))}{1 - m(x)} - \\theta.$$" - ] - }, - { - "cell_type": "markdown", - "id": "13a5f6f7-64c5-499b-b68a-16ca98943cd6", - "metadata": {}, - "source": [ - "Because the data set was simulated we are aware of the true ATE, $\\theta_0=0.8$. The interpretation of this is that exposure to the new ad increases sales (in $100\\$$) by around $0.8$ on average. In the following, we try to estimate this causal effect using the [DoubleML](https://docs.doubleml.org/stable/index.html) package and assess whether the estimated effect is significantly different from zero." - ] - }, - { - "cell_type": "markdown", - "id": "69f0731d", - "metadata": {}, - "source": [ - "### Assess predictive performance in the IRM" - ] - }, - { - "cell_type": "markdown", - "id": "6d494c68", - "metadata": {}, - "source": [ - "In the following, we will compare the estimate of the ATE based on different learners. Moreover, we will also have a look how well the learners can predict the nuisance components of the causal model. \n", - "\n", - "To evaluate the predictive performance, we'll first define a helper function that uses a DoubleML model object and returns a summary for a predictive measure. We'll use the root mean squared error (RMSE) for the main regression and the log loss measure $L_{log}$ for the propensity score estimation.\n", - "\n", - "Estimation of the IRM delivers two arrays for the prediction function $g_0(D, X)$: `ml_g0` for $g_0(0, X)$ and `ml_g1` for $g_0(1, X)$. If we want to get the correct prediction for each observation based on the treatment realization, we pick the corresponding value of either `ml_g0` (for $D=0$) or `ml_g1` (for $D=1$). As we apply random sample splitting repeatedly in every model, the RMSE and the log loss can be calculated for each repetition. We are interested in mean and standard deviation across all repetitions." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "aa2a8f81", - "metadata": {}, - "outputs": [], - "source": [ - "def pred_acc_irm(DoubleML, prop):\n", - " \"\"\"\n", - " A function to calculate prediction accuracy values for every repetition\n", - " of a Double Machine Learning model using IRM, DoubleMLIRM\n", - " \n", - " ...\n", - " \n", - " Parameters\n", - " ----------\n", - " DoubleML : doubleml.double_ml_irm.DoubleMLIRM\n", - " The IRM Double Machine Learning model\n", - " prop : bool\n", - " Indication if RMSE values have to be computed for main regression or\n", - " log loss values for propensity score\n", - " \"\"\"\n", - " \n", - " # export data and predictions of the DoubleML model\n", - " y = DoubleML._dml_data.y\n", - " d = DoubleML._dml_data.d\n", - " g0 = DoubleML.predictions.get('ml_g0')\n", - " g1 = DoubleML.predictions.get('ml_g1') \n", - " m = DoubleML.predictions.get('ml_m')\n", - " \n", - " # dimensions of prediction array\n", - " h = g0.shape[0]\n", - " w = DoubleML.n_rep\n", - " \n", - " # check whether treatment is binary \n", - " if np.isin(d, [0,1]).all() == False:\n", - " raise ValueError(\"Treatment must be a binary variable.\")\n", - " \n", - " # prepare array to store prediction accuracy measure values\n", - " pred_acc_array = np.zeros((w,))\n", - " \n", - " # check whether to assess main regression or propensity score accuracy: \n", - " if prop == False:\n", - " \n", - " # evaluate main regression accuracy\n", - " # export an array with correctly picked prediction values \n", - " export_pred_array = np.zeros((h, w)) \n", - " for i in range(w):\n", - " for j in range(h):\n", - " if d[j] == 0:\n", - " export_pred_array[j,i] = g0[j,i]\n", - " else:\n", - " export_pred_array[j,i] = g1[j,i]\n", - " \n", - " # fill array that contains rmse of each repetition\n", - " for i in range(w):\n", - " pred_acc_array[i] = mean_squared_error(y, export_pred_array[:,i], squared=False) \n", - " else:\n", - " \n", - " # evaluate propensity score accuracy\n", - " # fill array that contains log loss of each repetition\n", - " for i in range(w):\n", - " pred_acc_array[i] = log_loss(d, m[:,i], eps=0.025)\n", - " \n", - " return pred_acc_array" - ] - }, - { - "cell_type": "markdown", - "id": "suburban-infrastructure", - "metadata": {}, - "source": [ - "### Benchmark: Model based on Linear and Logistic Regression" - ] - }, - { - "cell_type": "markdown", - "id": "93f3af17-bcf9-429b-af9a-b90ea1153937", - "metadata": {}, - "source": [ - "Let us first start with a benchmark model that is based on linear and logistic regression. Hence, we estimate the functions $g_0(D,X)$ using a linear regression model and $m_0(X)$ by using an (unpenalized) logistic regression. In both cases, we include all available characteristics $V$. Later we will assess whether we can find a \"better\" estimator based on ML methods like lasso, random forests and boosting. Because we have 200 variables and 1000 observations, this is approaching a high dimentional setting, therefore the linear and the logistic regression may not estimate the parameters well." - ] - }, - { - "cell_type": "markdown", - "id": "authorized-school", - "metadata": {}, - "source": [ - "We start by initializing the learners for linear regression and logistic regression. Then, we initialize a causal model object, here of the class [DoubleMLIRM](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLIRM.html). The latter is based on the data-backend we have specified above. To reduce the disproportionate impact of extreme propensity score weights in the interactive model we trim the propensity score from below and above at thresholds of 0.025 and 0.975." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "jewish-listing", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 1.057833 0.624814 1.693035 0.090449 -0.166781 2.282446" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize Linear and Logistic Regression learners\n", - "linreg = make_pipeline(StandardScaler(), LinearRegression())\n", - "logreg_class = make_pipeline(StandardScaler(), LogisticRegression(penalty=\"none\"))\n", - "\n", - "# Initialize DoubleMLIRM model\n", - "np.random.seed(1234)\n", - "dml_irm_regression = dml.DoubleMLIRM(data_dml,\n", - " ml_g = linreg,\n", - " ml_m = logreg_class,\n", - " trimming_threshold = 0.025,\n", - " n_folds = 3,\n", - " n_rep=3)\n", - "\n", - "dml_irm_regression.fit(store_predictions=True)\n", - "\n", - "reg_summary = dml_irm_regression.summary\n", - "reg_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "controlling-collapse", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [0.25783258]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_irm_regression.coef - 0.8)" - ] - }, - { - "cell_type": "markdown", - "id": "emerging-highlight", - "metadata": {}, - "source": [ - "We see that the causal estimate suffers from a substantial bias and is quite noisy: The ATE is overestimated by around 0.26 and the standard error is around 0.62. The corresponding 95%-confidence interval is relatively wide. It even covers the value of zero. Hence, we cannot reject the null hypothesis that the average treatment effect is different from zero at the 5% significance level.\n", - "\n", - "Next, we'll calculate the RMSE and the log loss for the nuisance functions in order to find out how the benchmark compares to other ML models." - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "7ad39856", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_linlog_irm = pred_acc_irm(dml_irm_regression, prop=False)\n", - "rmse_main_linlog_irm_mean = np.mean(rmse_main_linlog_irm)\n", - "rmse_main_linlog_irm_std = np.std(rmse_main_linlog_irm)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_linlog_irm = pred_acc_irm(dml_irm_regression, prop=True)\n", - "logloss_prop_linlog_irm_mean = np.mean(logloss_prop_linlog_irm)\n", - "logloss_prop_linlog_irm_std = np.std(logloss_prop_linlog_irm)" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "dd39c325", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 1.727905012276966\n", - "Standard deviation of the RMSE is 0.026526079197961804\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_linlog_irm_mean)\n", - "print(\"Standard deviation of the RMSE is\", rmse_main_linlog_irm_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "e21456ef", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 1.0228568161263911\n", - "Standard deviation of log loss is 0.027536454508812133\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_linlog_irm_mean)\n", - "print(\"Standard deviation of log loss is\", logloss_prop_linlog_irm_std)" - ] - }, - { - "cell_type": "markdown", - "id": "neutral-converter", - "metadata": {}, - "source": [ - "Next, let us find out if we are able to use ML methods to find estimators that have a lower bias and a smaller standard error than the benchmark." - ] - }, - { - "cell_type": "markdown", - "id": "723b8e6c", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Lasso\n", - "\n", - "We estimate the nuisance components $g_0$ and $m_0$ using lasso as provided by [scikit-learn](https://scikit-learn.org). We load the learner by initializing instances from the classes [LassoCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html) and [LogisticRegressionCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegressionCV.html). Here we specify that the lasso should use the value of $\\lambda$ that minimizes the cross-validated mean squared error, which is based on 5-fold cross validation. We initialize the [DoubleMLIRM](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLIRM.html) object and use the newly defined learners." - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "73cbfd4b", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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A0.8555590.07092812.0624171.668137e-330.7165440.994575
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.855559 0.070928 12.062417 1.668137e-33 0.716544 0.994575" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize Lasso learners\n", - "lasso = make_pipeline(StandardScaler(), LassoCV(cv=5, max_iter=20000)) \n", - "lasso_class = make_pipeline(StandardScaler(),\n", - " LogisticRegressionCV(cv=5, penalty='l1', solver='liblinear', \n", - " Cs = 4, max_iter=1000)) \n", - "\n", - "# Initialize DoubleMLIRM model\n", - "np.random.seed(1234)\n", - "dml_irm_lasso = dml.DoubleMLIRM(data_dml,\n", - " ml_g = lasso,\n", - " ml_m = lasso_class,\n", - " trimming_threshold = 0.025, \n", - " n_folds = 3,\n", - " n_rep = 3)\n", - "\n", - "dml_irm_lasso.fit(store_predictions=True)\n", - "\n", - "lasso_summary = dml_irm_lasso.summary\n", - "lasso_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "stock-bookmark", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [0.05555945]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_irm_lasso.coef - 0.8)" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "id": "85c6e74e", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_lasso_irm = pred_acc_irm(dml_irm_lasso, prop=False)\n", - "rmse_main_lasso_irm_mean = np.mean(rmse_main_lasso_irm)\n", - "rmse_main_lasso_irm_std = np.std(rmse_main_lasso_irm)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_lasso_irm = pred_acc_irm(dml_irm_lasso, prop=True)\n", - "logloss_prop_lasso_irm_mean = np.mean(logloss_prop_lasso_irm)\n", - "logloss_prop_lasso_irm_std = np.std(logloss_prop_lasso_irm)" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "id": "c659681b", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 1.1143405452234652\n", - "Standard deviation of RMSE is 0.005869688113839954\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_lasso_irm_mean)\n", - "print(\"Standard deviation of RMSE is\", rmse_main_lasso_irm_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "id": "388cdfcf", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 0.6686766530020503\n", - "Standard deviation of log loss is 0.0032543941531603953\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_lasso_irm_mean)\n", - "print(\"Standard deviation of log loss is\", logloss_prop_lasso_irm_std)" - ] - }, - { - "cell_type": "markdown", - "id": "religious-algebra", - "metadata": {}, - "source": [ - "We see that the lasso-based estimate for the ATE is $0.86$ and, hence, much closer to the true value of $0.8$ than in the benchmark $1.06$. Moreover, we can achieve improvements in terms of estimation precision as can be recognized from the smaller standard error. Also the prediction measures for the nuisance components are much smaller for Lasso than in the linear/logistic benchmark. Using the Lasso learners makes it now possible to conclude that the ATE is significantly different from zero at a significance level of 5%." - ] - }, - { - "cell_type": "markdown", - "id": "33d06b0d", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Random Forest" - ] - }, - { - "cell_type": "markdown", - "id": "4d9d008a-5b6a-4acf-93b9-b26599541653", - "metadata": {}, - "source": [ - "Alternatively, we can repeat this procedure with other machine learning methods, for example a random forest learner as provided by the [RandomForestRegressor](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html) and [RandomForestClassifier](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html) class in [scikit-learn](https://scikit-learn.org)." - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "id": "2092891a", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A0.8931760.07742111.536558.631791e-310.7414331.044919
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.893176 0.077421 11.53655 8.631791e-31 0.741433 1.044919" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize Random Forest learners\n", - "randomForest = RandomForestRegressor()\n", - "randomForest_class = RandomForestClassifier()\n", - "\n", - "# Initialize DoubleMLIRM model\n", - "np.random.seed(1234)\n", - "dml_irm_forest = dml.DoubleMLIRM(data_dml,\n", - " ml_g = randomForest,\n", - " ml_m = randomForest_class,\n", - " trimming_threshold = 0.025,\n", - " n_folds = 3,\n", - " n_rep = 3)\n", - "\n", - "# Set nuisance-part specific parameters\n", - "dml_irm_forest.set_ml_nuisance_params('ml_g0', 'A', {\n", - " 'max_features': 200, 'n_estimators': 250})\n", - "dml_irm_forest.set_ml_nuisance_params('ml_g1', 'A', {\n", - " 'max_features': 200, 'n_estimators': 250})\n", - "dml_irm_forest.set_ml_nuisance_params('ml_m', 'A', {\n", - " 'max_features': 200, 'n_estimators': 250})\n", - "\n", - "dml_irm_forest.fit(store_predictions=True) \n", - "\n", - "forest_summary = dml_irm_forest.summary\n", - "forest_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "id": "vital-insight", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [0.09317591]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_irm_forest.coef - 0.8)" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "id": "14c230b0", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_forest_irm = pred_acc_irm(dml_irm_forest, prop=False)\n", - "rmse_main_forest_irm_mean = np.mean(rmse_main_forest_irm)\n", - "rmse_main_forest_irm_std = np.std(rmse_main_forest_irm)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_forest_irm = pred_acc_irm(dml_irm_forest, prop=True)\n", - "logloss_prop_forest_irm_mean = np.mean(logloss_prop_forest_irm)\n", - "logloss_prop_forest_irm_std = np.std(logloss_prop_forest_irm)" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "id": "1d633282", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 1.1688034544446142\n", - "Standard deviation of RMSE is 0.00826647072034282\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_forest_irm_mean)\n", - "print(\"Standard deviation of RMSE is\", rmse_main_forest_irm_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "id": "16a7a785", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 0.6823242335385794\n", - "Standard deviation of log loss is 0.0026223238604172463\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_forest_irm_mean)\n", - "print(\"Standard deviation of log loss is\", logloss_prop_forest_irm_std)" - ] - }, - { - "cell_type": "markdown", - "id": "d4b6e16b-6cb9-40d8-a4fa-c438f23b49f3", - "metadata": {}, - "source": [ - "The results are relatively similar to the one obtained by lasso with a bias and standard errors that are slightly greater than before. The predictive accuracy of the random forest learners is also slightly worse than that of Lasso." - ] - }, - { - "cell_type": "markdown", - "id": "9ac68b60", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Extreme Gradient Boosting" - ] - }, - { - "cell_type": "markdown", - "id": "cc71c762-8497-43e5-a151-a5239641d510", - "metadata": {}, - "source": [ - "Next, we estimate the ATE using extreme gradient boosting as provided by [xgboost](https://docs.getml.com/latest/api_reference/predictors.html)." - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "id": "90b9ef4e", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A0.7909060.1043067.5825883.387302e-140.5864710.995341
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.790906 0.104306 7.582588 3.387302e-14 0.586471 0.995341" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize Extreme Gradient Boosting learners\n", - "boost = XGBRegressor(n_jobs=1, objective = \"reg:squarederror\")\n", - "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", - " objective = \"binary:logistic\", eval_metric = \"logloss\")\n", - "\n", - "# Initialize DoubleMLIRM model\n", - "np.random.seed(1234)\n", - "dml_irm_boost = dml.DoubleMLIRM(data_dml,\n", - " ml_g = boost,\n", - " ml_m = boost_class,\n", - " trimming_threshold = 0.025,\n", - " n_folds = 3,\n", - " n_rep = 3)\n", - "\n", - "# Set nuisance-part specific parameters\n", - "dml_irm_boost.set_ml_nuisance_params('ml_g0', 'A', {\n", - " 'n_estimators': 30, 'eta': 0.2})\n", - "dml_irm_boost.set_ml_nuisance_params('ml_g1', 'A', {\n", - " 'n_estimators': 30, 'eta': 0.2})\n", - "dml_irm_boost.set_ml_nuisance_params('ml_m', 'A', {\n", - " 'n_estimators': 15, 'eta': 0.2})\n", - "\n", - "dml_irm_boost.fit(store_predictions=True)\n", - "\n", - "boost_summary = dml_irm_boost.summary\n", - "boost_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "id": "traditional-ribbon", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [-0.0090944]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_irm_boost.coef - 0.8)" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "id": "efd04e78", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_boost_irm = pred_acc_irm(dml_irm_boost, prop=False)\n", - "rmse_main_boost_irm_mean = np.mean(rmse_main_boost_irm)\n", - "rmse_main_boost_irm_std = np.std(rmse_main_boost_irm)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_boost_irm = pred_acc_irm(dml_irm_boost, prop=True)\n", - "logloss_prop_boost_irm_mean = np.mean(logloss_prop_boost_irm)\n", - "logloss_prop_boost_irm_std = np.std(logloss_prop_boost_irm)" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "id": "114aa5cf", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 1.2287566646120192\n", - "Standard deviation of RMSE is 0.010275338353331828\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_boost_irm_mean)\n", - "print(\"Standard deviation of RMSE is\", rmse_main_boost_irm_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "id": "c1ebde27", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 0.7204831015081563\n", - "Standard deviation of log loss is 0.01297502257820836\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_boost_irm_mean)\n", - "print(\"Standard deviation of log loss is\", logloss_prop_boost_irm_std)" - ] - }, - { - "cell_type": "markdown", - "id": "9ee7f068-1ac4-4d7d-99a7-5c68c91e8b51", - "metadata": {}, - "source": [ - "The estimated coefficient is very close to the true ATE of $0.8$ but has a small negative bias. The interpretation of the results obtained with lasso, random forests and boosting are very similar. In all cases we are able to reject the null hypothesis that the ad has no effect on the sales." - ] - }, - { - "cell_type": "markdown", - "id": "fba54a14-c685-4948-819d-94a99d88e94a", - "metadata": {}, - "source": [ - "#### IRM - Summary of coefficient estimates\n", - "\n", - "We save the estimates, bias and confidence intervals for later peresentation and comparision." - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "id": "5e16a294", - "metadata": { - "scrolled": false, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefBias2.5 %97.5 %
regression1.0580.258-0.1672.282
lasso0.8560.0560.7170.995
forest0.8930.0930.7411.045
xgboost0.791-0.0090.5860.995
\n", - "
" - ], - "text/plain": [ - " coef Bias 2.5 % 97.5 %\n", - "regression 1.058 0.258 -0.167 2.282\n", - "lasso 0.856 0.056 0.717 0.995\n", - "forest 0.893 0.093 0.741 1.045\n", - "xgboost 0.791 -0.009 0.586 0.995" - ] - }, - "execution_count": 35, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "irm_summary = pd.concat((reg_summary, lasso_summary, forest_summary, boost_summary))\n", - "irm_summary.index = ['regression','lasso', 'forest', 'xgboost']\n", - "irm_summary = irm_summary[['coef', '2.5 %', '97.5 %']]\n", - "irm_summary.insert(1, \"Bias\", [irm_summary.loc['regression','coef'] - 0.8, \n", - " irm_summary.loc['lasso','coef'] - 0.8, \n", - " irm_summary.loc['forest','coef'] - 0.8, \n", - " irm_summary.loc['xgboost','coef'] - 0.8])\n", - "irm_summary.round(3)" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "id": "4b478603", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "errors = np.full((2, irm_summary.shape[0]), np.nan)\n", - "errors[0, :] = irm_summary['coef'] - irm_summary['2.5 %']\n", - "errors[1, :] = irm_summary['97.5 %'] - irm_summary['coef']\n", - "plt.errorbar(irm_summary.index, irm_summary.coef, fmt='o', yerr=errors)\n", - "plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", - "\n", - "plt.title('Interactive Regression Model (IRM)')\n", - "plt.xlabel('ML method')\n", - "_ = plt.ylabel('Coefficients and 95%-CI')" - ] - }, - { - "cell_type": "markdown", - "id": "8c891e02", - "metadata": {}, - "source": [ - "#### IRM - Summary of prediction assessment metric's mean values" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "id": "6790aad8", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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main RMSEmain RMSE (sd)prop log lossprop log loss (sd)
regression1.7280.0271.0230.028
lasso1.1140.0060.6690.003
forest1.1690.0080.6820.003
xgboost1.2290.0100.7200.013
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" - ], - "text/plain": [ - " main RMSE main RMSE (sd) prop log loss prop log loss (sd)\n", - "regression 1.728 0.027 1.023 0.028\n", - "lasso 1.114 0.006 0.669 0.003\n", - "forest 1.169 0.008 0.682 0.003\n", - "xgboost 1.229 0.010 0.720 0.013" - ] - }, - "execution_count": 37, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "irm_rmse_index = ['regression','lasso', 'forest', 'xgboost']\n", - "irm_rmse = pd.DataFrame([[rmse_main_linlog_irm_mean, rmse_main_linlog_irm_std, \n", - " logloss_prop_linlog_irm_mean, logloss_prop_linlog_irm_std],\n", - " [rmse_main_lasso_irm_mean, rmse_main_lasso_irm_std,\n", - " logloss_prop_lasso_irm_mean, logloss_prop_lasso_irm_std],\n", - " [rmse_main_forest_irm_mean, rmse_main_forest_irm_std,\n", - " logloss_prop_forest_irm_mean, logloss_prop_forest_irm_std],\n", - " [rmse_main_boost_irm_mean, rmse_main_boost_irm_std,\n", - " logloss_prop_boost_irm_mean, logloss_prop_boost_irm_std]],\n", - " index=irm_rmse_index,\n", - " columns=['main RMSE', 'main RMSE (sd)',\n", - " 'prop log loss', 'prop log loss (sd)'])\n", - "irm_rmse.round(3)" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "id": "a5be2641", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 38, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAU8AAADyCAYAAADN7kftAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAch0lEQVR4nO3de1RU5f4G8Ac76CnxgpJiSdnFQRxmHOCAID9MyQKJvHDQLLW8JmkcMy9g5Uo7WiodO0hlkkfMSy2jjBKNFMIb3slQyUzFI15CUZQYEEj5/v5wMTUHU3xnI0M8n7VcS/Z+593f/e49z+wbjIOICIiI6JY0qe8CiIgaIoYnEZEChicRkQKGJxGRAoYnEZGCBhueubm59V3CnwrHU3scU+3Z05g22PAsLy+v7xL+VDie2uOYas+exrTBhicRUX1ieBIRKWB4EhEpYHgSESlgeBIRKWB4EhEpYHgSESlgeBIRKfhLfRegYvSrr8JsNmO1j099l0JEjRSPPImIFDA8iYgUMDyJiBQwPImIFDA8iYgUMDyJiBQwPImIFDA8iYgUMDyJiBQwPImIFDA8iYgUMDyJiBQwPImIFDA8iYgUMDyJiBQwPImIFDA8iYgUMDyJiBQwPImIFNgcniKCZcuWISQkBEajEf369cPatWu1qI2IyG7Z/AVwixcvxsKFCxEdHQ2TyYQtW7ZgypQpuOOOOxAWFqZFjUREdsem8Pz111+xdOlSPP3003jhhRcAAAEBATh48CBWrlzJ8CSiPy2bwvOOO+7AihUr0Lp1a6vpjo6OKCsrs6VrIiK7ZlN4NmnSBO7u7gCuXfu8cOEC1qxZg+3bt+ONN97QpEAiIntk8zXPahs2bMA//vEPAECvXr3Qr1+/Wr82NzcX5eXltW5vNpsBANnZ2bdWJN0Qx1N7HFPt3cqY+vj41FkdDiIiWnR08uRJFBQU4PDhw4iPj4eHhweWL1+uRdc1jH71VZjNZqyOj6+T/huj7OzsOt3RGiOOqfbsaUw1O/J0c3ODm5sbfH194eTkhJiYGOzbtw9eXl5aLYKIyG7Y9JznpUuXkJKSgrNnz1pN79q1KwDUmE5E9GdhU3hWVVUhNjYWq1evtpqelZUFANDpdLZ0T0Rkt2w6bW/Tpg2eeeYZJCYm4q9//SsMBgOys7OxePFiDBo0CA8++KBWdRIR2RWbr3lOnz4dHTp0wGeffYaEhAS4uroiOjoaY8aM0aI+IiK7ZHN4Ojo6YuzYsRg7dqwW9RARNQj8q0pERAoYnkREChieREQKGJ5ERAoYnkREChieREQKGJ5ERAoYnkREChieREQKGJ5ERAoYnkREChieREQKGJ5ERAoYnkREChieREQKGJ5ERAoYnkREChieREQKGJ5ERAoYnkREChieREQKbP72TCKi22H0q6/CbDZjtY9PfZcCgEeeRERKGJ5ERAoYnkREChieREQKGJ5ERAp4t52oDtjbnWHSHo88iYgUMDyJiBQwPImIFDA8iYgUMDyJiBTwbjvxzjCRAh55EhEpYHgSESlgeBIRKWB4EhEpYHgSESlgeBIRKbD5UaWqqiqsXr0aH3/8MU6dOoW2bdvi0UcfRXR0NJycnLSokYjI7tgcnkuWLMG///1vjB49GgEBATh+/DgWLlyIo0eP4j//+Y8WNRIR2R2bwlNEsGTJEjz11FOYPHkyAKBHjx5wdnbGpEmTcOjQIXh4eGhSKBGRPbHpmmdpaSn69euH8PBwq+kPPvggACA/P9+W7omI7JZNR55OTk547bXXakxPT08HADz88MO2dE9EZLc0v9uek5ODxMRE9OnTBw899JDW3RMR2QVN/zBIdnY2oqKi0LFjR8yePbvWr8vNzUV5eXmt25vNZsvyyHYcT+1xTLWnMqY+dfjHbjQLz/Xr1yM2NhadOnXCkiVL4OzsXOvX6vX6W1qW05o1MJvNdTowjQnHU3scU+3Z25hqctqelJSEl19+GSaTCatWrUK7du206JaIyG7ZHJ7JycmYO3cu+vbtiyVLlqBFixZa1EVEZNdsOm2/cOEC5syZg3vvvRdDhw7FDz/8YDX/vvvuQ5s2bWwqkIjIHtkUnlu3bsXly5dx+vRpDB06tMb8+fPno3///rYsgojILtkUngMGDMCAAQM0KoWIqOHgX1UiIlLA8CQiUsDwJCJSwPAkIlLQoMIzac0a7DlwwGrangMHkLRmTT1VRESNVYMKT8/OnTEtLg4lpaUArgXntLg4eHbuXM+VEVFj06DC09dgwPypU5F38iTOX7qEaXFxmD91KnwNhvoujYgamQYVnsC1AL27TRtcKC7GoNBQBicR1YsGF557DhxAYVER2rZqheS0tBrXQImIbocGFZ7V1zgfdHODS+vWmD91KqbFxTFAiei2a1DhefDIEcyfOhUtmjcH8Ns10INHjtRzZUTU2DSo8BwZEVHjGqevwYCRERH1VBERNVYNKjyJiOwFw5OISAHDk4hIAcOTiEgBw5OISAHDk4hIAcOTiEgBw5OISAHDk4hIAcOTiEgBw5OISAHDk4hIAcOTiEgBw5OISAHDk4hIAcOTiEgBw5OISAHDk4hIAcOTiEgBw5OI7FrSmjU1viF3z4EDSFqzpp4quobhSUR2zbNzZ0yLi0NJaSmA376C3LNz53qti+FJRHat+ivG806exPlLlzAtLg7zp06t8U26txvDk0hD9nqK2dD5Ggy4u00bXCguxqDQ0HoPToDhSaQpez3FbOj2HDiAwqIitG3VCslpaTU+oOoDw5NIQ/Z6itmQVX8APejmBpfWrTF/6lRMi4ur9wBleDZiPMWsG/Z4itmQHTxyBPOnTkWL5s0B/PYBdfDIkXqti+HZiPEUs27Y4ylmQzYyIqLGB5CvwYCRERH1VNE1DM9GjKeY2rPXU0zSHsOzkeMpprbs9RSTtKdpeB46dAh6vR4FBQVadkt1iKeY2rLXU0zSnmbhmZeXh3HjxuHKlStadUl1jKeYROpsDs8rV65g1apViIyMREVFhRY10W3CU0widTaHZ3Z2Nt5++22MGjUKU6ZM0aImuk14ikmk7i+2dvDQQw8hPT0dbdu2xRo+H0hEjYTN4eni4mJzEbm5uSgvL691e7PZDODaUS/ZjuOpPY6p9lTG1MfHp67KsT08taDX62+pvdOaNTCbzXU6MI0Jx1N7HFPt2duY8jlPIiIFDE8iIgUMTyIiBQxPIiIFDE8iIgWahmdERAQOHz4MV1dXLbslIrI7PPIkIlLA8CQiUsDwJCJSwPAkIlLA8CQiUsDwJCJSwPAkIlLA8CQiUsDwJCJSwPAkIlLA8CQiUsDwJCJSwPAkIlLA8CQiUsDwJCJSwPAkIlLA8CQiUsDwJCJSwPAkIlLA8CQiUsDwJCJSwPAkIlLA8CQiUsDwJCJSwPAkIlLA8CQiUsDwJCJSwPAkIlLA8CQiUsDwJCJSwPAkIlLA8CQiUsDwJCJSwPAkIlLA8CQiUsDwJCJSwPAkIlLA8CQiUsDwJCJSwPAkIlKgSXimpqbiiSeegNFoRN++fZGSkqJFt0REdsvm8Pz6668xZcoUBAYG4r333oOfnx9iYmKQlpamRX1ERHbpL7Z2sGDBAvTt2xevvPIKACAoKAjFxcWIj49HaGiozQUSEdkjm448T548ifz8fDz++ONW00NCQpCXl4eTJ0/aVBwRkb2y6cgzLy8PAPDAAw9YTb///vsBAMePH4ebm5sti7iu/8yZg+zsbM37JSKqLZvCs6SkBADg5ORkNb158+YAALPZXKt+cnNzUV5efsvLZ4BqY3xEBACOp5Y4ptpTGVMfH5+6Kse28BQRAICDg8N1pzdpUrurAnq9/paXnZ2dXacD09hwPLXHMdWePY2pTdc8W7RoAaDmEWZpaanVfCKiPxubwrP6Wmd+fr7V9BMnTljNJyL6s7EpPO+//3507NixxjOdGzZsQKdOnXDPPffYVBwRkb2y+TnPCRMmYPr06WjVqhV69eqFb7/9Fl9//TXeeecdLeojIrJLNodnREQEKisrsXTpUiQnJ8PNzQ3z5s1DWFiYFvUREdklm8MTAIYMGYIhQ4Zo0RURUYPAv6pERKTAQaofyiQiolrjkScRkQKGJxGRAoYnEZEChicRkQKGJxGRAoYnEZEChicRkQKGJxGRAoYnEZEChieRHeMvAN5+tR3zRhueCQkJ6Nq1a32XYTN3d3e8//779V3Gn8LZs2cxfPhwGAwG9OjRAxUVFfVaz+eff4558+bVaw11zd7eh5mZmYiJialVW03+qlJDNGjQIPTs2bO+yyA7smLFCnz33XeIi4uDq6srmjVrVq/1fPDBB3bzfT2NxUcffYSrV6/Wqm2jDU9XV1e4urrWdxlkRy5duoR27drxb9FSrdz0tD04OBhz587F8OHD4e3tjbfeegsXL17Ea6+9hoCAABiNRjz99NM1vg60pKQE06dPR/fu3eHj44MZM2ZgwYIFCA4OvmHfAGrVf1ZWFgYPHgwvLy/4+vpi/PjxOHbsmGV+fn4+oqKi0L17d3Tr1g1PPfUUNm/ebJl/vdOFlJQUDBw4ECaTCT179sS8efOsvhI5NjYWo0ePRnJyMh5//HF4enqif//+2Lp1a23G+rY4dOgQJkyYAH9/f+j1evTs2RNz5syxOgW1dewA4Pvvv8fIkSPh6+sLX19fTJw4EadOnbpt66m14OBgJCcn48yZM3B3d0dCQgIKCgowbdo0BAUFoVu3bhg6dCh2795tec2pU6fg7u6OZcuWISQkBN27d8f69esBAIcPH8bYsWPh5eUFHx8fTJw4EQUFBVbL/OijjxAaGgqDwYCgoCDMnDnT8mWKwcHByM/PxxdffAF3d3e7HNv09HS4u7tj0aJFlmmHDh2Cp6en5b2cnJyMkJAQGI1GDB48GBkZGXB3d8euXbus+kpLS8Njjz0Go9GIYcOGYf/+/Vbzjx07hvHjxyMgIABeXl4YM2YMfvzxR6s2N9teAJCamop+/frBaDQiICAAU6ZMwdmzZwEAw4cPx44dO7B79+7r1liD3ETv3r2la9euMnfuXNmyZYvs3r1b+vXrJ4GBgfLpp59KZmamjBs3Tjw9PSUnJ8fyumHDhomfn598+umnkpGRIUOGDBFPT0/p3bv3H/adk5Mj5eXlN+0/Pz9fjEajzJo1S3bs2CFpaWkSEhIijz76qFRVVcnVq1clNDRUnn32Wdm0aZNs27ZNnn/+efHw8JATJ06IiMjChQvFw8PDUkt8fLy4u7vLnDlzZOvWrbJ06VIxmUzy3HPPSVVVlYiIxMTEiI+Pj/Tt21dSU1Nl06ZNMnDgQDGZTPLLL7/cbCjrhE6nk/fee09ERAoKCsTLy0tGjx4tmzZtkqysLHnrrbdEp9NJYmKiiGgzdllZWeLh4SFjxoyRjIwM+eqrr+Sxxx6TwMBAKSwsrJdxsFVubq5ERUVJYGCg7Nu3T86cOSOBgYHy+OOPy1dffSUZGRkyatQo6dq1q2zfvl1ERE6ePCk6nU6MRqN8/vnnsn79eiksLJS8vDzx8vKSQYMGycaNG2XdunUSGhoqwcHBlv1k7dq1otfrZfny5bJr1y755JNPxGQySWxsrKWenj17ytixY2Xfvn1SUVFRb2NzI5MnTxaDwSAnTpyQiooKefLJJyU8PFwqKirks88+E51OJ7NmzZItW7bI/PnzxWg0ik6nk507d4rItfehTqcTPz8/+eSTTyQ9PV0iIyPFZDLJuXPnRETkxx9/FJPJJJGRkfLNN9/IN998IxEREWIymeTIkSMiInL27Nmbbq+9e/eKh4eHJCQkyK5duyQlJUUCAwNl2LBhIiJy5MgR+fvf/y4DBgyQffv2SUlJyQ3XvVbhGRwcbAmQ1atXi7u7u+zfv9/S5urVqzJw4EAZMWKEiIhs375ddDqdZGZmWtqUlpaKv79/jfD8fd+17T81NVV0Op0UFBRY2uTk5MiCBQukpKREzp07JzqdTr766ivL/F9++UXefPNN+emnn0TEOjwvXrwonp6eMmvWLKt1X7dundV6xMTEiE6nk/z8fEub3bt3i06nk40bN95sKOvE78Nz8+bNMnToUDGbzVZtwsPDZezYsSKizdhFRERIeHi4XL161dLm9OnT4unpKXPnzq2zda1rr7zyimX/nDt3rhgMBjlz5oxl/tWrVyU8PFwiIiJE5LfwjImJsern5ZdflsDAQKvtcO7cOTEajfL++++LiMiMGTMkJCTEat//8ssvZfny5Zaf+/TpU6Nve3Px4kUJDAyUMWPGyDvvvCN6vV4OHTokIiK9evWS6Ohoq/avv/76dcNzw4YNljZFRUViMplk/vz5IiISHR0tAQEBUlpaamljNpslICDA0n9tttfixYvFy8vL6oNo06ZNkpCQYNkOzz33nCVMb6ZWd9s7d+4MBwcHAMCOHTvQvn17eHh44MqVK7hy5QqqqqrQu3dv7NmzB5WVldi5cyeaNWuGRx55xNLHXXfdhV69et2w79r2361bNzRr1gyRkZGYM2cOtm7dii5dumDSpElwcnKCi4sLHn74YcyYMQMxMTFYu3YtqqqqMH36dHTu3LlGDTk5OaisrMQTTzxhNT00NBSOjo5Wh+9333033NzcLD9XXze9fPlybYayTvXs2RMrV65E06ZNcfToUWRkZGDRokUoKirCr7/+CgA2j11ZWRlyc3MRFhaGJk1+233uuece/O1vf6txmtRQ7d27Fz4+PujQoYNlWpMmTRAWFobc3FzL6TUA6HQ6q9fu3LkT/v7+aNasmWUfdnZ2htFoxPbt2wEA/v7+OH78OAYOHIh3330XBw4cwJNPPonhw4ffnhXUSOvWrTFr1ixs2bIFixcvxsSJE9GlSxecOHECZ86cQUhIiFX7611PdnR0xKOPPmr52dnZGd7e3pZT97179yI4OBh33XWXpU3z5s0RHBxs2d9qs718fX1x+fJlPPnkk/jXv/6FvXv34v/+7//w4osvWmVQbdXqhlHbtm0t/7906RIKCgqg1+uv2/bixYu4ePEinJ2daxTk4uJyw75r23/Hjh2xcuVKJCYm4rPPPsPy5cvRsmVLPPPMM3jppZfg4OCApUuXYtGiRdi4cSNSUlLg6OiIPn36YNasWWjVqpVVn8XFxQCuBePvNWnSBG3atLF6o9x5551WbarXsaqq6rr13k5VVVVYsGABVq1ahbKyMnTo0AFGoxHNmjWzPLtm69iVl5dDRP5wW545c+Z2r3adKC4uRqdOnWpMd3FxgYigtLTUMu16+/DatWuxdu3aGq+v7jMsLAxVVVX4+OOP8f777yMhIQH33nsvpkyZ0uBuWAUFBcHFxQXnz5+3HCAVFRUBANq0aWPV9nr7jbOzs9UHcfXrqsOzuLj4D/e36vdmbbaXl5cXEhMTsWzZMiQlJSExMREuLi6IiopS+tC65bvtLVq0wEMPPfSHz585OzujXbt2KCoqgohYBeiFCxc06R8AjEYj3n33XVRWViI7OxurV6/GBx98gK5duyIkJATt27fHzJkz8frrr+PHH39EWloaPvzwQ7Rt2xYzZsyw6rM6TAsLC3HfffdZpldVVaGoqMiyTHtXvWO88cYbeOyxx9CiRQsAQGRkpFU7W8bu5ZdfhoODA86fP19j+YWFhQ1mrG6mZcuW113Hc+fOAbi2H1b//385OTmhZ8+eePbZZ2vMa9q0qeX/4eHhCA8PR0lJCbZt24YPP/wQU6dOhZ+f33XDwl7Fx8fDbDajU6dOePXVV/HJJ5+gffv2AGq+56tD9fdKSkpqZMX58+ct+9IfbYvCwkK0bt36hm1+v72Aa0EfFBSEy5cvY+fOnVi+fDlmz54NLy8veHp63tJ63/JD8r6+vjhz5gzatWsHg8Fg+ZeRkYEVK1bA0dERvr6+qKystLoL/b8/29L/ihUrEBwcjMrKSjRt2hQBAQH45z//CQD4+eefsX//fvTo0QP79++Hg4MDPDw8MGnSJOh0Ovz88881ltmtWzc0bdoU69ats5qelpaGX3/9tcE8a5ednQ13d3dERERYgvPs2bP46aefLEfGto5d8+bNodfrsX79equj7Z9//hnfffcdvL29b/+K1wFfX19kZ2db3SGvqqpCWloaDAaDVQj+Lz8/Pxw7dgx6vd6y/3bt2hWJiYnYsmULAGDy5Ml48cUXAVw7YOjbty/Gjx+PK1euoLCwEABqHI3Zo5ycHCQlJSE6OhpvvfUW9u/fj6SkJHTo0AEdO3ZERkaGVfv09PQafVy+fBl79+61/FxYWIjs7Gx0794dwLVtkZmZibKyMkubsrIyZGZmWt6btdlecXFxiIyMhIjgzjvvRO/evS0PxFe/7o477qj1ut/y1omIiED79u0xcuRIfPnll9i5cyfmzp2LRYsWwc3NDQ4ODujevTu6d++O2NhYJCcnY9OmTRg3bhzOnz9/02sLtenf398fhYWFmDBhAjZv3oxt27Zh+vTpaNasGXr37o0uXbrgrrvuwrRp07Bu3Trs2rUL77zzDg4dOlTjGgxw7brN6NGj8fHHH+PNN99EVlYWli1bhhkzZsDPzw9BQUG3Okz1wmg04ocffsCHH36I3bt3Izk5GUOHDkVlZaXlmqwWYzdp0iQcPXoUUVFRyMzMRGpqKkaMGAEnJyeMGDGiHkdAOyNHjoSTkxOee+45pKamIjMzE+PGjcOxY8cwadKkG752woQJOHr0KF544QVkZGRg8+bNiIqKwrfffmu5HOXv74+NGzdi3rx52LFjB7755hvEx8fjgQcesFyXb9myJX744Qfs3r3b6pE5e1FRUYHp06dDp9NhxIgR8Pb2xuDBg7Fw4ULk5eUhOjoa69evx+zZs5GVlYWEhASsXLkSgPUHg6OjI2JiYrB+/Xqkp6dj9OjRaNGiheXIfcKECTCbzRgxYgQ2btyIDRs2YMSIESgrK8OECRMA1G579ejRAwcPHkRsbCyysrKwadMmzJ49G87OzvDz8wNw7YPs+PHj2LFjh+Vy3h+62R2l3r17yyuvvGI1rbCwUGJjY8Xf318MBoOEhYXJihUrrNoUFRXJlClTxNvbW3x8fGTmzJkSHR0t4eHhN+y7tv1nZWXJkCFDxNvbW7p16yZDhw6VPXv2WOb/97//tdyl0+v18sQTT8jq1ast8//3USURkRUrVkhISIjo9Xp55JFHZN68eVJWVmaZHxMTI3369LF6TfUd15SUlJsNZZ34/d32iooKmTVrlgQGBorRaJSQkBBZuHChJCQkiMFgsDx6YevYVffx1FNPicFgED8/P3nppZfk1KlTt2/F68Dv77aLXBuHF198Uby9vcVkMsmwYcMsd4lFbrzt9+/fL6NGjRKTySReXl7y9NNPy7Zt26zarFy5UsLCwsRoNIqfn59MnDhRTp8+bZmfnp4uAQEB4unpKdnZ2XWwxraZN2+eeHh4WD0ZU1xcLIGBgTJ48GC5cuWKrFy5UoKDg0Wv18uQIUMkKSlJdDqdHDx4UESuvQ+DgoIkJSVFevXqJQaDQUaNGiV5eXlWyzpw4ICMHDlSTCaTeHt7y/PPP2+5q1/tZttL5NoTNNWPF3p5ecmYMWPk8OHDlvnff/+99OrVS/R6vaxbt+6G618nXz18+vRp5OTkoE+fPlanN5GRkXB1dcW7776r9SKJyM6kpqbCYDDg/vvvt0xbtWoVZs+ejV27dqFly5b1WJ3t6uzXM2NiYtC3b18MGDAAIoKvv/4aBw8exOTJk+tqkURkR7744gskJCRg4sSJuPvuu3HkyBHEx8ejf//+DT44AaBOjjyBa78C+N577+Hw4cOoqqpCly5dMH78+AZz/ZCIbHPhwgW8/fbb2Lp1Ky5dugRXV1f0798fUVFRcHR0rO/ybFZn4UlE9Gdm/89CEBHZIYYnEZEChicRkQKGJxGRAoYnEZGC/wdbaj4YdcAOmwAAAABJRU5ErkJggg==\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# graphical illustration of RMSE for main regression\n", - "errors_irm_rmse = np.full((2, irm_rmse.shape[0]), np.nan)\n", - "errors_irm_rmse[0, :] = irm_rmse['main RMSE'] - irm_rmse['main RMSE (sd)']\n", - "errors_irm_rmse[1, :] = irm_rmse['main RMSE'] + irm_rmse['main RMSE (sd)']\n", - "plt.errorbar(x=irm_rmse.index, y=irm_rmse['main RMSE'], fmt='x',\n", - " yerr=errors_irm_rmse, c='darkslategray')" - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "id": "9255bc0a", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 39, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# graphical illustration of log loss for main regression\n", - "errors_irm_logloss = np.full((2, irm_rmse.shape[0]), np.nan)\n", - "errors_irm_logloss[0, :] = irm_rmse['prop log loss'] - irm_rmse['prop log loss (sd)']\n", - "errors_irm_logloss[1, :] = irm_rmse['prop log loss'] + irm_rmse['prop log loss (sd)']\n", - "plt.errorbar(x=irm_rmse.index, y=irm_rmse['prop log loss'], fmt='x',\n", - " yerr=errors_irm_logloss, c='darkslategray')" - ] - }, - { - "cell_type": "markdown", - "id": "27c6157d", - "metadata": {}, - "source": [ - "### Inspection of the benchmark model\n", - "\n", - "It is natural to investigate why the the benchmark model performs so much worse as compared to the ML models. First of all, we can conclude that the predictive performance of the linear and logistic regression for the nuisance functions is considerably worse and more variable than for lasso, random forest and xgboost. Moreover, we can also inspect the propensity score estimates of the logistic regression which appear to be very close to zero and one for many observations.\n", - "\n", - "We first define a helper function that plots the propensity scores for each of the cross-fitting repetitions." - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "id": "78afa7eb", - "metadata": {}, - "outputs": [], - "source": [ - "def rep_propscore_plot(DoubleML):\n", - " \"\"\"\n", - " A function to create histograms as sublots for every repetition's propensity score density \n", - " of a Double Machine Learning model\n", - " \n", - " ...\n", - " \n", - " Parameters\n", - " ----------\n", - " DoubleML : doubleml\n", - " The Double Machine Learning model\n", - " \"\"\"\n", - " \n", - " \n", - " #export nuisance part from the DoubleML model\n", - " m = DoubleML.predictions.get('ml_m')\n", - " \n", - " # dimensions of nuisance array\n", - " h = m.shape[0]\n", - " rep = DoubleML.n_rep\n", - " \n", - " # create histograms as subplots covering the propensity score densities of all repetitions\n", - " fig, ax = plt.subplots(1, rep, figsize=[20,4.8])\n", - " for i in range(rep):\n", - " ax[i].hist(np.reshape(m[:,i], h), bins=25)\n", - " ax[i].set_title('repetition ' + str(i+1))\n", - " ax[i].set_xlabel(\"prop_score\")\n", - " ax[i].set_ylabel(\"density\")\n", - " \n", - " plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "id": "53d9d81d", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "rep_propscore_plot(dml_irm_regression)" - ] - }, - { - "cell_type": "markdown", - "id": "4f8d0f9f", - "metadata": {}, - "source": [ - "Let's compare this to the corresponding plot for the lasso-based model." - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "id": "e67ebd28", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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W6eTJk2revLni4uI0duxYSVJYWJgWLVqk1NRUJSYmqkmTJpoyZYri4uIcHDkAAHA0ZvAAjkXBCQDgtEwmkyZNmqRJkyaV2ycyMlKRkZE1GBUAAACAK2HRcAAAAAAAANgUBScAAAAAAADYFAUnAAAAAIDTKygsdnQIAKzAGk4AAAAAAKfHIuCAa2GGEwAAAAAAAGyKghMAAAAAAABsyuEFpy+//FL33XefOnbsqO7du+upp57S2bNnzdszMjI0ePBgdezYUb169dKKFSscGC0AAAAAAACuxKEFp507dyo2NlbXXXedli1bpsTERG3YsEEzZsyQJGVlZWncuHEKCAjQokWL1K9fP6WkpCgtLc2RYQMAAAAAAKACDl00fN68eerUqZOef/55eXh4qFu3brp48aJWrlyp8+fPKzU1Ve3bt9fcuXMlSeHh4SoqKtLy5csVExMjk8nkyPABAAAAAABwGQ6b4XTq1Cnt2LFD9913nzw8PMztw4cP17Zt2+Tp6akdO3aod+/eFveLiorS6dOnlZWVVdMhAwAAAAAAoBIcVnD65ptvZBiGGjZsqKSkJHXq1EkhISGaOXOmLly4oNzcXBUWFqpNmzYW9/P395ckHTp0yBFhAwAAAAAA4AqsOqXuzJkz8vX1tckTnzp1SpI0depURUZGatmyZTpw4IAWLlyo/Px8DRs2TJLk4+NjcT9vb29JUl5eXqWfa+/evbpw4YJN4q6KzMxMhz23vbny2EJCQhwdAqxU2febK78vK8OW47Pmc2DLHAAAcC/kCABAaVYVnLp166YePXro7rvvVs+ePVWvXr0qP3FhYaEk6eabb9bMmTMlSWFhYTIMQ88++6yGDh0qSRan213K07Pyk7OCgoKqHGd1ZWZmum1hw53HBudUmfebu78vHTk+W+YAAIB7IUcAAEqz6pS6kSNHav/+/UpKSlK3bt30yCOP6JNPPlFxcbHVT1wyUyk8PNyivXv37jIMQ7t375ZUdiZTyW1+QQGAmmXLHAAAcC/kCABAaVbNcHr44Yf18MMPKzs7W5s2bdLmzZu1fv16XXPNNYqKitLdd9+t0NDQSj1W69atJUkFBQUW7SUzn1q0aCEvLy/l5ORYbC+5XXptJwCAfdkyBwAA3As5AnB/BYXFMtX1slt/uB+rCk4lOnfurM6dO+vRRx/VF198oQ8++EAff/yx1q5dq6ZNm6pfv34aMGCAAgICyn2Mtm3bqnnz5nr33Xd1//33m9s//PBD1alTR507d1ZoaKi2bNmiUaNGmU+t27x5s3x9fRUcHFyV0AEA1WSLHAAAcE/kCMB9mep6qV/y+kr33zi/vx2jgSuo1lXqPDw81KBBA/M/wzB05swZvfbaa+rbt68SExPNi4Nf7r6TJ0/Wjh07NHnyZH322Wd68cUXtWzZMsXExMjPz08JCQnKysrSxIkT9fHHH2vhwoVKS0tTfHy8GjRoUJ3QAQDVVJ0cAABwb+QIAECVZjjt3r1b6enp2rx5s44dO6a6deuqR48eGjdunHr27ClJ2rRpk5544glNmjRJq1atuuzj9OnTRyaTSUuWLFF8fLwaN26sxMRExcfHS/p9EfFFixYpNTVViYmJatKkiaZMmaK4uLiqjRYAUG22ygFATWt3o+MuIgLUFuQIAEAJqwpO8+bN03vvvaejR4/Kw8NDt9xyixISEhQVFVVmEe+BAwfq/fff1/bt2yt8zIiICEVERJS7PTIyUpGRkdaECQCwA3vkAKAmeV9Vn1MBADtxZI748ssv9dxzz2nfvn3y9fVVVFSUJk2aZL5IUUZGhhYsWKDvvvtOjRs31ogRI/gBGwBqgFUFp5dfflnt27fXiBEj1KdPH11//fUV9g8JCVGnTp2qEx8AwEmQAwAA5XFUjti5c6diY2PVq1cvLVu2TIcPH9Zzzz2nU6dOacGCBcrKytK4ceMUHR2tCRMmKDMzUykpKTIMQ6NHj6728wMAymdVwSk9Pb3Cq8NdvHhRR48eVcuWLSVJsbGx1YsOAOA0yAEAgPI4KkfMmzdPnTp10vPPPy8PDw9169ZNFy9e1MqVK3X+/Hmlpqaqffv2mjt3riQpPDxcRUVFWr58uWJiYmQymWwSBwCgLKsWDe/Tp4/eeeedcre/+eabGjBgQHVjAgA4IXIAAKA8jsgRp06d0o4dO3TfffeZr2gtScOHD9e2bdvk6empHTt2qHfv3hb3i4qK0unTp5WVlWXTeAAAliqc4XTixAn95z//Md82DENffvmlioqKyvS9ePGiNm7caLGzBwC4LnIAAKA8zpAjvvnmGxmGoYYNGyopKUkfffSRvLy8dPfdd2vatGk6cuSICgsLy8y88vf3lyQdOnRIXbt2tWlMAIA/VFhw8vPz0/Lly/XDDz9I+v3ypmvXrtXatWvLvU9MTIxNAwQAOAY5AABQHmfIEadOnZIkTZ06VZGRkVq2bJkOHDighQsXKj8/X8OGDZMk+fj4WNyvZDHxvLw8m8YDALBUYcGpbt26WrFihY4cOSLDMDRq1CjFx8frtttuK9PX09NTfn5+CggIsFuwAICaQw4AAJTHGXJEYWGhJOnmm2/WzJkzJUlhYWEyDEPPPvushg4dKknlzqzy9Kz86iJ79+6VJGVmZlYnZKfmCmMLCQlxdAiwUnXeV67wnqwOdxlfRZ/LKy4a3qxZMzVr1kySNHv2bIWGhpoX+wMAuDdyAJxZQWGxTHW9HB0GUGs5OkeUzFQKDw+3aO/evbvmzJmj3bt3Syo7k6nktq+vb6WfKygoSJmZmW5b8HDnscGxqvq+cvf3pLuPr4RVV6kbOHCgveIAADg5cgCcjamul/olr690/43z+9sxGqB2c0SOaN26tSSpoKDAor1k5lOLFi3k5eWlnJwci+0ltyu6qh4AoPoqLDjdeOONSklJUb9+/SRJ7dq1u+Jifx4eHtq3b5/tIgQAOAQ5AABQHmfIEW3btlXz5s317rvv6v777ze3f/jhh6pTp446d+6s0NBQbdmyRaNGjTLHt3nzZvn6+io4ONhmsQAAyqqw4DRgwAC1atXK4jZXIAKA2oEcAAAojzPkCA8PD02ePFmTJk3S5MmTNWjQIO3Zs0fLli1TTEyM/Pz8lJCQoNjYWE2cOFEDBw5Udna20tLSlJycrAYNGtRovABQ21RYcJo9e7bF7Tlz5tg1GACA8yAHAADK4yw5ok+fPjKZTFqyZIni4+PVuHFjJSYmKj4+XtLvi4gvWrRIqampSkxMVJMmTTRlyhTFxcU5JF4AqE2sWsPpcgoLC7V9+3Z5enqqW7duqlOn2g8JAHAR5AAAQHlqKkdEREQoIiKi3O2RkZGKjIy0y3MDAMpn1V6/oKBAs2bN0pEjR7RixQoVFBRo2LBh+vrrryX9fh71K6+8osaNG9slWACA4zgqB3z55Zd67rnntG/fPvn6+ioqKkqTJk0yX50oIyNDCxYs0HfffafGjRtrxIgR/HINADWM7wkAgNI8rem8ePFivf766/rTn/4kSXr77be1f/9+xcTE6JlnntH//vc/Pf/883YJFADgWI7IATt37lRsbKyuu+46LVu2TImJidqwYYNmzJghScrKytK4ceMUEBCgRYsWqV+/fkpJSVFaWppN4wAAVIzvCQCA0qya4ZSenq4hQ4Zo1qxZkv64wsOUKVNUp04d5ebmat26dXYJFADgWI7IAfPmzVOnTp30/PPPy8PDQ926ddPFixe1cuVKnT9/XqmpqWrfvr3mzp0rSQoPD1dRUZGWL1+umJgYmUwmm8YDALg8vicAAEqzaobTjz/+qE6dOkmSzp8/ry+//FJhYWHm87H/9Kc/6fTp0zYPEgDgeDWdA06dOqUdO3bovvvus7jy0fDhw7Vt2zZ5enpqx44d6t27t8X9oqKidPr0aWVlZdksFgBAxfieAAAozaqC07XXXquff/5ZkvTpp5+qoKBAd9xxh3n7gQMHdP3119s0QACAc6jpHPDNN9/IMAw1bNhQSUlJ6tSpk0JCQjRz5kxduHBBubm5KiwsVJs2bSzu5+/vL0k6dOiQzWIBAFSM7wkAgNKsOqXu1ltv1SuvvKJ69epp9erVatCggSIiInT69Gm98cYbev3113XvvffaK1YAgAPVdA44deqUJGnq1KmKjIzUsmXLdODAAS1cuFD5+fkaNmyYJMnHx8fifiWLiefl5VX6ufbu3asLFy7YKPI/ZGZm2vwx8YeQkBBHh1Dr2eI9zufE+Vz6mlT2c8b3BABAaVYVnKZPn64TJ07o2Wef1VVXXaVZs2bp6quvVmZmpp599lndcsstGj9+vL1iBQA4UE3ngMLCQknSzTffrJkzZ0qSwsLCZBiGnn32WQ0dOlSSLE63u5SnZ+Un8QYFBVUz2rIyMzMpiMDtVfc9zufE+VT1NeF7AgCgNKsKTldffbVWrlypU6dOycfHx7wY64033qi1a9eqY8eOdgkSAOB4NZ0DSmYqhYeHW7R3795dc+bM0e7duyWVnclUctvX19em8QAAysf3BABAaVYVnEr4+flZ3L7qqqtIIgBQS9RUDmjdurUkqaCgwKK9ZOZTixYt5OXlpZycHIvtJbdLr+0EALA/vicAAEpYXXD65JNPtHHjRv38888qLi4us93Dw0OvvPKKTYIDADiXmswBbdu2VfPmzfXuu+/q/vvvN7d/+OGHqlOnjjp37qzQ0FBt2bJFo0aNMp9aV3Ip7uDgYJvEAQCoHL4nAAAuZVXBafXq1Zo1a5YkqXHjxuapsgAA91fTOcDDw0OTJ0/WpEmTNHnyZA0aNEh79uzRsmXLFBMTIz8/PyUkJCg2NlYTJ07UwIEDlZ2drbS0NCUnJ6tBgwZ2jQ8A8Ae+JwAASrOq4PTPf/5T7dq100svvaRrr73WXjEBAJyQI3JAnz59ZDKZtGTJEsXHx6tx48ZKTExUfHy8pN8XEV+0aJFSU1OVmJioJk2aaMqUKYqLi6uR+AAAv+N7AgCgNKsKTsePH9f06dNJIgBQCzk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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "rep_propscore_plot(dml_irm_lasso)" - ] - }, - { - "cell_type": "markdown", - "id": "b282c8d9", - "metadata": {}, - "source": [ - "We observe that the propensity score estimates of the lasso-based model are more centered and only close to zero and one for very few observations." - ] - }, - { - "cell_type": "markdown", - "id": "b29e412d-d86f-46b4-840f-cbbe082faf0b", - "metadata": {}, - "source": [ - "### Conclusion\n", - "\n", - "We can conclude that the interactive regression model (IRM) estimates are close to the true coefficient value, if the nuisance components are estimated with machine learning methods. The performance of Lasso and the tree-based methods random forests and extreme gradient boosting are comparable. All of the ML-based estimators have exhibited a superior performance to the benchmark based on linear and logistic regression, which seems to be rather unstable in the data example considered.\n" - ] - }, - { - "cell_type": "markdown", - "id": "f50297c5", - "metadata": {}, - "source": [ - "## 2. Partially Linear Regression Model (PLR)\n", - "\n", - "The [DoubleML](https://docs.doubleml.org/stable/index.html) package also includes the [Partial Linear Regression (PLR)](https://docs.doubleml.org/stable/guide/models.html#partially-linear-regression-model-plr) model, which assumes the population regression has a linear and additive structure. Although in reality, we never know if this structure really holds for the underlying data generating process, we can apply this model and see how the estimates compare to those from the IRM." - ] - }, - { - "cell_type": "markdown", - "id": "fa24e6e1-b878-401f-b38a-c29cc0620c2c", - "metadata": {}, - "source": [ - "We estimate the function $g_0$ and $m_0$ in the following PLR model:\n", - "\n", - "\\begin{eqnarray}\n", - "& Y = D\\theta_0 + g_0(X) + \\zeta, &\\quad E[\\zeta \\mid D,X]= 0,\\\\\n", - "& D = m_0(X) + V, &\\quad E[V \\mid X] = 0.\n", - "\\end{eqnarray}\n", - "\n", - "To estimate the causal parameter $\\theta_0$, we use double machine learning with 3-fold cross-fitting again. The steps of our analysis are very similar to the IRM cases with the difference being that we use a model class [DoubleMLPLR](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLPLR.html) for estimation." - ] - }, - { - "cell_type": "markdown", - "id": "8e7ad0b5", - "metadata": {}, - "source": [ - "### Assess predictive performance in the PLR" - ] - }, - { - "cell_type": "markdown", - "id": "73c26a84", - "metadata": {}, - "source": [ - "As in the IRM, we want to calculate mean and standard deviation of the RMSE / log loss values across all repetitions to evaluate the prediction performance. Once again, a helper function is used as follows:" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "id": "54a843e3", - "metadata": {}, - "outputs": [], - "source": [ - "def pred_acc_plr(DoubleML, prop):\n", - " \"\"\"\n", - " A function to calculate prediction accuracy values for every repetition\n", - " of a Double Machine Learning model using PLR, DoubleMLPLR\n", - " \n", - " ...\n", - " \n", - " Parameters\n", - " ----------\n", - " DoubleML : doubleml.double_ml_plr.DoubleMLPLR\n", - " The PLR Double Machine Learning model\n", - " prop : bool\n", - " Indication if RMSE values have to be computed for main regression or log loss values for propensity score\n", - " \"\"\"\n", - " \n", - " \n", - " # export data, fitted coefficient and predictions of the DoubleML model\n", - " y = DoubleML._dml_data.y\n", - " d = DoubleML._dml_data.d\n", - " theta = DoubleML.coef\n", - " g0 = DoubleML.predictions.get('ml_g')\n", - " m = DoubleML.predictions.get('ml_m')\n", - " \n", - " # dimensions of prediction array\n", - " h = g0.shape[0]\n", - " w = DoubleML.n_rep\n", - " \n", - " # check whether treatment is binary \n", - " if np.isin(d, [0,1]).all() == False:\n", - " raise ValueError(\"Treatment must be a binary variable.\")\n", - " \n", - " # prepare array to store prediction accuracy values\n", - " pred_acc_array = np.zeros((w,))\n", - " \n", - " # check whether to assess main regression or propensity score accuracy: \n", - " if prop == False:\n", - " \n", - " # evaluate main regression accuracy\n", - " # export array with prediction values\n", - " export_pred_array = np.zeros((h, w)) \n", - " for i in range(w):\n", - " for j in range(h):\n", - " export_pred_array[j,i] = theta*d[j] + g0[j,i]\n", - " \n", - " # fill array that contains rmse of each repetition\n", - " for i in range(w):\n", - " pred_acc_array[i] = mean_squared_error(y, export_pred_array[:,i], squared=False)\n", - " \n", - " else:\n", - " \n", - " # evaluate propensity score accuracy\n", - " # fill array that contains log loss of each repetition\n", - " for i in range(w):\n", - " pred_acc_array[i] = log_loss(d, m[:,i], eps=0.025)\n", - " \n", - " return pred_acc_array" - ] - }, - { - "cell_type": "markdown", - "id": "331a36d6", - "metadata": {}, - "source": [ - "### Benchmark: Model based on Linear and Logistic Regression" - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "id": "1432e567-d221-490d-9361-39b9072cb6d4", - "metadata": { - "scrolled": true, - "tags": [] - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A0.7849990.06712711.6941911.364815e-310.6534320.916565
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.784999 0.067127 11.694191 1.364815e-31 0.653432 0.916565" - ] - }, - "execution_count": 44, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize Linear and Logistic Regression learners\n", - "linreg = make_pipeline(StandardScaler(), LinearRegression())\n", - "logreg_class = make_pipeline(StandardScaler(), LogisticRegression(penalty=\"none\"))\n", - "\n", - "# Initialize DoubleMLPLR model\n", - "np.random.seed(1234)\n", - "dml_plr_regression = dml.DoubleMLPLR(data_dml,\n", - " ml_g = linreg,\n", - " ml_m = logreg_class,\n", - " n_folds = 3,\n", - " n_rep = 3)\n", - "\n", - "dml_plr_regression.fit(store_predictions=True)\n", - "\n", - "reg_summary = dml_plr_regression.summary\n", - "reg_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "id": "ff708453", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [-0.01500149]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_plr_regression.coef - 0.8)" - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "id": "88392566", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_linlog_plr = pred_acc_plr(dml_plr_regression, prop=False)\n", - "rmse_main_linlog_plr_mean = np.mean(rmse_main_linlog_plr)\n", - "rmse_main_linlog_plr_std = np.std(rmse_main_linlog_plr)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_linlog_plr = pred_acc_plr(dml_plr_regression, prop=True)\n", - "logloss_prop_linlog_plr_mean = np.mean(logloss_prop_linlog_plr)\n", - "logloss_prop_linlog_plr_std = np.std(logloss_prop_linlog_plr)" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "id": "08227dfc", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 1.3418428467276253\n", - "Standard deviation of RMSE is 0.009847706467828324\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_linlog_plr_mean)\n", - "print(\"Standard deviation of RMSE is\", rmse_main_linlog_plr_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "id": "c91ed6e8", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 1.0228568161263911\n", - "Standard deviation of log loss is 0.027536454508812133\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_linlog_plr_mean)\n", - "print(\"Standard deviation of log loss is\", logloss_prop_linlog_plr_std)" - ] - }, - { - "cell_type": "markdown", - "id": "4dd8948f", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Lasso" - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "id": "0bbbc3ce", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A0.8047950.07027111.4528072.276523e-300.6670670.942522
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.804795 0.070271 11.452807 2.276523e-30 0.667067 0.942522" - ] - }, - "execution_count": 49, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize DoubleMLPLR model\n", - "np.random.seed(1234)\n", - "dml_plr_lasso = dml.DoubleMLPLR(data_dml,\n", - " ml_g = lasso,\n", - " ml_m = lasso_class,\n", - " n_folds = 3,\n", - " n_rep = 3)\n", - "\n", - "dml_plr_lasso.fit(store_predictions=True)\n", - "\n", - "lasso_summary=dml_plr_lasso.summary\n", - "lasso_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "id": "30aef0c8", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [0.00479477]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_plr_lasso.coef - 0.8)" - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "id": "96383f94", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_lasso_plr = pred_acc_plr(dml_plr_lasso, prop=False)\n", - "rmse_main_lasso_plr_mean = np.mean(rmse_main_lasso_plr)\n", - "rmse_main_lasso_plr_std = np.std(rmse_main_lasso_plr)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_lasso_plr = pred_acc_plr(dml_plr_lasso, prop=True)\n", - "logloss_prop_lasso_plr_mean = np.mean(logloss_prop_lasso_plr)\n", - "logloss_prop_lasso_plr_std = np.std(logloss_prop_lasso_plr)" - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "id": "10a66c25", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 1.1394799633725696\n", - "Standard deviation of RMSE is 0.003190385536736178\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_lasso_plr_mean)\n", - "print(\"Standard deviation of RMSE is\", rmse_main_lasso_plr_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 53, - "id": "afe3b2b9", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 0.6686763881131824\n", - "Standard deviation of log loss 0.003254281706002184\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_lasso_plr_mean)\n", - "print(\"Standard deviation of log loss\", logloss_prop_lasso_plr_std)" - ] - }, - { - "cell_type": "markdown", - "id": "a4ed2694", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Random Forests" - ] - }, - { - "cell_type": "code", - "execution_count": 54, - "id": "e5f3ac90", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A0.7993070.07329710.9050281.090595e-270.6556470.942967
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.799307 0.073297 10.905028 1.090595e-27 0.655647 0.942967" - ] - }, - "execution_count": 54, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize Random Forest learners\n", - "randomForest = RandomForestRegressor()\n", - "randomForest_class = RandomForestClassifier()\n", - "\n", - "# Initialize DoubleMLPLR model\n", - "np.random.seed(1234)\n", - "dml_plr_forest = dml.DoubleMLPLR(data_dml,\n", - " ml_g = randomForest,\n", - " ml_m = randomForest_class,\n", - " n_folds = 3,\n", - " n_rep = 3)\n", - "\n", - "dml_plr_forest.fit(store_predictions=True)\n", - "\n", - "forest_summary = dml_plr_forest.summary\n", - "forest_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "id": "4c40246d", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [-0.00069288]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_plr_forest.coef - 0.8)" - ] - }, - { - "cell_type": "code", - "execution_count": 56, - "id": "a977c34b", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_forest_plr = pred_acc_plr(dml_plr_forest, prop=False)\n", - "rmse_main_forest_plr_mean = np.mean(rmse_main_forest_plr)\n", - "rmse_main_forest_plr_std = np.std(rmse_main_forest_plr)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_forest_plr = pred_acc_plr(dml_plr_forest, prop=True)\n", - "logloss_prop_forest_plr_mean = np.mean(logloss_prop_forest_plr)\n", - "logloss_prop_forest_plr_std = np.std(logloss_prop_forest_plr)" - ] - }, - { - "cell_type": "code", - "execution_count": 57, - "id": "1f54fed6", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 1.1886867050333019\n", - "Standard deviation of RMSE is 0.006048072563384578\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_forest_plr_mean)\n", - "print(\"Standard deviation of RMSE is\", rmse_main_forest_plr_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 58, - "id": "8101acf6", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 0.6836880652313276\n", - "Standard deviation of log loss is 0.005321479254441978\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_forest_plr_mean)\n", - "print(\"Standard deviation of log loss is\", logloss_prop_forest_plr_std)" - ] - }, - { - "cell_type": "markdown", - "id": "6aa9af04", - "metadata": {}, - "source": [ - "### Double Machine Learning based on Extreme Gradient Boosting" - ] - }, - { - "cell_type": "code", - "execution_count": 59, - "id": "6fab5d3a", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefstd errtP>|t|2.5 %97.5 %
A0.823840.07167611.4939881.414286e-300.6833580.964321
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" - ], - "text/plain": [ - " coef std err t P>|t| 2.5 % 97.5 %\n", - "A 0.82384 0.071676 11.493988 1.414286e-30 0.683358 0.964321" - ] - }, - "execution_count": 59, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Initialize Extreme Gradient Boosting learners\n", - "boost = XGBRegressor(n_jobs = 1, objective = \"reg:squarederror\", \n", - " eta = 0.1, n_estimators = 57, max_depth = 2)\n", - "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", - " objective = \"binary:logistic\",\n", - " eval_metric = \"logloss\",\n", - " eta = 0.1, n_estimators = 10,\n", - " max_depth = 3)\n", - "\n", - "# Initialize DoubleMLPLR model\n", - "np.random.seed(1234)\n", - "dml_plr_boost = dml.DoubleMLPLR(data_dml,\n", - " ml_g = boost,\n", - " ml_m = boost_class,\n", - " n_folds = 3,\n", - " n_rep = 3)\n", - "\n", - "dml_plr_boost.fit(store_predictions=True)\n", - "\n", - "boost_summary = dml_plr_boost.summary\n", - "boost_summary" - ] - }, - { - "cell_type": "code", - "execution_count": 60, - "id": "6e3252f8", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Bias: [0.02383965]\n" - ] - } - ], - "source": [ - "print(\"Bias:\", dml_plr_boost.coef - 0.8)" - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "id": "e90a61cc", - "metadata": {}, - "outputs": [], - "source": [ - "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", - "rmse_main_boost_plr = pred_acc_plr(dml_plr_boost, prop=False)\n", - "rmse_main_boost_plr_mean = np.mean(rmse_main_boost_plr)\n", - "rmse_main_boost_plr_std = np.std(rmse_main_boost_plr)\n", - "\n", - "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", - "logloss_prop_boost_plr = pred_acc_plr(dml_plr_boost, prop=True)\n", - "logloss_prop_boost_plr_mean = np.mean(logloss_prop_boost_plr)\n", - "logloss_prop_boost_plr_std = np.std(logloss_prop_boost_plr)" - ] - }, - { - "cell_type": "code", - "execution_count": 62, - "id": "72121d00", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the main regression RMSE across 3 repetitions is 1.1560362080432272\n", - "Standard deviation of RMSE is 0.0027129250049691073\n" - ] - } - ], - "source": [ - "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_boost_plr_mean)\n", - "print(\"Standard deviation of RMSE is\", rmse_main_boost_plr_std)" - ] - }, - { - "cell_type": "code", - "execution_count": 63, - "id": "8513cd4e", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean of the propensity score's log loss across 3 repetitions is 0.677578683851663\n", - "Standard deviation of log loss is 0.005774390874769318\n" - ] - } - ], - "source": [ - "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_boost_plr_mean)\n", - "print(\"Standard deviation of log loss is\", logloss_prop_boost_plr_std)" - ] - }, - { - "cell_type": "markdown", - "id": "a979a78b", - "metadata": {}, - "source": [ - "#### PLR - Summary of coefficient estimates" - ] - }, - { - "cell_type": "code", - "execution_count": 64, - "id": "dba8d33c", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefBias2.5 %97.5 %
regression0.785-0.0150.6530.917
lasso0.8050.0050.6670.943
forest0.799-0.0010.6560.943
xgboost0.8240.0240.6830.964
\n", - "
" - ], - "text/plain": [ - " coef Bias 2.5 % 97.5 %\n", - "regression 0.785 -0.015 0.653 0.917\n", - "lasso 0.805 0.005 0.667 0.943\n", - "forest 0.799 -0.001 0.656 0.943\n", - "xgboost 0.824 0.024 0.683 0.964" - ] - }, - "execution_count": 64, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "plr_summary = pd.concat((reg_summary, lasso_summary, forest_summary, boost_summary))\n", - "plr_summary.index = ['regression','lasso', 'forest', 'xgboost']\n", - "plr_summary = plr_summary[['coef', '2.5 %', '97.5 %']]\n", - "plr_summary.insert(1, \"Bias\", [plr_summary.loc['regression','coef'] - 0.8, \n", - " plr_summary.loc['lasso','coef'] - 0.8, \n", - " plr_summary.loc['forest','coef'] - 0.8, \n", - " plr_summary.loc['xgboost','coef'] - 0.8])\n", - "plr_summary.round(3) " - ] - }, - { - "cell_type": "code", - "execution_count": 65, - "id": "86fe5d87", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "errors = np.full((2, plr_summary.shape[0]), np.nan)\n", - "errors[0, :] = plr_summary['coef'] - plr_summary['2.5 %']\n", - "errors[1, :] = plr_summary['97.5 %'] - plr_summary['coef']\n", - "plt.errorbar(plr_summary.index, plr_summary.coef, fmt='o', yerr=errors)\n", - "plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", - "\n", - "plt.title('Partially Linear Regression Model (PLR)')\n", - "plt.xlabel('ML method')\n", - "_ = plt.ylabel('Coefficients and 95%-CI')" - ] - }, - { - "cell_type": "markdown", - "id": "19fc42af", - "metadata": {}, - "source": [ - "#### PLR - Summary of prediction accuracy metric's mean values" - ] - }, - { - "cell_type": "code", - "execution_count": 66, - "id": "b8937548", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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main RMSEmain RMSE (sd)prop log lossprop log loss (sd)
regression1.3420.0101.0230.028
lasso1.1390.0030.6690.003
forest1.1890.0060.6840.005
xgboost1.1560.0030.6780.006
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" - ], - "text/plain": [ - " main RMSE main RMSE (sd) prop log loss prop log loss (sd)\n", - "regression 1.342 0.010 1.023 0.028\n", - "lasso 1.139 0.003 0.669 0.003\n", - "forest 1.189 0.006 0.684 0.005\n", - "xgboost 1.156 0.003 0.678 0.006" - ] - }, - "execution_count": 66, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "plr_rmse_index = ['regression','lasso', 'forest', 'xgboost']\n", - "plr_rmse = pd.DataFrame([[rmse_main_linlog_plr_mean, rmse_main_linlog_plr_std, \n", - " logloss_prop_linlog_plr_mean, logloss_prop_linlog_plr_std],\n", - " [rmse_main_lasso_plr_mean, rmse_main_lasso_plr_std,\n", - " logloss_prop_lasso_plr_mean, logloss_prop_lasso_plr_std],\n", - " [rmse_main_forest_plr_mean, rmse_main_forest_plr_std,\n", - " logloss_prop_forest_plr_mean, logloss_prop_forest_plr_std],\n", - " [rmse_main_boost_plr_mean, rmse_main_boost_plr_std,\n", - " logloss_prop_boost_plr_mean, logloss_prop_boost_plr_std]],\n", - " index=plr_rmse_index,\n", - " columns=['main RMSE', 'main RMSE (sd)',\n", - " 'prop log loss', 'prop log loss (sd)'])\n", - "plr_rmse.round(3)" - ] - }, - { - "cell_type": "code", - "execution_count": 67, - "id": "79fe38ed", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 67, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# graphical illustration of RMSE for main regression\n", - "errors_plr_rmse = np.full((2, plr_rmse.shape[0]), np.nan)\n", - "errors_plr_rmse[0, :] = plr_rmse['main RMSE'] - plr_rmse['main RMSE (sd)']\n", - "errors_plr_rmse[1, :] = plr_rmse['main RMSE'] + plr_rmse['main RMSE (sd)']\n", - "plt.errorbar(x=plr_rmse.index, y=plr_rmse['main RMSE'], fmt='x',\n", - " yerr=errors_plr_rmse, c='darkslategray')" - ] - }, - { - "cell_type": "code", - "execution_count": 68, - "id": "bb40406b", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 68, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# graphical illustration of log loss for main regression\n", - "errors_plr_logloss = np.full((2, plr_rmse.shape[0]), np.nan)\n", - "errors_plr_logloss[0, :] = plr_rmse['prop log loss'] - plr_rmse['prop log loss (sd)']\n", - "errors_plr_logloss[1, :] = plr_rmse['prop log loss'] + plr_rmse['prop log loss (sd)']\n", - "plt.errorbar(x=plr_rmse.index, y=plr_rmse['prop log loss'], fmt='x',\n", - " yerr=errors_plr_logloss, c='darkslategray')" - ] - }, - { - "cell_type": "markdown", - "id": "27d1d2a9-beed-493d-ae92-8d4e92cde8ae", - "metadata": {}, - "source": [ - "### Summary of IRM and PLR Results" - ] - }, - { - "cell_type": "code", - "execution_count": 69, - "id": "1b4ddf50-50de-4bab-a110-767b8d50df21", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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coefBias2.5 %97.5 %
ModelML
IRMregression1.0580.258-0.1672.282
lasso0.8560.0560.7170.995
forest0.8930.0930.7411.045
xgboost0.791-0.0090.5860.995
PLRregression0.785-0.0150.6530.917
lasso0.8050.0050.6670.943
forest0.799-0.0010.6560.943
xgboost0.8240.0240.6830.964
\n", - "
" - ], - "text/plain": [ - " coef Bias 2.5 % 97.5 %\n", - "Model ML \n", - "IRM regression 1.058 0.258 -0.167 2.282\n", - " lasso 0.856 0.056 0.717 0.995\n", - " forest 0.893 0.093 0.741 1.045\n", - " xgboost 0.791 -0.009 0.586 0.995\n", - "PLR regression 0.785 -0.015 0.653 0.917\n", - " lasso 0.805 0.005 0.667 0.943\n", - " forest 0.799 -0.001 0.656 0.943\n", - " xgboost 0.824 0.024 0.683 0.964" - ] - }, - "execution_count": 69, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df_summary = pd.concat((irm_summary,plr_summary)).reset_index().rename(columns={'index': 'ML'})\n", - "df_summary['Model'] = np.concatenate((np.repeat('IRM', 4), np.repeat('PLR', 4)))\n", - "df_summary.set_index(['Model', 'ML']).round(3)" - ] - }, - { - "cell_type": "markdown", - "id": "64aa3065-da5c-49b9-88f2-5c08c1b7e617", - "metadata": {}, - "source": [ - "### Conclusion\n", - "\n", - "As in the IRM model, the ML-based PLR models are associated with a smaller bias as compared to the model that is based on linear and logistic regression. It seems that the estimates obtained from the PLR are slightly closer to the true ATE than those from the IRM analysis. This might suggest, that the parametric assumptions (i.e., an additive and homogeneous causal effect) that are incorporated in the PLR turn out to be **not restrictive** in our example data set. However, if both models are based on appropriate ML learners, the conclusions are very similar. In all cases, the ML-based estimates were very close to the true ATE and we were always able to reject the null hypothesis of a zero effect at all common significance levels. In terms of the A/B testing example, it can be concluded that the new ad increases customers purchases (in $100\\$$) by around 0.8 on average and that this effect is significantly different from zero at the 5% significance level. The results are summarized in the graphic below." - ] - }, - { - "cell_type": "code", - "execution_count": 70, - "id": "c80cadcc", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize=(8, 9))\n", - "colors = sns.color_palette()\n", - "for ind, model in enumerate(['IRM', 'PLR']):\n", - " sns.set(font_scale=1.15)\n", - " plt.subplot(3, 1, ind+1)\n", - " this_df = df_summary.query('Model == @model')\n", - " errors = np.full((2, this_df.shape[0]), np.nan)\n", - " errors[0, :] = this_df['coef'] - this_df['2.5 %']\n", - " errors[1, :] = this_df['97.5 %'] - this_df['coef']\n", - " plt.errorbar(this_df.ML, this_df.coef, fmt='o', yerr=errors,\n", - " color=colors[ind], ecolor=colors[ind])\n", - " plt.ylim([0.5, 1.2])\n", - " plt.title(model)\n", - " plt.ylabel('Coeff. and 95%-CI')\n", - " plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", - " plt.legend(bbox_to_anchor=(1.04,0.5), loc=\"best\", borderaxespad=0)\n", - "\n", - "_ = plt.xlabel('ML method')" - ] - }, - { - "cell_type": "markdown", - "id": "90109d08", - "metadata": {}, - "source": [ - "## Appendix" - ] - }, - { - "cell_type": "markdown", - "id": "e42903ad", - "metadata": {}, - "source": [ - "### Propensity score estimates" - ] - }, - { - "cell_type": "markdown", - "id": "157d7295", - "metadata": {}, - "source": [ - "For both the IRM and the PLR model, we want to compare the propensity score estimates of all learners. Since repeated sample splitting is used for every learner, we first want to check whether the repetitions provide similare propensity score estimates. If that is the case, it should be legitimate to pick any of the repetitions for the comparision across all learners." - ] - }, - { - "cell_type": "markdown", - "id": "bb614dd1", - "metadata": {}, - "source": [ - "#### IRM - Repetitions of the Linear and Logistic regression model" - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "id": "a2a753a7", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "rep_propscore_plot(dml_irm_lasso)" - ] - }, - { - "cell_type": "markdown", - "id": "6ae81d8d", - "metadata": {}, - "source": [ - "#### IRM - Repetitions of the Random Forest model" - ] - }, - { - "cell_type": "code", - "execution_count": 73, - "id": "2775a78e", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "h = dml_irm_regression.predictions.get('ml_m').shape[0]\n", - "fig, ax = plt.subplots(1, 4, figsize=(20,4.8))\n", - "\n", - "#regression histogram\n", - "ax[0].hist(np.reshape(dml_irm_regression.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[0].set_title('regression')\n", - "ax[0].set_xlabel(\"prop_score\")\n", - "ax[0].set_ylabel(\"density\")\n", - "\n", - "#lasso histogram\n", - "ax[1].hist(np.reshape(dml_irm_lasso.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[1].set_title('lasso')\n", - "ax[1].set_xlabel(\"prop_score\")\n", - "ax[1].set_ylabel(\"density\")\n", - "\n", - "#random forest histogram\n", - "ax[2].hist(np.reshape(dml_irm_forest.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[2].set_title('random forest')\n", - "ax[2].set_xlabel(\"prop_score\")\n", - "ax[2].set_ylabel(\"density\")\n", - "\n", - "#boosting histogram\n", - "ax[3].hist(np.reshape(dml_irm_boost.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[3].set_title('xgboost')\n", - "ax[3].set_xlabel(\"prop_score\")\n", - "ax[3].set_ylabel(\"density\")\n", - " \n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "7a9a161d", - "metadata": {}, - "source": [ - "#### PLR - Repetitions of the Linear and Logistic regression model" - ] - }, - { - "cell_type": "code", - "execution_count": 76, - "id": "c4da298e", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "rep_propscore_plot(dml_plr_lasso)" - ] - }, - { - "cell_type": "markdown", - "id": "768dabe2", - "metadata": {}, - "source": [ - "#### PLR - Repetitions of the Random Forest model" - ] - }, - { - "cell_type": "code", - "execution_count": 78, - "id": "7639ef46", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "rep_propscore_plot(dml_plr_boost)" - ] - }, - { - "cell_type": "markdown", - "id": "70375158", - "metadata": {}, - "source": [ - "#### PLR - Propensity score estimates across learners" - ] - }, - { - "cell_type": "code", - "execution_count": 80, - "id": "1aeded78", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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fPjmdTi1YsEB1dXW64oorNHz4cEnSokWL5HQ6VVZWpkcffVSDBw9W9+7dGz2POl4/jk8SDmvjSia0qOuuu06HDx/WjBkztGfPHkVFRWnKlCkaPXq0JOnRRx/13HGgW7duGjFihKch1ZDf//73kqRJkyaprKxMMTExevTRRzVo0CBJ0oMPPqiHHnpIP/74oyIjI3Xrrbfq2muvVVBQkEpKSpSRkaEDBw7o7LPP1v33369f/OIX+vTTTz3779Gjh/7rv/5LixYt0l/+8hdFREQoNTVVU6dObbXXCIB1DRkyRLfccotuvfVW1dXVqUePHrr11lv1xBNPaP/+/Ro/frz27t2rm2++WVVVVerRo4f+8pe/6JxzztG0adP08MMP69e//rVqamoUHx+vJUuWKDw8XNdee62qqqr08MMPa8+ePTrnnHM0c+ZMjRo1KtBPGcBpmDVrlh588EENGjRInTp10uWXX65f/vKX+uabb5r8f0NCQpSbm6sHH3xQQ4YM0dlnn60rr7xS69atk+Tfc5PTOdaCBQu0YMECpaSk6MiRI+rdu7eef/55RUZGNlojjTEaOXKkxo4dq1mzZunGG29s8ecDwDtPPvmkKioqNGPGDEnSI488otTUVL333nt64okn9Nhjj2n27Nnq16+fBg8eXO9KppEjRyo3N1dTp07V+eefr+eff94zrPaxxx7TggULNHr0aB05ckSXXnqpVqxYoTPPPFOS9OKLL2r+/PmehtNVV12le++9V5IaPY9KSEhQv379lJycrMWLFys5OdmPrxaaK8gcn2gC8IOPP/5Y/fv3V3h4uKRjVwU8+OCD2rBhQ4CTAQAAAED79f333+vgwYPq3bu3Z9nx6Uj++Mc/BjAZ7IThcvCrefPm6bnnnpPb7daBAwe0bNkyXX755YGOBQAAAADtWnl5uX7zm99o+/btkqQtW7Zow4YNGjZsWICTwU64kgl+tX37ds2ZM0fbt29Xhw4ddPXVV2vGjBmeiS8BAAAAAIHxyiuv6MUXX1R5ebnOOecc3X777Z6pTwBv0GQCAAAAAACAzxguBwAAAAAAAJ/RZAIAAAAAAIDPOgQ6QGs6cOCw6uqaHg0YFdVZ5eVVfkjUMsjb+uyWua3mDQ4OUpcu9p+vy9ta1Fx2+LmTsWWQsWWcbsbWqkWrV6/WSy+9pJUrV0qSCgoKlJ2dreLiYiUkJGjevHmKi4trcp23Dhw4rC5dOln+59QQO7y/GkJu/2rruTkvanl2e8/YLa9EZn/xZ+amalGbbjLV1RmvC5hVCp23yNv67JaZvNbVnFp0Ovu2OjK2DDK2DCtkdLvdWr58uRYtWqSLL75YklRTU6PMzExNmzZNKSkpys3NVVZWlvLy8hpd1xzHn7sVXoPTQW7/Ird/2TX36WjN86LTYaUs3rBbXonM/mKVzAyXAwAA8KMFCxZo/fr1mjRpkmfZpk2b1KlTJ6WnpyssLEwZGRnatWuXCgsLG10HAABgJTSZAAAA/GjChAl65ZVX1KNHD8+y4uJixcfHex6HhIQoNjZWRUVFja4DAACwkjY9XA4AAMBqunbtetKyI0eOyOFw1FvmcDjkdDobXdccUVGdJUnR0ZHNTGwN5PYvcvuXXXMDwE/RZAIAAAiwhppG1dXV6tixY6PrmqO8vEpRUZ1VVlbpc15/i46OJLcfkdu/vM0dHBzkaRYDgFUxXA4AACDA4uLiVFJS4nnsdrtVWlqquLi4RtcBAABYCU0mAACAAEtKSlJFRYXy8/Plcrm0ZMkSxcTEqFevXo2uAwAAsBKaTAAAAAEWERGhpUuXauXKlUpKStLGjRuVk5OjoKCgRtcBAABYCXMyAQAABEB6errS09M9jxMTE5Wfn9/gto2tAwAAsAquZAIAAAAAAIDPaDIBAAAAAADAZwyXk+Q66lZ0dGSj2zhralV5qNpPiQAAbV3kGQ5FhDf+a7jG5VZ4WIgkNfh7it9NABrjTZ2hjgBoTFN1hBqCn6LJJCksNESp099udJtVC0ep0k95AABtX0R4B69+9zS2Db+bADTG2zpDHQFwKk3VEWoIfoomEwAAAOBHXBkAAGiraDIBAAAAfsSVAQCAtoqJvwEAAAAAAOAzrmQCAAAALISb0gAA7IomEwAAAGAh3JQGAGBXDJcDAAAAAACAz2gyAQAAAAAAwGd+bTKtXr1at9xyi+fxhx9+qFGjRqlfv3667rrrtG7dOs+6goICpaWlqW/fvho7dqx27tzpz6gAAAAAAABoBr80mdxut1544QXde++9MsZIksrKyjR16lTdfffd2rJli+6//37NmDFDu3btUk1NjTIzMzVu3Dht3rxZycnJysrK8kdUAAAAAAAAnAa/NJkWLFig9evXa9KkSZ5l33//vVJSUjRixAgFBwdr6NChOu+88/TFF19o06ZN6tSpk9LT0xUWFqaMjAzt2rVLhYWF/ogLAAAAAACAZvLL3eUmTJigrl276s033/Qsu+SSS3TJJZd4Hu/evVs7duxQQkKCNmzYoPj4eM+6kJAQxcbGqqioSAkJCf6IDAAAAAAAgGbwS5Opa9euja7ft2+fJk+erJtuuknx8fFau3atHA5HvW0cDoecTmezjhsV1bnZWRsTHR3ZovvzhZWyeMNueSX7ZSYv4LvIMxyKCG/8V6OzplaVh6r9lAgAAACwD780mRrzzTff6Pbbb1dycrLuv/9+SQ03lKqrq9WxY8dm7bu8vEp1dabJ7bz9sltWVtms47eW6OhIy2Txht3ySvbL3FbzBgcHtXizGGhMRHgHpU5/u9FtVi0cJft82gAAAAD/8evd5X5qy5YtuvXWW3XzzTdr9uzZCgoKkiTFxcWppKTEs53b7VZpaani4uIClBQAAAAAAACNCViT6YcfflBmZqbuvffeehOCS1JSUpIqKiqUn58vl8ulJUuWKCYmRr169QpQWgAAAABoe1avXq1bbrnF87igoEBpaWnq27evxo4dq507d3q1DgCkADaZ3njjDR08eFBz587VpZde6vn31ltvKSIiQkuXLtXKlSuVlJSkjRs3Kicnx3OlEwAAAADg9Lndbr3wwgu69957ZcyxKUZqamqUmZmpcePGafPmzUpOTlZWVlaT6wDgOL/OyZSenq709HRJ0p133qk777zzlNsmJiYqPz/fX9EAAAAAoN1YsGCBCgoKNGnSJH3yySeSpE2bNqlTp06e72wZGRlavny5CgsL9cMPP5xyHXcAB3BcQOdkAgAAAAD434QJE/TKK6+oR48enmXFxcWKj4/3PA4JCVFsbKyKiooaXQcAxwX87nIAAAAAAP/q2rXrScuOHDkih8NRb9nxO383tq45rHbnYG/vNG4VVszbVCYrZm4KmU8fTSYAAAAAQINNo+rqanXs2LHRdc1RXl6lujrjc9aWEB0dqbKyykDH8Fog8nrTuGgsk91eY4nMTQkODmq0WcxwOQAAAACA4uLiVFJS4nnsdrtVWlqquLi4RtcBwHE0mQAAAAAASkpKUkVFhfLz8+VyubRkyRLFxMSoV69eja4DgONoMgEAAAAAFBERoaVLl2rlypVKSkrSxo0blZOTo6CgoEbXAcBxzMkEAAAAAO1Uenq60tPTPY8TExOVn5/f4LaNrQMAiSuZAAAAAAAA0AJoMgEAAAAAAMBnNJkAAAAAAADgM5pMAAAAAAAA8BlNJgAAAAAAAPiMJhMAAAAAAAB8RpMJAAAAAAAAPusQ6AAAAACAHUSe4VBEeOOnz86aWlUeqvZTIgAArIUmEwAAAOCFiPAOSp3+dqPbrFo4SpV+ygMAgNUwXA4AJG3ZskWjR49Wv379lJqaqg0bNkiSCgoKlJaWpr59+2rs2LHauXNngJMCAAAAgDXRZALQ7tXW1uqOO+7Q9OnTtXXrVt11112aMmWKnE6nMjMzNW7cOG3evFnJycnKysoKdFwAAAAAsCSaTADavQMHDqiiokJHjx6VMUZBQUGKiIjQp59+qk6dOik9PV1hYWHKyMjQrl27VFhYGOjIAAAAAGA5zMkEoN2Ljo7WmDFjlJGRoZCQEAUHB2vx4sUqLi5WfHy8Z7uQkBDFxsaqqKhICQkJAUwMAAAAANZDkwlAu1dbWyuHw6Gnn35aw4YN05o1azRjxgyNHz9eDoej3rYOh0NOp7NZ+4+K6tySceuJjo5stX23lLaY0UrPiSzNY/WMW7Zs0Zw5c1RaWqru3bsrKytLycnJKigoUHZ2toqLi5WQkKB58+YpLi4u0HEBAADqockEoN1bt26dioqKNGvWLEnS9ddfr7y8PEk6qaFUXV2tjh07Nmv/5eVVqqszLRP2BNHRkSors/Y9jOyW0dsGREs8p5Zqdljl9bXbz7o5goODWrVZfNzx+eEWLFig5ORkvffee5oyZYo+/fRTZWZmatq0aUpJSVFubq6ysrI8dQoAAMAqaDIBaPf27t2r2traestCQ0PVpUsXlZSUeJa53W6VlpZy9QCAVuHN/HCSlJGRoeXLl6uwsJChuwCAgHIddTf5h7PIMxyqPFTtp0QINJpMANq9IUOG6IknntC7776ra6+9Vv/4xz/02Wef6eGHH9Yzzzyj/Px8paamKjc3VzExMerVq1egI8PiIs9wKCKcX7FoHuaHAwDYTVhoiFKnv93oNqsWjpK1r3VGS+IMGEC7l5CQoEWLFunJJ5/UAw88oHPPPVfPPPOMunfvrqVLlyo7O1tz5sxR7969lZOTo6CgoEBHhsVFhHfw6oQLOJG/5oez+rxUp2Kn3Cdmbc3cLbXvhvZjp9f7ROQGgMCiyQQAkkaOHKmRI0eetDwxMVH5+fkBSASr8uaycH/xJouzppZL1G3CH/PDRUV1tvzcWQ2xypxfzZ237VS5/TUn2+nOM2eV17u52npuf80PBwC+oMkEAEAzeHtZuJWy2O8rV/vE/HAAAMDuggMdAAAAAMfmh/v888/17rvvyhij9evX67PPPtPll1+uiooK5efny+VyacmSJcwPBwAALIkmEwAAgAUcnx9uyZIlGjBggJ5++ul688OtXLlSSUlJ2rhxI/PDAQAAS/LrcLnVq1frpZde0sqVKyVJBQUFys7OVnFxsRISEjRv3jzPpd+NrQMAAGiLmB8OANDWMIdk++KXJpPb7dby5cu1aNEiXXzxxZKkmpoaZWZmatq0aUpJSVFubq6ysrKUl5fX6DoAAAAAAGAPzCHZvvhluNyCBQu0fv16TZo0ybNs06ZN6tSpk9LT0xUWFqaMjAzt2rVLhYWFja4DAAAAAACA9fjlSqYJEyaoa9euevPNNz3LiouLFR8f73kcEhKi2NhYFRUV6ccffzzluoSEBH9EBgAAACAp8gyHIsIb/9rAUBcAgOSnJlPXrl1PWnbkyBE5HI56yxwOh5xOZ6PrAAAAAPhPRHgHhroAALzi14m/T9RQ06i6ulodO3ZsdF1zREV19jnniZqarMyfrJTFG3bLK9kvM3kBAAAAAIEUsCZTXFxcvYm83W63SktLFRcXJ4fDccp1zVFeXqW6OtPkdt5+2S0rs8bfZ6KjIy2TxRt2yyvZL3NbzRscHNTizWIAAAAAQOvwy8TfDUlKSlJFRYXy8/Plcrm0ZMkSxcTEqFevXo2uAwAAAAAAgPUErMkUERGhpUuXauXKlUpKStLGjRuVk5OjoKCgRtcBAAAAaBmuo25FR0fW+yfppMcAAHjDr8Pl0tPTlZ6e7nmcmJio/Pz8BrdtbB0AAPDO8S+QjeGuUED7FRYa4tWk3gAAeCNgczIBAIDW5+0XSPvM6gYAAACroskEAAAAAEAbEnmGQxHhjX/d50pmtAaaTAAAAAAAtCER4R24khkBEbCJvwEAAAAAANB20GQCAAAAAHhs2bJFo0ePVr9+/ZSamqoNGzZIkgoKCpSWlqa+fftq7Nix2rlzZ4CTArAamkwAgHYh8gzHSbfp/umtugEAaO9qa2t1xx13aPr06dq6davuuusuTZkyRU6nU5mZmRo3bpw2b96s5ORkZWVlBTouAIthTiYAQLvg7dwEANonbybJBdqDAwcOqKKiQkePHpUxRkFBQYqIiNCnn36qTp06KT09XZKUkZGh5cuXq7CwUAkJCQFODcAq+E0KAACAdo9GNHBMdHS0xowZo4yMDIWEhCg4OFiLFy9WcXGx4uPjPduFhIQoNjZWRUVFNJkAeNBkAgAAAABIOjZczuFw6Omnn9awYcO0Zs0azZgxQ+PHj5fD4ai3rcPhkNPpbNb+o6I6t2Rcn9ltuHxL57XS8yeLb6ySmSYTAAAAAECStG7dOhUVFWnWrFmSpOuvv155eXmSdFJDqbq6Wh07dmzW/svLq1RXZ1omrI+ioyNVVlYZ6Bhea05ebxsOTe3Pn40Lq/ws7Pa+kPybOTg4qNFmMRN/AwAAAAAkSXv37lVtbW29ZaGhoerSpYtKSko8y9xut0pLSxUXF+fnhACsjCYTAAAAAECSNGTIEH3++ed69913ZYzR+vXr9dlnn+nyyy9XRUWF8vPz5XK5tGTJEsXExKhXr16BjgzAQhguBwBAO+c66m7ycnhnTa0qD1X7KREAIFASEhK0aNEiPfnkk3rggQd07rnn6plnnlH37t21dOlSZWdna86cOerdu7dycnIUFBQU6MgALIQmEwAA7VxYaIhXd9Wy1+wEAIDTNXLkSI0cOfKk5YmJicrPzw9AIgB2wXA5AAAAAAAA+IwrmQAAAAAAsInIMxyKCPf9q7w3w+WB5qLJBAAAAACATUSEd/BqmHtTvB0uDzQHw+UAAAAAAADgM5pMAAAAAAAA8BnD5QAAAIAW8tM5TpjvBADQntBkAgAAAFoIc5wAANozhssBAAAAAADAZ1zJBAAAAAAAAuanQ40b4qypVeWhaj8lwumiyQQAAAAAAALG26HGlX7Kg9PHcDkAAAAAAAD4jCYTAAAAAAAAfEaTCQAAAAAAAD6jyQQAAAAAAACf0WQCAAAAAACAzwLeZNqyZYtGjx6tfv36KTU1VRs2bJAkFRQUKC0tTX379tXYsWO1c+fOACcF0Jbt3btXGRkZSkpK0ogRI/T228fubkEtAgAAAADvBLTJVFtbqzvuuEPTp0/X1q1bddddd2nKlClyOp3KzMzUuHHjtHnzZiUnJysrKyuQUQG0YcYYTZw4URdccIE2btyohQsXKjs7W0VFRdQiAAAAAPBSQJtMBw4cUEVFhY4ePSpjjIKCghQREaFPP/1UnTp1Unp6usLCwpSRkaFdu3apsLAwkHEBtFFbt27V4cOHdffdd6tDhw669NJLlZeXp127dlGLAAAAAMBLAW0yRUdHa8yYMcrIyFCfPn00depUzZ8/X8XFxYqPj/dsFxISotjYWBUVFQUwLYC26quvvtL555+vOXPmaPDgwUpJSVFpaalKS0upRQD8iqG7AADAzjoE8uC1tbVyOBx6+umnNWzYMK1Zs0YzZszQ+PHj5XA46m3rcDjkdDoDlBRAW3bo0CF99NFHuu+++/TBBx/o008/1V133aWJEye2SC2KiurcknHriY6ObLV9txQ7ZIR3mvpZ2uFnbeWMx4fujhgxQosXL9a//vUvTZgwQYmJicrMzNS0adOUkpKi3NxcZWVlKS8vL9CRAQAA6glok2ndunUqKirSrFmzJEnXX3+954Tpp1/iqqur1bFjx2btv6W/2FnpxNRKWbxht7yS/TKT9/SFhYWpa9euGj9+vCQpOTlZ/fv3lzGmRWpReXmV6upMi+U9Ljo6UmVllS2+35ZkpYxWes/ZVWM/Syv9rE/ldDMGBwe1arP4uBOH7gYHBzc4dFeSMjIytHz5chUWFiohIaHVcwEAAHgroE2mvXv3qra2tt6y0NBQdenSRSUlJZ5lbrdbpaWliouLa9b+vf1i5+0XD6ucPNvhRP5Edssr2S9zW83rry92PXv21OHDhz1zw0lSXV2dIiMjW6QWAYA3Thy6u3r1akVFRWnatGmNDt2lyQQAAKwkoHMyDRkyRJ9//rneffddGWO0fv16ffbZZ7r88stVUVGh/Px8uVwuLVmyRDExMerVq1cg4wJoo4YOHarw8HAtXrxYbrdbH3zwgbZt26aRI0dSiwD4zfGhuz179tQHH3ygGTNmaPr06Tp8+DDTCAAAAFsI6JVMCQkJWrRokZ588kk98MADOvfcc/XMM8+oe/fuWrp0qbKzszVnzhz17t1bOTk5nisMAKAlORwOrVixQg8//LCSkpIUFRWlBQsWUIsA+FVrD909fmWoXYeO2jV3a7Laa2KFPFbIcDrsmhsAfiqgTSZJGjlypEaOHHnS8sTEROXn5wcgEYD2KC4uTsuWLTtpObUIgL+09tDd8vIqRUV1ttXw6uP8MSzcjl/ym3pN/P2cAv3estv0AcdZbRoBAPBFQIfLAQAA4BiG7gIAALvzqsn0X//1X9q3b19rZwHQBkSe4VB0dGSj/1xH3S1+XOoUAH9prXpzfOju1q1blZSUpLlz59Yburty5UolJSVp48aNDN0FwLkPAEvyarjcBx98oL/85S8aOnSo0tPTNWLECIWGhrZ2NgA2FBHeQanT3250m1ULR7X4calTAPylNesNQ3cBeItzHwBW5NWVTC+99JLWrl2rX/ziF3riiSf0y1/+Uo888oi++OKL1s4HAF6hTgHwF+oNACugFgGwIq/nZOrevbsyMzO1Zs0aPfPMM9q2bZvGjBmj66+/Xn/9619VV1fXmjkBoEnUKQD+Qr0BYAXUIgBW4/Xd5dxutzZs2KC//e1v+t///V/FxsZqxowZ6t69u5599ll9/PHH+stf/tKKUQGgcdQpAP5CvQFgBdQiAFbjVZPp4Ycf1po1a+R2u5WSkqKXX35Zffr08ayPjY3VzTff3GohAaAp1CkA/kK9AWAF1CIAVuRVk6m0tFQPPPCArrzySoWFhZ20vlu3blq8eHGLhwMAb1GnAPgL9QaAFVCLAFiRV3MyxcfH69prrz2peM2cOVOS1KVLFyUnJ7d8OgDwEnUKgL9QbwBYAbUIgBWd8kqmvXv36pNPPpEkvfbaa7rwwgvrra+srNSaNWs0b9681k0IAKdAnQLgL9QbAFZALQJgdadsMnXp0kUvv/yy9u/fL5fLpZycnHrrw8LCdMcdd7R6QAA4FeoUAH+h3gCNcx11Kzo68pTrnTW1qjxU7cdEbZO/atHevXv10EMPaevWrerUqZPuvvtujRo1SgUFBcrOzlZxcbESEhI0b948xcXF+Xw8AG3HKZtMYWFhysvLkyT9/ve/1/PPP++3UADgDeoUAH+h3gCNCwsNUer0t0+5ftXCUar0Y562yh+1yBijiRMnasSIEVq8eLH+9a9/acKECUpMTFRmZqamTZumlJQU5ebmKisry5MHAKQmJv7+4YcfdM455+iRRx7Rnj17GtwmJiamVYJZTVN/nZH4Cw0QCNQpAP5CvQFgBa1di7Zu3arDhw/r7rvvVnBwsC699FLl5eVp165d6tSpk9LT0yVJGRkZWr58uQoLC5WQkHDaxwPQtjTaZLruuuu0detWjRgxQkFBQTLG1FsfFBSkr776qlUDWkVTf52R+AsNEAjUKQD+Qr0BYAWtXYu++uornX/++ZozZ45Wr16tqKgoTZs2TaWlpYqPj/dsFxISotjYWBUVFdFkAuDRaJPp73//uyRp/fr1fgkDAM1FnQLgL9QbAFbQ2rXo0KFD+uijj3Tffffpgw8+0Keffqq77rpLEydOlMPhqLetw+GQ0+lslRwA7KnRJtPPf/5zSVL37t1VXl6uqKgouVwu5eXl6ayzztI111zjl5AAcCrUKQD+Qr0BYAWtXYvCwsLUtWtXjR8/XpKUnJys/v37yxhzUkOpurpaHTt2bNb+o6I6+5SvpTU1JYq/uY66FRYacsr1Vsvrb/56/nZ8na2SudEm03H//d//rdmzZ2vbtm16/PHH9e677yooKEglJSWaPHlya2cEgCZRpwD4C/UGVuDNfKFo21qrFvXs2VOHDx+WMUZBQUGSpLq6OkVGRqqkpMSzndvtVmlpabPvLldeXqW6OtP0hn4QHR2psjJrTXgSHR3p1TQt7ZU/fl5WfF80xZ+Zg4ODGm0We9VkWrZsmZ566im53W69+eabys3NVdeuXTVu3DhOpgBYAnUKgL9Qb2AF3s4XirartWrR0KFDFR4ersWLF+uOO+7QRx99pG3btumRRx5Rbm6u8vPzlZqaqtzcXMXExKhXr14t+KwA2J1XTaY9e/Zo6NCh2rp1q0JCQtSvXz8FBQXp0KFDrZ0PALxCnQLgL9QbAFbQWrXI4XBoxYoVevjhh5WUlKSoqCgtWLBA3bt319KlS5Wdna05c+aod+/eysnJ8VztBACSl02mn/3sZyouLtbq1as1cOBABQUFadOmTYqOjm7tfADgFeoUAH+h3gCwgtasRXFxcVq2bNlJyxMTE5Wfn+/z/gG0XV41mSZMmKCUlBQFBwdr+fLl+uc//6nbb79d2dnZrZ0PALxCnQLgL9QbAFZALQJgRV41mW655RYlJyerQ4cO+vnPf679+/frlVdeUWJiYmvnAwCvUKcA+Av1BoAVUIuAk0We4VBE+KnbHM6aWlUeqvZjovbHqyaTJHXr1k379+/Xnj17JElnnXWW9uzZo5iYmFYLBwDNQZ0C4C/UGwBWQC0C6osI79DoTRFWLRwle903zn68ajKtXr1a2dnZqqz8vx/H8VtafvXVV60WDgC8RZ0C4C/UGwBWQC0CYEVeNZkWL16sW265RWlpaerQweuLnwDAb6hTAPyFegPACqhFAKzIq2r0/fffa8qUKRQvAJZFnQLgL9QbAFZALQJgRcHebHTRRRdpx44drZ0FAE4bdQqAv1BvAFgBtQiAFXnV9u7fv79++9vf6pprrtHZZ59db92UKVNaJRgANAd1CoC/UG8AWAG1CIAVedVk2rZtm3r16qWioiIVFRV5lgcFBbVaMABoDuoUAH+h3gCwAmoRACvyqsn00ksvtXYOAPAJdQqAv1BvAFgBtQiAFXk1J5N0rFM+Y8YMjR8/Xvv379czzzwjY4zPAfbu3auMjAwlJSVpxIgRevvttyVJBQUFSktLU9++fTV27Fjt3LnT52MBaNtaq04BwE9RbwBYAbUI7YnrqFvR0ZGN/kPgeXUl07p16zRr1iylpqbqiy++0NGjR5WXlyeXy6WpU6ee9sGNMZo4caJGjBihxYsX61//+pcmTJigxMREZWZmatq0aUpJSVFubq6ysrKUl5d32scC0La1Vp0CcMzxE7vGRJ7hUOWhaj8lChzqDQAroBahvQkLDVHq9Lcb3WbVwlF+SoNT8arJ9NRTT+npp5/WwIED9be//U3dunVTbm6uJk6c6FMB27p1qw4fPqy7775bwcHBuvTSS5WXl6ddu3apU6dOSk9PlyRlZGRo+fLlKiwsVEJCwmkfr7V5cwLurKltFyfggL+1Vp0CcIy3J3aVfsoTSNQbAFZALQJgRV41mfbs2aMBAwZI+r+J5M4//3xVVVX5dPCvvvpK559/vubMmaPVq1crKipK06ZNU2lpqeLj4z3bhYSEKDY2VkVFRZZuMnECDgROa9UpAPgp6g0AK6AWAbAir5pM5557rt5//31dccUVnmWbNm3Sf/zHf/h08EOHDumjjz7Sfffdpw8++ECffvqp7rrrLk2cOFEOh6Petg6HQ06ns1n7j4rq7FO+1tISY0XtNt7Ubnkl+2Vu73lbq04BwE9RbwBYAbUIgBV51WSaOnWq7rzzTl155ZVyOp2aPXu2Vq1apccff9yng4eFhalr164aP368JCk5OVn9+/eXMeakhlJ1dbU6duzYrP2Xl1eprq7pie/8/eW8rMy3a5mioyN93oc/2S2vZL/MVsrr7efJm7zBwUFeN4tbq04BwE9RbwBYAbUIgBV5dXe55ORkvfbaazrjjDN02WWXye126/nnn6/XNT8dPXv21OHDh+vdAaGurk6RkZEqKSnxLHO73SotLVVcXJxPxwPQdrVWnQKAn6LeALACahEAK2r0SqZx48Z5xvceZ4xRSUmJFi5cKElasWLFaR986NChCg8P1+LFi3XHHXfoo48+0rZt2/TII48oNzdX+fn5Sk1NVW5urmJiYtSrV6/TPhaAtqm16xQAHEe9AWAF1CIAVtbolUxJSUkaNGiQYmJi9OWXX+rCCy/UNddco1/84hcqLCzUeeed59PBHQ6HVqxYoa1btyopKUlz587VggUL1L17dy1dulQrV65UUlKSNm7cqJycnJOKKQC0dp0CgOOoNwCsgFoEwMoavZJpypQpkqRbbrlFubm56tevn2fdVVddpezsbJ8DxMXFadmyZSctT0xMVH5+vs/7B9C2+aNOwR4iz3AoItyrqQaB00K9AVqXN3XcWVOrykPVfkpkTdQiAFbm1dn4V199pV/84hf1ll144YX15k0CgECiTiEivINSp799yvWrFo7yYxq0ZdQboHU0VcelY7XcGrc6CTxqkf3wBzG0B169w+Pj47VixQpNmDDBs+zZZ59V7969Wy0YADQHdQqAv1Bv7IcvdmiLqEX2420jFbAzr37b/ulPf9LkyZO1YsUKdevWTXv27FFdXZ2ef/751s4HAF5pqTq1Y8cOpaWl6Z133tG5556rgoICZWdnq7i4WAkJCZo3bx53ugTaOc6L7IcvdmiLqEUArMirJlO/fv20bt06vf/++9q7d6+6deumK6+8UpGRka2dDwC80hJ1qra2VjNnzpTL5ZIk1dTUKDMzU9OmTVNKSopyc3OVlZWlvLy81noaAGyA8yIAVkAtAmBFXl83fOaZZ2r06NGtGAUAfONrnVq6dKn69++vgoICSdKmTZvUqVMnpaenS5IyMjK0fPlyFRYWKiEhoSUiA7ApzosAWAG1CIDVBAc6AABYwfbt27V69WpNnTrVs6y4uFjx8fGexyEhIYqNjVVRUVEAEgJoT3bs2KGLL75Yu3btkiQVFBQoLS1Nffv21dixY7Vz584AJwQAADgZTSYA7Z7L5dLMmTM1e/ZsRUREeJYfOXJEDoej3rYOh0NOp9PfEQG0I6caujtu3Dht3rxZycnJysrKCnBKAACAk3GbDQDt3tNPP61Bgwapf//+9ZY31FCqrq5Wx44dm7X/qKjOPmc8leho68+7YIeMaDlW/3lbPZ/E0F0AAGBfNJkAtHtr165VWVmZ8vPzPcvS0tI0e/ZslZSUeJa53W6VlpY2++5y5eVVqqszLRXXIzo6UmVllS2+35bkz4x2aB60B1Z+T57u+zE4OKhVm8UnOj50Ny8vTy+++KKkxofu0mQCAABWQpMJQLu3Zs2aeo8TEhL01ltvqVu3bpo/f77y8/OVmpqq3NxcxcTEqFevXgFKCqAta+2hu8cbZXZtyNo1N/5PS/0MG9uPXd8nds0NAD9FkwkATiEiIkJLly5Vdna25syZo969eysnJ0dBQUGBjgagDWrtobvl5VWKiups6avNTsXXqyL5Am8NTf0Mvf05nWo/drjCtyHe5vbnVZUAcLpoMgHATxQWFnr+OzExsd4wOgBoLa09dBcAAKC1cXc5AAAAC1izZo3++c9/asuWLdqyZYsk6a233tJVV12liooK5efny+VyacmSJQzdBQAAlkSTCQAAwMKOD91duXKlkpKStHHjRobuAgAAS2K4HAAAgAUxdBcAANgNVzIBAAAAAADAZzSZAAAAAAAn2bFjhy6++GLt2rVLklRQUKC0tDT17dtXY8eO1c6dOwOcEIDV0GQC4LXIMxyKjo5s9B8AAADsr7a2VjNnzpTL5ZIk1dTUKDMzU+PGjdPmzZuVnJysrKysAKcEYDXMyQTAaxHhHZQ6/e1Gt1m1cJSf0gAAAKC1LF26VP3791dBQYEkadOmTerUqZPS09MlSRkZGVq+fLkKCwuVkJAQyKgALIQrmQAAAAAAHtu3b9fq1as1depUz7Li4mLFx8d7HoeEhCg2NlZFRUUBSAjAqriSCQAAAAAgSXK5XJo5c6Zmz56tiIgIz/IjR47I4XDU29bhcMjpdDZr/1FRnVskZ0vxdroH11G3wkJDfN4GgefNz9yO04BYJTNNJgAAAACAJOnpp5/WoEGD1L9//3rLG2ooVVdXq2PHjs3af3l5lerqjM85W0J0dKTKyiq93tabaSMa259VmgDtXVM/8+a8L6zCn5mDg4MabRbTZAIAAAAASJLWrl2rsrIy5efne5alpaVp9uzZKikp8Sxzu90qLS1VXFxcAFJak+uom0YS2j2aTH7WVOFx1tSq8lC1HxMBAAAAwDFr1qyp9zghIUFvvfWWunXrpvnz5ys/P1+pqanKzc1VTEyMevXqFaCk1hMWGtLo1U7cIAftAU0mP/Om8NjrwjwAAAAAbV1ERISWLl2q7OxszZkzR71791ZOTo6CgoICHQ2AhdBkAgAAAAA0qLCw0PPfiYmJ9YbRAcBPBQc6AAAAAAAAAOyPJhMAAAAAAAB8xnA5AIDlRZ7hUEQ4v7IAAAAAK7PMGfuOHTuUlpamd955R+eee64KCgqUnZ2t4uJiJSQkaN68edweEwDaqYjwDo3eNEHiji0AAABAoFliuFxtba1mzpwpl8slSaqpqVFmZqbGjRunzZs3Kzk5WVlZWQFOCQBoDZFnOBQdHdnoPwAAAADWZ4krmZYuXar+/furoKBAkrRp0yZ16tRJ6enpkqSMjAwtX75chYWFSkhICGRUAEAL4yolAAAAoG0I+JVM27dv1+rVqzV16lTPsuLiYsXHx3seh4SEKDY2VkVFRQFICAAAAAAAgKYE9Eoml8ulmTNnavbs2YqIiPAsP3LkiBwOR71tHQ6HnE5ns/YfFdW5RXL6mzdDQ+w2fMRueSX7ZSYvAAAAACCQAtpkevrppzVo0CD179+/3vKGGkrV1dXq2LFjs/ZfXl6lujrT5HZW+7JbVlbZ6Pro6Mgmt7ESu+WV7JfZX3lb8rPiTd7g4CDbNosBAP7B3ScBALCOgP5GXrt2rcrKypSfn+9ZlpaWptmzZ6ukpMSzzO12q7S0lLv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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "h = dml_plr_regression.predictions.get('ml_m').shape[0]\n", - "fig, ax = plt.subplots(1, 4, figsize=(20,4.8))\n", - "\n", - "#regression histogram\n", - "ax[0].hist(np.reshape(dml_plr_regression.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[0].set_title('regression')\n", - "ax[0].set_xlabel(\"prop_score\")\n", - "ax[0].set_ylabel(\"density\")\n", - "\n", - "#lasso histogram\n", - "ax[1].hist(np.reshape(dml_plr_lasso.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[1].set_title('lasso')\n", - "ax[1].set_xlabel(\"prop_score\")\n", - "ax[1].set_ylabel(\"density\")\n", - "\n", - "#random forest histogram\n", - "ax[2].hist(np.reshape(dml_plr_forest.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[2].set_title('random forest')\n", - "ax[2].set_xlabel(\"prop_score\")\n", - "ax[2].set_ylabel(\"density\")\n", - "\n", - "#boosting histogram\n", - "ax[3].hist(np.reshape(dml_plr_boost.predictions.get('ml_m')[:,0], h), bins=25)\n", - "ax[3].set_title('xgboost')\n", - "ax[3].set_xlabel(\"prop_score\")\n", - "ax[3].set_ylabel(\"density\")\n", - " \n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "3aa8d603-0df5-48c6-ad62-ac5ffe3e8ada", - "metadata": {}, - "source": [ - "______\n", - "\n", - "**Notes and Acknowledgement**\n", - "\n", - "We would like to thank the organizers of the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge) for setting up this data challenge and making the numerous synthetic data examples publicly available. Although the data examples in the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge) do not explicitly adress A/B testing, we put the data example here in this context to give a tractable example on the use of causal machine learning in practice. The parameters for the random forests and extreme gradient boosting learners have been tuned externally. The corresponding tuning notebook will be uploaded in the examples gallery in the future." - ] - }, - { - "cell_type": "markdown", - "id": "egyptian-platform", - "metadata": {}, - "source": [ - "## References\n", - "\n", - "Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W. and Robins, J. (2018), Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21: C1-C68. doi:10.1111/ectj.12097." - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.12" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} +{ + "cells": [ + { + "cell_type": "markdown", + "id": "consecutive-cabinet", + "metadata": {}, + "source": [ + "# Python: A/B Testing with DoubleML" + ] + }, + { + "cell_type": "markdown", + "id": "opponent-indonesian", + "metadata": {}, + "source": [ + "\"An\n", + "\n", + "Image Source Freepik http://www.freepik.com, Designed by macrovector\n" + ] + }, + { + "cell_type": "markdown", + "id": "c7c96f88", + "metadata": {}, + "source": [ + "In this notebook, we demontrate exemplarily how the [DoubleML](https://docs.doubleml.org/stable/index.html) package can be used to estimate the causal effect of seeing a new ad design on customers' purchases in a webshop.\n", + "\n", + "## A/B Testing\n", + "\n", + "A/B testing is a frequently used framework to perform causal inference in practice. For example, a manager of a webshop might want to optimally adapt the webshop design according to users' preferences. For instance, she might want to estimate the effect of a new ad design, which is displayed on the starting page, on customers' purchases (in $100\\$$). A/B tests refer to an experimental design in which a certain treatment, for example a new ad design (called \"Version $A$\"), is randomly assigned to groups of individuals, like website visitors or app users. If a user is not \"treated\", i.e., he is not exposed to Version $A$, he sees an alternative design \"Version $B$\" like the old design of the ad. The assignment of the treatment might either be unconditionally random, i.e., randomly assigned to all visitors of the online shop or directed towards specific groups of them. In the latter case, the treatment assignment would be provided conditional on their characteristics, like their shopping history. An example would be a discount that is only granted to loyal customers who already made some purchases in the past.\n", + "\n", + "In general, the goal of the A/B test is to assess whether the treatment has an effect on the outcome variable of interest. In our example, the manager wants to evaluate whether the new ad design changed the monetary value of products purchased (in $100\\$$) on average. Alternative settings of A/B tests refer to improvement of a user experience on a website or estimation of price elasticities. Websites and apps are ideal for running A/B tests because they make it very easy to precisely direct the treatment to visitors and users (or to specific subgroups of them) as well as to collect the data required for evaluation of the intervention.\n", + "\n", + "## Scenario\n", + "\n", + "Let's consider the following stylized scenario. The manager of a webshop performs an A/B test to estimate the effect a new ad design $A$ has on customers' purchases, $Y$, on average. This effect is called the **A**verage **T**reatment **E**ffect (**ATE**). The treatment is assigned randomly conditional on the visitors' characteristics, which we call $V$. Such characteristics could be collected from a customer's shoppers account, for example. These might include the number of previous purchases, time since the last purchase, length of stay on a page as well as whether a customer has a rewards card, among other characteristics.
\n", + "\n", + "In the following, we use a **D**irected **A**cyclical **G**raph (DAG) to illustrate our assumptions on the causal structure of the scenario. As not only the outcome, but also the treatment is dependent on the individual characteristics, there are arrows going from $V$ to both $A$ and $Y$. In our example, we also assume that the treatment $A$ is a direct cause of the customers' purchases $Y$.\n", + "\n", + "\n", + "![Scenario illustration with a DAG](figures/DAG.svg)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "220997c6", + "metadata": {}, + "source": [ + "Let's assume the conditional randomization has been conducted properly, such that a tidy data set has been collected. Now, a data scientist wants to evaluate whether the new ad design causally affected the sales, by using the [DoubleML](https://docs.doubleml.org/stable/index.html) package.\n", + "\n", + "### Why control for individual characteristics?\n", + "\n", + "Before we start the case study, let us briefly address the question why we need to include individual characteristics in our analysis at all. There are mainly two reasons why we want to control for observable characteristics. First, so-called confounders, i.e., variables that have a causal effect on both the treatment variable and the outcome variable, possibly create a bias in our estimate. In order to uncover the true causal effect of the treatment, it is necessary that our causal framework takes all confounding variables into account. Otherwise, the average causal effect of the treatment on the outcome is not identified. A second reason to include individual characteristics is efficiency. The more variation can be explained within our causal framework, the more precise will be the resulting estimate. In practical terms, greater efficiency leads to tighter confidence intervals and smaller standard errors and p-values. This might help to improve the power of A/B tests even if the treatment variable is unconditionally assigned to individuals.\n", + "\n", + "### Why use machine learning to analyze A/B tests?\n", + "\n", + "ML methods have turned out to be very flexible in terms of modeling complex relationships of explanatory variables and dependent variables and, thus, have exhibited a great predictive performance in many applications. In the double machine learning approach ([Chernozhukov et al. (2018)](https://arxiv.org/abs/1608.00060)), ML methods are used for modelling so-called nuisance functions. In terms of the A/B case study considered here, ML tools can be used to flexibly control for confounding variables. For example, a linear parametric specification as in a standard linear regression model might not be correct and, hence, not sufficient to account for the underlying confounding. Moreover, by using powerful ML techniques, the causal model will likely be able to explain a greater share of the total variation and, hence, lead to more precise estimation." + ] + }, + { + "cell_type": "markdown", + "id": "0ec5b0cf", + "metadata": {}, + "source": [ + "## Data \n", + "\n", + "As an illustrative example we use a data set from the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge). In this challenge, a great number of data sets have been generated in a way that they mimic distributional relationships that are found in many economic real data applications. Although the data have not been generated explicitly to address an A/B testing case study, they are well-suited for demonstration purposes. We will focus on one of the many different data genereting processes (DGP) that we picked at random, in this particualar case a data set called `high42`. An advantage of using the synthetic [ACIC 2019 data](https://sites.google.com/view/acic2019datachallenge/data-challenge) is that we know the true average treatment effect which is 0.8 in our data set.\n", + "\n", + "First we load the data." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "e39d4dd0", + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "\n", + "# Load data set from url (internet connection required)\n", + "url = 'https://raw.githubusercontent.com/DoubleML/doubleml-docs/p-add-ACIC-dataset/doc/examples/data/high42.CSV'\n", + "df = pd.read_csv(url)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "10edc74d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(1000, 202)\n" + ] + } + ], + "source": [ + "print(df.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "6760c009", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " Y A V1 V2 V3 V4 V5 V6 V7 V8 ... \\\n", + "0 7.358185 1 10 0 0 7 192.793769 23.676950 8 0.185443 ... \n", + "1 8.333672 1 12 0 1 4 199.653596 19.281270 7 0.514842 ... \n", + "2 7.472758 0 14 1 1 2 194.207792 24.589331 5 0.309199 ... \n", + "3 6.502319 1 0 1 0 9 201.838024 25.513918 4 0.160160 ... \n", + "4 7.043758 1 12 0 0 9 201.360443 31.160641 6 0.291976 ... \n", + "\n", + " V191 V192 V193 V194 V195 V196 V197 V198 V199 \\\n", + "0 1.462837 1 1627.274196 0 0 4.683956 0.565667 0 3 \n", + "1 1.330522 1 1661.484439 1 0 6.766661 -0.395402 0 4 \n", + "2 1.384151 1 1658.939293 0 0 5.647794 1.112766 0 0 \n", + "3 1.220303 1 1650.801625 0 0 5.370363 -0.305842 0 4 \n", + "4 1.170094 1 1676.818876 0 0 3.446532 2.440661 0 1 \n", + "\n", + " V200 \n", + "0 0.024338 \n", + "1 0.056518 \n", + "2 0.013442 \n", + "3 0.034632 \n", + "4 0.017514 \n", + "\n", + "[5 rows x 202 columns]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.head()" + ] + }, + { + "cell_type": "markdown", + "id": "11525056-cdec-4916-9cb4-aa4268e99175", + "metadata": {}, + "source": [ + "We see that the data set consists of 1000 observations (= website visitors) and 202 variables. The $Y$ column represents the customers' purchases (in $100\\$$). The treatment variable $A$ is binary with a value 1 indicating that a customer has been exposed to the new ad design (and value 0 otherwise). The remaining 200 columns $V$ represent individual characteristics of the customers." + ] + }, + { + "cell_type": "markdown", + "id": "c6e32feb", + "metadata": {}, + "source": [ + "### Descriptive Statistics\n" + ] + }, + { + "cell_type": "markdown", + "id": "horizontal-hanging", + "metadata": {}, + "source": [ + "Once we loaded the data, we find that the outcome variable, $Y$, is continuous with mean around $7.33$. The treatment variable $A$ is binary with a value of $1$ indicating that a visitor was exposed to the new ad design $A$ as opposed to design $B$ (corresponding to a value of the treatment variable $A$ equal to $1$). The control variables $V$ are a collection of mixed data types, including continuous, discrete and binary variables." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "d14f929c-178b-47fc-8293-29a634194f21", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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YAV1V2V3V4V5V6V7V8...V191V192V193V194V195V196V197V198V199V200
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50%7.3352480.00000010.0000000.0000001.0000007.000000199.87611726.2025826.0000000.282867...1.2937901.000001667.7634800.0000000.0000005.236465-0.0910560.000001.0000000.034009
75%8.2718811.00000012.0000001.0000001.0000008.000000204.39806733.0711898.0000000.374078...1.4768281.000001695.9726311.0000000.0000006.8982400.5946471.000002.0000000.049100
max13.1972601.00000020.0000001.0000001.00000015.000000220.58441095.41002014.0000000.706249...2.4486611.000001825.6970961.0000001.00000038.4279742.8326731.000009.0000000.139716
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" + ], + "text/plain": [ + " Y A V1 V2 V3 \\\n", + "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 \n", + "mean 7.331239 0.443000 9.290000 0.377000 0.616000 \n", + "std 1.379852 0.496989 3.889605 0.484877 0.486601 \n", + "min 3.435052 0.000000 0.000000 0.000000 0.000000 \n", + "25% 6.405583 0.000000 7.000000 0.000000 0.000000 \n", + "50% 7.335248 0.000000 10.000000 0.000000 1.000000 \n", + "75% 8.271881 1.000000 12.000000 1.000000 1.000000 \n", + "max 13.197260 1.000000 20.000000 1.000000 1.000000 \n", + "\n", + " V4 V5 V6 V7 V8 ... \\\n", + "count 1000.000000 1000.000000 1000.000000 1000.000000 1000.000000 ... \n", + "mean 6.477000 200.088758 28.066028 6.031000 0.294206 ... \n", + "std 2.870141 6.105408 9.920941 2.480361 0.119454 ... \n", + "min 0.000000 183.123067 12.020630 0.000000 0.047160 ... \n", + "25% 5.000000 195.941569 21.206230 4.000000 0.204260 ... \n", + "50% 7.000000 199.876117 26.202582 6.000000 0.282867 ... \n", + "75% 8.000000 204.398067 33.071189 8.000000 0.374078 ... \n", + "max 15.000000 220.584410 95.410020 14.000000 0.706249 ... \n", + "\n", + " V191 V192 V193 V194 V195 \\\n", + "count 1000.000000 1000.00000 1000.000000 1000.000000 1000.000000 \n", + "mean 1.318209 0.94200 1667.454561 0.254000 0.174000 \n", + "std 0.270178 0.23386 44.191913 0.435515 0.379299 \n", + "min 0.668093 0.00000 1524.291675 0.000000 0.000000 \n", + "25% 1.119369 1.00000 1637.699514 0.000000 0.000000 \n", + "50% 1.293790 1.00000 1667.763480 0.000000 0.000000 \n", + "75% 1.476828 1.00000 1695.972631 1.000000 0.000000 \n", + "max 2.448661 1.00000 1825.697096 1.000000 1.000000 \n", + "\n", + " V196 V197 V198 V199 V200 \n", + "count 1000.000000 1000.000000 1000.00000 1000.000000 1000.000000 \n", + "mean 5.804205 -0.076921 0.29400 1.629000 0.037936 \n", + "std 2.655835 1.002754 0.45582 1.388988 0.021688 \n", + "min 1.097708 -3.644652 0.00000 0.000000 0.001478 \n", + "25% 4.065465 -0.751355 0.00000 1.000000 0.021711 \n", + "50% 5.236465 -0.091056 0.00000 1.000000 0.034009 \n", + "75% 6.898240 0.594647 1.00000 2.000000 0.049100 \n", + "max 38.427974 2.832673 1.00000 9.000000 0.139716 \n", + "\n", + "[8 rows x 202 columns]" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.describe()" + ] + }, + { + "cell_type": "markdown", + "id": "d7e45649", + "metadata": {}, + "source": [ + "From the explanatory variables $V1$ to $V200$, 107 variables are continuous, while 95 are integers. From the integer-variables 59 are binary variables. " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "bde50bfe", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "float64 107\n", + "int64 95\n", + "dtype: int64\n", + "Number of binary variables: 59\n" + ] + } + ], + "source": [ + "print(df.dtypes.value_counts())\n", + "print(\"Number of binary variables:\", len(df[df.columns[df.isin([0,1]).all()]].columns))" + ] + }, + { + "cell_type": "markdown", + "id": "0ce90b4b", + "metadata": {}, + "source": [ + "Let's continue with some visual inspection." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "b4d2dfb4", + "metadata": {}, + "outputs": [], + "source": [ + "# Define the settings for the graphs first\n", + "import seaborn as sns\n", + "sns.set()\n", + "colors = sns.color_palette()\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "plt.rcParams['figure.figsize'] = 5., 3.75\n", + "sns.set(font_scale=1.5)\n", + "sns.set_style('whitegrid', {'axes.spines.top': False,\n", + " 'axes.spines.bottom': False,\n", + " 'axes.spines.left': False,\n", + " 'axes.spines.right': False})" + ] + }, + { + "cell_type": "markdown", + "id": "11045894", + "metadata": {}, + "source": [ + "The first figure shows that 443 out of the 1000 customers have been exposed to the new ad design." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "2b5037d3", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "df['A'].value_counts().plot(kind='bar', color=colors)\n", + "\n", + "plt.title('Treatment')\n", + "plt.xlabel('A')\n", + "_ = plt.ylabel('count')" + ] + }, + { + "cell_type": "markdown", + "id": "8c2dc825", + "metadata": {}, + "source": [ + "### Unconditional Estimate of ATE" + ] + }, + { + "cell_type": "markdown", + "id": "8da84d00", + "metadata": {}, + "source": [ + "As a first naive estimate, we could calculate the unconditional average treatment effect. In other words, we simply take the difference between $Y$ observed for the customers who have been exposed to the treatment $(A=1)$ and those who haven't been exposed $(A=0)$. As a visualization, we plot the density of the outcome variable separately for those who have been exposed to the new ad and those who have not to get a first impression on the descriptive relationship of $A$ and $Y$." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "57392f09", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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" + ], + "text/plain": [ + " Y\n", + "A \n", + "0 NaN\n", + "1 1.117603" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df[['A', 'Y']].groupby('A').mean().diff()" + ] + }, + { + "cell_type": "markdown", + "id": "e6f3fa75-a5d4-480c-b627-4b99c6f6afe3", + "metadata": {}, + "source": [ + "The uncoditional effect is around $1.118$. Because we use a simulated data set in this example, we know that the true effect is $0.8$. Therefore the unconditional ATE overestimates the true effect, because it does not account for the confounding variables. In order to get an estimate for the ATE that explicitly takes the confounding variables $V$ into account, we apply the [DoubleML](https://docs.doubleml.org/stable/index.html) package in the next section." + ] + }, + { + "cell_type": "markdown", + "id": "9e21e9bb", + "metadata": {}, + "source": [ + "## Estimate ATE with the `DoubleML` package" + ] + }, + { + "cell_type": "markdown", + "id": "19830a0a", + "metadata": {}, + "source": [ + "Let’s use the package [DoubleML](https://docs.doubleml.org/stable/index.html) to estimate the average treatment effect of the new ad design on the value of customers' purchases. First, the required packages are imported." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "afaf4106", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import doubleml as dml\n", + "\n", + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.linear_model import LogisticRegression\n", + "from sklearn.linear_model import LassoCV, LogisticRegressionCV\n", + "from sklearn.ensemble import RandomForestClassifier, RandomForestRegressor\n", + "from sklearn.preprocessing import StandardScaler\n", + "from sklearn.pipeline import make_pipeline\n", + "from sklearn.metrics import mean_squared_error\n", + "from sklearn.metrics import log_loss\n", + "from xgboost import XGBClassifier, XGBRegressor\n", + "\n", + "import matplotlib.pyplot as plt\n", + "import scipy.stats as stats" + ] + }, + { + "cell_type": "markdown", + "id": "49242003", + "metadata": {}, + "source": [ + "### The Data Backend: `DoubleMLData`" + ] + }, + { + "cell_type": "markdown", + "id": "3653b53a", + "metadata": {}, + "source": [ + "To start our analysis, we initialize the data backend from the previously loaded data set, i.e., we create a new instance of a [DoubleMLData](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLData.html#doubleml.DoubleMLData) object. During initialization, we specify the roles of the variables in the data set, i.e., in our example the outcome variable $Y$ via the parameter `y_col`, the treatment variable $A$ via `d_cols` and the confounding variables $V$ via `x_cols`." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "abdd10b7", + "metadata": {}, + "outputs": [], + "source": [ + "# Specify explanatory variables for data-backend\n", + "features_base = list(df.columns.values)[2:]\n", + "\n", + "# Initialize DoubleMLData (data-backend of DoubleML)\n", + "data_dml = dml.DoubleMLData(df,\n", + " y_col='Y',\n", + " d_cols='A',\n", + " x_cols=features_base)" + ] + }, + { + "cell_type": "markdown", + "id": "5800ca50-c293-4266-8dd7-00fadcea8d51", + "metadata": {}, + "source": [ + "We can print the data-backend to see the variables, which we have assigned as outcome, treatment and controls." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "37b9bd8a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "================== DoubleMLData Object ==================\n", + "\n", + "------------------ Data summary ------------------\n", + "Outcome variable: Y\n", + "Treatment variable(s): ['A']\n", + "Covariates: ['V1', 'V2', 'V3', 'V4', 'V5', 'V6', 'V7', 'V8', 'V9', 'V10', 'V11', 'V12', 'V13', 'V14', 'V15', 'V16', 'V17', 'V18', 'V19', 'V20', 'V21', 'V22', 'V23', 'V24', 'V25', 'V26', 'V27', 'V28', 'V29', 'V30', 'V31', 'V32', 'V33', 'V34', 'V35', 'V36', 'V37', 'V38', 'V39', 'V40', 'V41', 'V42', 'V43', 'V44', 'V45', 'V46', 'V47', 'V48', 'V49', 'V50', 'V51', 'V52', 'V53', 'V54', 'V55', 'V56', 'V57', 'V58', 'V59', 'V60', 'V61', 'V62', 'V63', 'V64', 'V65', 'V66', 'V67', 'V68', 'V69', 'V70', 'V71', 'V72', 'V73', 'V74', 'V75', 'V76', 'V77', 'V78', 'V79', 'V80', 'V81', 'V82', 'V83', 'V84', 'V85', 'V86', 'V87', 'V88', 'V89', 'V90', 'V91', 'V92', 'V93', 'V94', 'V95', 'V96', 'V97', 'V98', 'V99', 'V100', 'V101', 'V102', 'V103', 'V104', 'V105', 'V106', 'V107', 'V108', 'V109', 'V110', 'V111', 'V112', 'V113', 'V114', 'V115', 'V116', 'V117', 'V118', 'V119', 'V120', 'V121', 'V122', 'V123', 'V124', 'V125', 'V126', 'V127', 'V128', 'V129', 'V130', 'V131', 'V132', 'V133', 'V134', 'V135', 'V136', 'V137', 'V138', 'V139', 'V140', 'V141', 'V142', 'V143', 'V144', 'V145', 'V146', 'V147', 'V148', 'V149', 'V150', 'V151', 'V152', 'V153', 'V154', 'V155', 'V156', 'V157', 'V158', 'V159', 'V160', 'V161', 'V162', 'V163', 'V164', 'V165', 'V166', 'V167', 'V168', 'V169', 'V170', 'V171', 'V172', 'V173', 'V174', 'V175', 'V176', 'V177', 'V178', 'V179', 'V180', 'V181', 'V182', 'V183', 'V184', 'V185', 'V186', 'V187', 'V188', 'V189', 'V190', 'V191', 'V192', 'V193', 'V194', 'V195', 'V196', 'V197', 'V198', 'V199', 'V200']\n", + "Instrument variable(s): None\n", + "No. Observations: 1000\n", + "\n", + "------------------ DataFrame info ------------------\n", + "\n", + "RangeIndex: 1000 entries, 0 to 999\n", + "Columns: 202 entries, Y to V200\n", + "dtypes: float64(107), int64(95)\n", + "memory usage: 1.5 MB\n", + "\n" + ] + } + ], + "source": [ + "print(data_dml)" + ] + }, + { + "cell_type": "markdown", + "id": "714346b8-90dd-4f15-b880-d71f4f60b04e", + "metadata": {}, + "source": [ + "## The Inference Problem and Choosing an Appropriate Model\n", + "\n", + "The inference problem is to determine the causal effect of seeing the new ad design $A$ on customers' purchases $Y$ once we control for individual characteristics $V$. In our example, we are interested in the average treatment effect. Basically, there are two causal models available in [DoubleMLData](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLData.html#doubleml.DoubleMLData) that can be used to estimate the ATE.\n", + "\n", + "The so-called interactive regression model (IRM) called by [DoubleMLIRM](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLIRM.html) is a flexible (nonparametric) model to estimate this causal quantity. The model does not impose functional form restrictions on the underlying regression relationships, for example, linearity or additivity as in a standard linear regression model. This means that the model hosts heterogeneous treatment effects, i.e., account for variation in the effect of the new ad design across customers. Moreover, it is possible to also estimate other causal parameters with the IRM, for example, the average treatment effect on the treated (= those customers who have been exposed to the new ad), which might be of interest too.\n", + "\n", + "The second causal model that can be used here is the partially linear regression model (PLR). The PLR incorporates stronger assumptions, for example, that the treatment effect is additive and constant, i.e., in the model it is assumed that the effect does not very across individuals. We will start with the IRM and include the PLR estimates at the end of the notebook." + ] + }, + { + "cell_type": "markdown", + "id": "9e798e44-8fc8-4c93-9cfb-2d3ad7486dc0", + "metadata": {}, + "source": [ + "## 1. Interactive Regression Model (IRM)\n", + "\n", + "We briefly introduce the [Interactive Regression Model](https://docs.doubleml.org/stable/guide/models.html#interactive-regression-model-irm) (IRM) where the main regression relationship of interest is provided by\n", + "\n", + "$$Y = g_0(D, X) + U, \\quad E(U | X, D) = 0,$$\n", + "\n", + "where the treatment variable is binary, $D \\in \\lbrace 0,1 \\rbrace$. We consider estimation of the average treatment effect (ATE):\n", + "\n", + "$$\\theta_0 = \\mathbb{E}[g_0(1, X) - g_0(0,X)],$$\n", + "\n", + "when treatment effects are heterogeneous. In order to be able to use ML methods, the estimation framework generally requires a property called \"double robustness\" or \"Neyman orthogonality\". In the IRM, double robustness can be achieved by including the first-stage estimation\n", + "\n", + "$$D = m_0(X) + V, \\quad E(V | X) = 0,$$\n", + "\n", + "which amounts to estimation of the propensity score, i.e., the probability that a customer is exposed to the treatment provided her observed characteristics. Both predictions are then combined in [the doubly robust score for the average treatment effect](https://docs.doubleml.org/stable/guide/scores.html#interactive-regression-model-irm) which is given by\n", + "\n", + "$$\\psi(W; \\theta, \\eta) := g(1,X) - g(0,X) + \\frac{D (Y - g(1,X))}{m(X)} - \\frac{(1 - D)(Y - g(0,X))}{1 - m(x)} - \\theta.$$" + ] + }, + { + "cell_type": "markdown", + "id": "13a5f6f7-64c5-499b-b68a-16ca98943cd6", + "metadata": {}, + "source": [ + "Because the data set was simulated we are aware of the true ATE, $\\theta_0=0.8$. The interpretation of this is that exposure to the new ad increases sales (in $100\\$$) by around $0.8$ on average. In the following, we try to estimate this causal effect using the [DoubleML](https://docs.doubleml.org/stable/index.html) package and assess whether the estimated effect is significantly different from zero." + ] + }, + { + "cell_type": "markdown", + "id": "69f0731d", + "metadata": {}, + "source": [ + "### Assess Predictive Performance in the IRM" + ] + }, + { + "cell_type": "markdown", + "id": "6d494c68", + "metadata": {}, + "source": [ + "In the following, we will compare the estimate of the ATE based on different learners. Moreover, we will also have a look how well the learners can predict the nuisance components of the causal model. \n", + "\n", + "To evaluate the predictive performance, we'll first define a helper function that uses a DoubleML model object and returns a summary for a predictive measure. We'll use the root mean squared error (RMSE) for the main regression and the log loss measure $L_{log}$ for the propensity score estimation.\n", + "\n", + "Estimation of the IRM delivers two arrays for the prediction function $g_0(D, X)$: `ml_g0` for $g_0(0, X)$ and `ml_g1` for $g_0(1, X)$. If we want to get the correct prediction for each observation based on the treatment realization, we pick the corresponding value of either `ml_g0` (for $D=0$) or `ml_g1` (for $D=1$). As we apply random sample splitting repeatedly in every model, the RMSE and the log loss can be calculated for each repetition. We are interested in mean and standard deviation across all repetitions." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "aa2a8f81", + "metadata": {}, + "outputs": [], + "source": [ + "def pred_acc_irm(DoubleML, prop):\n", + " \"\"\"\n", + " A function to calculate prediction accuracy values for every repetition\n", + " of a Double Machine Learning model using IRM, DoubleMLIRM\n", + " \n", + " ...\n", + " \n", + " Parameters\n", + " ----------\n", + " DoubleML : doubleml.double_ml_irm.DoubleMLIRM\n", + " The IRM Double Machine Learning model\n", + " prop : bool\n", + " Indication if RMSE values have to be computed for main regression or\n", + " log loss values for propensity score\n", + " \"\"\"\n", + " \n", + " # export data and predictions of the DoubleML model\n", + " y = DoubleML._dml_data.y\n", + " d = DoubleML._dml_data.d\n", + " g0 = DoubleML.predictions.get('ml_g0')\n", + " g1 = DoubleML.predictions.get('ml_g1') \n", + " m = DoubleML.predictions.get('ml_m')\n", + " \n", + " # dimensions of prediction array\n", + " h = g0.shape[0]\n", + " w = DoubleML.n_rep\n", + " \n", + " # check whether treatment is binary \n", + " if np.isin(d, [0,1]).all() == False:\n", + " raise ValueError(\"Treatment must be a binary variable.\")\n", + " \n", + " # prepare array to store prediction accuracy measure values\n", + " pred_acc_array = np.zeros((w,))\n", + " \n", + " # check whether to assess main regression or propensity score accuracy: \n", + " if prop == False:\n", + " \n", + " # evaluate main regression accuracy\n", + " # export an array with correctly picked prediction values \n", + " export_pred_array = np.zeros((h, w)) \n", + " for i in range(w):\n", + " for j in range(h):\n", + " if d[j] == 0:\n", + " export_pred_array[j,i] = g0[j,i]\n", + " else:\n", + " export_pred_array[j,i] = g1[j,i]\n", + " \n", + " # fill array that contains rmse of each repetition\n", + " for i in range(w):\n", + " pred_acc_array[i] = mean_squared_error(y, export_pred_array[:,i], squared=False) \n", + " else:\n", + " \n", + " # evaluate propensity score accuracy\n", + " # fill array that contains log loss of each repetition\n", + " for i in range(w):\n", + " pred_acc_array[i] = log_loss(d, m[:,i], eps=0.025)\n", + " \n", + " return pred_acc_array" + ] + }, + { + "cell_type": "markdown", + "id": "suburban-infrastructure", + "metadata": {}, + "source": [ + "### Benchmark: Model based on Linear and Logistic Regression" + ] + }, + { + "cell_type": "markdown", + "id": "93f3af17-bcf9-429b-af9a-b90ea1153937", + "metadata": {}, + "source": [ + "Let us first start with a benchmark model that is based on linear and logistic regression. Hence, we estimate the functions $g_0(D,X)$ using a linear regression model and $m_0(X)$ by using an (unpenalized) logistic regression. In both cases, we include all available characteristics $V$. Later we will assess whether we can find a \"better\" estimator based on ML methods like lasso, random forests and boosting. Because we have 200 variables and 1000 observations, this is approaching a high dimentional setting, therefore the linear and the logistic regression may not estimate the parameters well." + ] + }, + { + "cell_type": "markdown", + "id": "authorized-school", + "metadata": {}, + "source": [ + "We start by initializing the learners for linear regression and logistic regression. Then, we initialize a causal model object, here of the class [DoubleMLIRM](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLIRM.html). The latter is based on the data-backend we have specified above. To reduce the disproportionate impact of extreme propensity score weights in the interactive model we trim the propensity score from below and above at thresholds of 0.025 and 0.975. For estimation, we perform 3-fold cross-fitting with 3 repetitions. Although this is not required for valid estimation of the ATE in the model with linear and logistic regression, we use cross-fitting algorithm to have a comparable evaluation of the nuisance estimation. As defined in the previous helper function `pred_acc_irm`, we compare the predictive performance of the nuisance learners based on hold-out/test observations." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "jewish-listing", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 1.057833 0.624814 1.693035 0.090449 -0.166781 2.282446" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Linear and Logistic Regression learners\n", + "linreg = make_pipeline(StandardScaler(), LinearRegression())\n", + "logreg_class = make_pipeline(StandardScaler(), LogisticRegression(penalty=\"none\"))\n", + "\n", + "# Initialize DoubleMLIRM model\n", + "np.random.seed(1234)\n", + "dml_irm_regression = dml.DoubleMLIRM(data_dml,\n", + " ml_g = linreg,\n", + " ml_m = logreg_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_irm_regression.fit(store_predictions=True)\n", + "\n", + "reg_summary = dml_irm_regression.summary\n", + "reg_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "controlling-collapse", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.25783258]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_irm_regression.coef - 0.8)" + ] + }, + { + "cell_type": "markdown", + "id": "emerging-highlight", + "metadata": {}, + "source": [ + "We see that the causal estimate suffers from a substantial bias and is quite noisy: The ATE is overestimated by around 0.26 and the standard error is around 0.62. The corresponding 95%-confidence interval is relatively wide. It even covers the value of zero. Hence, we cannot reject the null hypothesis that the average treatment effect is different from zero at the 5% significance level.\n", + "\n", + "Next, we'll calculate the RMSE and the log loss for the nuisance functions in order to find out how the benchmark compares to other ML models." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "7ad39856", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_linlog_irm = pred_acc_irm(dml_irm_regression, prop=False)\n", + "rmse_main_linlog_irm_mean = np.mean(rmse_main_linlog_irm)\n", + "rmse_main_linlog_irm_std = np.std(rmse_main_linlog_irm)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_linlog_irm = pred_acc_irm(dml_irm_regression, prop=True)\n", + "logloss_prop_linlog_irm_mean = np.mean(logloss_prop_linlog_irm)\n", + "logloss_prop_linlog_irm_std = np.std(logloss_prop_linlog_irm)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "dd39c325", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.727905012276966\n", + "Standard deviation of the RMSE is 0.026526079197961804\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_linlog_irm_mean)\n", + "print(\"Standard deviation of the RMSE is\", rmse_main_linlog_irm_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "e21456ef", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 1.0228568161263911\n", + "Standard deviation of log loss is 0.027536454508812133\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_linlog_irm_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_linlog_irm_std)" + ] + }, + { + "cell_type": "markdown", + "id": "neutral-converter", + "metadata": {}, + "source": [ + "Next, let us find out if we are able to use ML methods to find estimators that have a lower bias and a smaller standard error than the benchmark." + ] + }, + { + "cell_type": "markdown", + "id": "723b8e6c", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Lasso\n", + "\n", + "We estimate the nuisance components $g_0$ and $m_0$ using lasso as provided by [scikit-learn](https://scikit-learn.org). We load the learner by initializing instances from the classes [LassoCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html) and [LogisticRegressionCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegressionCV.html). Here we specify that the lasso should use the value of $\\lambda$ that minimizes the cross-validated mean squared error, which is based on 5-fold cross validation. We initialize the [DoubleMLIRM](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLIRM.html) object and use the newly defined learners." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "73cbfd4b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.855559 0.070928 12.062417 1.668137e-33 0.716544 0.994575" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Lasso learners\n", + "lasso = make_pipeline(StandardScaler(), LassoCV(cv=5, max_iter=20000)) \n", + "lasso_class = make_pipeline(StandardScaler(),\n", + " LogisticRegressionCV(cv=5, penalty='l1', solver='liblinear', \n", + " Cs = 4, max_iter=1000)) \n", + "\n", + "# Initialize DoubleMLIRM model\n", + "np.random.seed(1234)\n", + "dml_irm_lasso = dml.DoubleMLIRM(data_dml,\n", + " ml_g = lasso,\n", + " ml_m = lasso_class,\n", + " trimming_threshold = 0.025, \n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_irm_lasso.fit(store_predictions=True)\n", + "\n", + "lasso_summary = dml_irm_lasso.summary\n", + "lasso_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "stock-bookmark", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.05555945]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_irm_lasso.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "85c6e74e", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_lasso_irm = pred_acc_irm(dml_irm_lasso, prop=False)\n", + "rmse_main_lasso_irm_mean = np.mean(rmse_main_lasso_irm)\n", + "rmse_main_lasso_irm_std = np.std(rmse_main_lasso_irm)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_lasso_irm = pred_acc_irm(dml_irm_lasso, prop=True)\n", + "logloss_prop_lasso_irm_mean = np.mean(logloss_prop_lasso_irm)\n", + "logloss_prop_lasso_irm_std = np.std(logloss_prop_lasso_irm)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "c659681b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.1143405452234652\n", + "Standard deviation of RMSE is 0.005869688113839954\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_lasso_irm_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_lasso_irm_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "388cdfcf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.6686766530020503\n", + "Standard deviation of log loss is 0.0032543941531603953\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_lasso_irm_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_lasso_irm_std)" + ] + }, + { + "cell_type": "markdown", + "id": "religious-algebra", + "metadata": {}, + "source": [ + "We see that the lasso-based estimate for the ATE is $0.86$ and, hence, much closer to the true value of $0.8$ than in the benchmark $1.06$. Moreover, we can achieve improvements in terms of estimation precision as can be recognized from the smaller standard error. Also the prediction measures for the nuisance components are much smaller for Lasso than in the linear/logistic benchmark. Using the Lasso learners makes it now possible to conclude that the ATE is significantly different from zero at a significance level of 5%." + ] + }, + { + "cell_type": "markdown", + "id": "33d06b0d", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Random Forest" + ] + }, + { + "cell_type": "markdown", + "id": "4d9d008a-5b6a-4acf-93b9-b26599541653", + "metadata": {}, + "source": [ + "Alternatively, we can repeat this procedure with other machine learning methods, for example a random forest learner as provided by the [RandomForestRegressor](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html) and [RandomForestClassifier](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html) class in [scikit-learn](https://scikit-learn.org)." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "2092891a", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.8931760.07742111.536558.631791e-310.7414331.044919
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.893176 0.077421 11.53655 8.631791e-31 0.741433 1.044919" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Random Forest learners\n", + "randomForest = RandomForestRegressor()\n", + "randomForest_class = RandomForestClassifier()\n", + "\n", + "# Initialize DoubleMLIRM model\n", + "np.random.seed(1234)\n", + "dml_irm_forest = dml.DoubleMLIRM(data_dml,\n", + " ml_g = randomForest,\n", + " ml_m = randomForest_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "# Set nuisance-part specific parameters\n", + "dml_irm_forest.set_ml_nuisance_params('ml_g0', 'A', {\n", + " 'max_features': 200, 'n_estimators': 250})\n", + "dml_irm_forest.set_ml_nuisance_params('ml_g1', 'A', {\n", + " 'max_features': 200, 'n_estimators': 250})\n", + "dml_irm_forest.set_ml_nuisance_params('ml_m', 'A', {\n", + " 'max_features': 200, 'n_estimators': 250})\n", + "\n", + "dml_irm_forest.fit(store_predictions=True) \n", + "\n", + "forest_summary = dml_irm_forest.summary\n", + "forest_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "vital-insight", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.09317591]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_irm_forest.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "14c230b0", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_forest_irm = pred_acc_irm(dml_irm_forest, prop=False)\n", + "rmse_main_forest_irm_mean = np.mean(rmse_main_forest_irm)\n", + "rmse_main_forest_irm_std = np.std(rmse_main_forest_irm)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_forest_irm = pred_acc_irm(dml_irm_forest, prop=True)\n", + "logloss_prop_forest_irm_mean = np.mean(logloss_prop_forest_irm)\n", + "logloss_prop_forest_irm_std = np.std(logloss_prop_forest_irm)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "1d633282", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.1688034544446142\n", + "Standard deviation of RMSE is 0.00826647072034282\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_forest_irm_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_forest_irm_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "16a7a785", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.6823242335385794\n", + "Standard deviation of log loss is 0.0026223238604172463\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_forest_irm_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_forest_irm_std)" + ] + }, + { + "cell_type": "markdown", + "id": "d4b6e16b-6cb9-40d8-a4fa-c438f23b49f3", + "metadata": {}, + "source": [ + "The results are relatively similar to the one obtained by lasso with a bias and standard errors that are slightly greater than before. The predictive accuracy of the random forest learners is also slightly worse than that of Lasso." + ] + }, + { + "cell_type": "markdown", + "id": "9ac68b60", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Extreme Gradient Boosting" + ] + }, + { + "cell_type": "markdown", + "id": "cc71c762-8497-43e5-a151-a5239641d510", + "metadata": {}, + "source": [ + "Next, we estimate the ATE using extreme gradient boosting as provided by [xgboost](https://docs.getml.com/latest/api_reference/predictors.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "90b9ef4e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.7909060.1043067.5825883.387302e-140.5864710.995341
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.790906 0.104306 7.582588 3.387302e-14 0.586471 0.995341" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Extreme Gradient Boosting learners\n", + "boost = XGBRegressor(n_jobs=1, objective = \"reg:squarederror\")\n", + "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", + " objective = \"binary:logistic\", eval_metric = \"logloss\")\n", + "\n", + "# Initialize DoubleMLIRM model\n", + "np.random.seed(1234)\n", + "dml_irm_boost = dml.DoubleMLIRM(data_dml,\n", + " ml_g = boost,\n", + " ml_m = boost_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "# Set nuisance-part specific parameters\n", + "dml_irm_boost.set_ml_nuisance_params('ml_g0', 'A', {\n", + " 'n_estimators': 30, 'eta': 0.2})\n", + "dml_irm_boost.set_ml_nuisance_params('ml_g1', 'A', {\n", + " 'n_estimators': 30, 'eta': 0.2})\n", + "dml_irm_boost.set_ml_nuisance_params('ml_m', 'A', {\n", + " 'n_estimators': 15, 'eta': 0.2})\n", + "\n", + "dml_irm_boost.fit(store_predictions=True)\n", + "\n", + "boost_summary = dml_irm_boost.summary\n", + "boost_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "traditional-ribbon", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [-0.0090944]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_irm_boost.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "efd04e78", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_boost_irm = pred_acc_irm(dml_irm_boost, prop=False)\n", + "rmse_main_boost_irm_mean = np.mean(rmse_main_boost_irm)\n", + "rmse_main_boost_irm_std = np.std(rmse_main_boost_irm)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_boost_irm = pred_acc_irm(dml_irm_boost, prop=True)\n", + "logloss_prop_boost_irm_mean = np.mean(logloss_prop_boost_irm)\n", + "logloss_prop_boost_irm_std = np.std(logloss_prop_boost_irm)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "114aa5cf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.2287566646120192\n", + "Standard deviation of RMSE is 0.010275338353331828\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_boost_irm_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_boost_irm_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "c1ebde27", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.7204831015081563\n", + "Standard deviation of log loss is 0.01297502257820836\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_boost_irm_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_boost_irm_std)" + ] + }, + { + "cell_type": "markdown", + "id": "9ee7f068-1ac4-4d7d-99a7-5c68c91e8b51", + "metadata": {}, + "source": [ + "The estimated coefficient is very close to the true ATE of $0.8$ but has a small negative bias. The interpretation of the results obtained with lasso, random forests and boosting are very similar. In all cases we are able to reject the null hypothesis that the ad has no effect on the sales." + ] + }, + { + "cell_type": "markdown", + "id": "fba54a14-c685-4948-819d-94a99d88e94a", + "metadata": {}, + "source": [ + "#### IRM - Summary of coefficient estimates\n", + "\n", + "We save the estimates, bias and confidence intervals for later peresentation and comparision." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "5e16a294", + "metadata": { + "scrolled": false, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefBiasstd err2.5 %97.5 %
regression1.0580.2580.625-0.1672.282
lasso0.8560.0560.0710.7170.995
forest0.8930.0930.0770.7411.045
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\n", + "
" + ], + "text/plain": [ + " coef Bias std err 2.5 % 97.5 %\n", + "regression 1.058 0.258 0.625 -0.167 2.282\n", + "lasso 0.856 0.056 0.071 0.717 0.995\n", + "forest 0.893 0.093 0.077 0.741 1.045\n", + "xgboost 0.791 -0.009 0.104 0.586 0.995" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "irm_summary = pd.concat((reg_summary, lasso_summary, forest_summary, boost_summary))\n", + "irm_summary.index = ['regression','lasso', 'forest', 'xgboost']\n", + "irm_summary = irm_summary[['coef', 'std err', '2.5 %', '97.5 %']]\n", + "irm_summary.insert(1, \"Bias\", [irm_summary.loc['regression','coef'] - 0.8, \n", + " irm_summary.loc['lasso','coef'] - 0.8, \n", + " irm_summary.loc['forest','coef'] - 0.8, \n", + " irm_summary.loc['xgboost','coef'] - 0.8])\n", + "irm_summary.round(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "4b478603", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "errors = np.full((2, irm_summary.shape[0]), np.nan)\n", + "errors[0, :] = irm_summary['coef'] - irm_summary['2.5 %']\n", + "errors[1, :] = irm_summary['97.5 %'] - irm_summary['coef']\n", + "plt.errorbar(irm_summary.index, irm_summary.coef, fmt='o', yerr=errors)\n", + "plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", + "\n", + "plt.title('Interactive Regression Model (IRM)')\n", + "plt.xlabel('ML method')\n", + "_ = plt.ylabel('Coefficients and 95%-CI')" + ] + }, + { + "cell_type": "markdown", + "id": "8c891e02", + "metadata": {}, + "source": [ + "#### IRM - Summary of prediction assessment metric's mean values" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "6790aad8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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main RMSEmain RMSE (sd)prop log lossprop log loss (sd)
regression1.7280.0271.0230.028
lasso1.1140.0060.6690.003
forest1.1690.0080.6820.003
xgboost1.2290.0100.7200.013
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" + ], + "text/plain": [ + " main RMSE main RMSE (sd) prop log loss prop log loss (sd)\n", + "regression 1.728 0.027 1.023 0.028\n", + "lasso 1.114 0.006 0.669 0.003\n", + "forest 1.169 0.008 0.682 0.003\n", + "xgboost 1.229 0.010 0.720 0.013" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "irm_rmse_index = ['regression','lasso', 'forest', 'xgboost']\n", + "irm_rmse = pd.DataFrame([[rmse_main_linlog_irm_mean, rmse_main_linlog_irm_std, \n", + " logloss_prop_linlog_irm_mean, logloss_prop_linlog_irm_std],\n", + " [rmse_main_lasso_irm_mean, rmse_main_lasso_irm_std,\n", + " logloss_prop_lasso_irm_mean, logloss_prop_lasso_irm_std],\n", + " [rmse_main_forest_irm_mean, rmse_main_forest_irm_std,\n", + " logloss_prop_forest_irm_mean, logloss_prop_forest_irm_std],\n", + " [rmse_main_boost_irm_mean, rmse_main_boost_irm_std,\n", + " logloss_prop_boost_irm_mean, logloss_prop_boost_irm_std]],\n", + " index=irm_rmse_index,\n", + " columns=['main RMSE', 'main RMSE (sd)',\n", + " 'prop log loss', 'prop log loss (sd)'])\n", + "irm_rmse.round(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "a5be2641", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# graphical illustration of RMSE for main regression\n", + "errors_irm_rmse = np.full((2, irm_rmse.shape[0]), np.nan)\n", + "errors_irm_rmse[0, :] = irm_rmse['main RMSE'] - irm_rmse['main RMSE (sd)']\n", + "errors_irm_rmse[1, :] = irm_rmse['main RMSE'] + irm_rmse['main RMSE (sd)']\n", + "plt.errorbar(x=irm_rmse.index, y=irm_rmse['main RMSE'], fmt='x',\n", + " yerr=errors_irm_rmse, c='darkslategray')" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "9255bc0a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# graphical illustration of log loss for main regression\n", + "errors_irm_logloss = np.full((2, irm_rmse.shape[0]), np.nan)\n", + "errors_irm_logloss[0, :] = irm_rmse['prop log loss'] - irm_rmse['prop log loss (sd)']\n", + "errors_irm_logloss[1, :] = irm_rmse['prop log loss'] + irm_rmse['prop log loss (sd)']\n", + "plt.errorbar(x=irm_rmse.index, y=irm_rmse['prop log loss'], fmt='x',\n", + " yerr=errors_irm_logloss, c='darkslategray')" + ] + }, + { + "cell_type": "markdown", + "id": "27c6157d", + "metadata": {}, + "source": [ + "### Inspection of the benchmark model\n", + "\n", + "It is natural to investigate why the the benchmark model performs so much worse than the ML models. First of all, we can conclude that the predictive performance of the linear and logistic regression for the nuisance functions is considerably worse and more variable than for lasso, random forest and xgboost. Moreover, we can also inspect the propensity score estimates of the logistic regression which appear to be very close to zero and one for many observations.\n", + "\n", + "We first define a helper function that generates a histogram of the propensity scores for each of the cross-fitting repetitions." + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "78afa7eb", + "metadata": {}, + "outputs": [], + "source": [ + "def rep_propscore_plot(DoubleML):\n", + " \"\"\"\n", + " A function to create histograms as sublots for every repetition's propensity score density \n", + " of a Double Machine Learning model\n", + " \n", + " ...\n", + " \n", + " Parameters\n", + " ----------\n", + " DoubleML : doubleml\n", + " The Double Machine Learning model\n", + " \"\"\"\n", + " \n", + " \n", + " #export nuisance part from the DoubleML model\n", + " m = DoubleML.predictions.get('ml_m')\n", + " \n", + " # dimensions of nuisance array\n", + " h = m.shape[0]\n", + " rep = DoubleML.n_rep\n", + " \n", + " # create histograms as subplots covering the propensity score densities of all repetitions\n", + " fig, ax = plt.subplots(1, rep, figsize=[20,4.8])\n", + " for i in range(rep):\n", + " ax[i].hist(np.reshape(m[:,i], h), range=[0,1], bins=25)\n", + " ax[i].set_title('repetition ' + str(i+1))\n", + " ax[i].set_xlabel(\"prop_score\")\n", + " ax[i].set_ylabel(\"density\")\n", + " \n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "53d9d81d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_irm_regression)" + ] + }, + { + "cell_type": "markdown", + "id": "4f8d0f9f", + "metadata": {}, + "source": [ + "Let's compare this to the corresponding plot for the lasso-based model." + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "e67ebd28", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_irm_lasso)" + ] + }, + { + "cell_type": "markdown", + "id": "b282c8d9", + "metadata": {}, + "source": [ + "We observe that the propensity score estimates of the lasso-based model are more centered and only close to zero and one for very few observations." + ] + }, + { + "cell_type": "markdown", + "id": "b29e412d-d86f-46b4-840f-cbbe082faf0b", + "metadata": {}, + "source": [ + "### Conclusion - IRM\n", + "\n", + "We can conclude that the interactive regression model (IRM) estimates are close to the true coefficient value, if the nuisance components are estimated with machine learning methods. The performance of Lasso and the tree-based methods random forests and extreme gradient boosting are comparable. All of the ML-based estimators have exhibited a superior performance to the benchmark based on linear and logistic regression, which seems to be rather unstable in the data example considered.\n" + ] + }, + { + "cell_type": "markdown", + "id": "f50297c5", + "metadata": {}, + "source": [ + "## 2. Partially Linear Regression Model (PLR)\n", + "\n", + "The [DoubleML](https://docs.doubleml.org/stable/index.html) package also includes the [Partial Linear Regression (PLR)](https://docs.doubleml.org/stable/guide/models.html#partially-linear-regression-model-plr) model, which assumes the population regression has a linear and additive structure. Although in reality, we never know if this structure really holds for the underlying data generating process, we can apply this model and see how the estimates compare to those from the IRM." + ] + }, + { + "cell_type": "markdown", + "id": "fa24e6e1-b878-401f-b38a-c29cc0620c2c", + "metadata": {}, + "source": [ + "We estimate the function $g_0$ and $m_0$ in the following PLR model:\n", + "\n", + "\\begin{eqnarray}\n", + "& Y = D\\theta_0 + g_0(X) + \\zeta, &\\quad E[\\zeta \\mid D,X]= 0,\\\\\n", + "& D = m_0(X) + V, &\\quad E[V \\mid X] = 0.\n", + "\\end{eqnarray}\n", + "\n", + "To estimate the causal parameter $\\theta_0$, we use double machine learning with 3-fold cross-fitting again. The steps of our analysis are very similar to the IRM cases with the difference being that we use a model class [DoubleMLPLR](https://docs.doubleml.org/stable/api/generated/doubleml.DoubleMLPLR.html) for estimation." + ] + }, + { + "cell_type": "markdown", + "id": "8e7ad0b5", + "metadata": {}, + "source": [ + "### Assess predictive performance in the PLR" + ] + }, + { + "cell_type": "markdown", + "id": "73c26a84", + "metadata": {}, + "source": [ + "As in the IRM, we want to calculate mean and standard deviation of the RMSE / log loss values across all repetitions to evaluate the prediction performance. Once again, a helper function is used as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "54a843e3", + "metadata": {}, + "outputs": [], + "source": [ + "def pred_acc_plr(DoubleML, prop):\n", + " \"\"\"\n", + " A function to calculate prediction accuracy values for every repetition\n", + " of a Double Machine Learning model using PLR, DoubleMLPLR\n", + " \n", + " ...\n", + " \n", + " Parameters\n", + " ----------\n", + " DoubleML : doubleml.double_ml_plr.DoubleMLPLR\n", + " The PLR Double Machine Learning model\n", + " prop : bool\n", + " Indication if RMSE values have to be computed for main regression or log loss values for propensity score\n", + " \"\"\"\n", + " \n", + " \n", + " # export data, fitted coefficient and predictions of the DoubleML model\n", + " y = DoubleML._dml_data.y\n", + " d = DoubleML._dml_data.d\n", + " theta = DoubleML.coef\n", + " g0 = DoubleML.predictions.get('ml_g')\n", + " m = DoubleML.predictions.get('ml_m')\n", + " \n", + " # dimensions of prediction array\n", + " h = g0.shape[0]\n", + " w = DoubleML.n_rep\n", + " \n", + " # check whether treatment is binary \n", + " if np.isin(d, [0,1]).all() == False:\n", + " raise ValueError(\"Treatment must be a binary variable.\")\n", + " \n", + " # prepare array to store prediction accuracy values\n", + " pred_acc_array = np.zeros((w,))\n", + " \n", + " # check whether to assess main regression or propensity score accuracy: \n", + " if prop == False:\n", + " \n", + " # evaluate main regression accuracy\n", + " # export array with prediction values\n", + " export_pred_array = np.zeros((h, w)) \n", + " for i in range(w):\n", + " for j in range(h):\n", + " export_pred_array[j,i] = theta*d[j] + g0[j,i]\n", + " \n", + " # fill array that contains rmse of each repetition\n", + " for i in range(w):\n", + " pred_acc_array[i] = mean_squared_error(y, export_pred_array[:,i], squared=False)\n", + " \n", + " else:\n", + " \n", + " # evaluate propensity score accuracy\n", + " # fill array that contains log loss of each repetition\n", + " for i in range(w):\n", + " pred_acc_array[i] = log_loss(d, m[:,i], eps=0.025)\n", + " \n", + " return pred_acc_array" + ] + }, + { + "cell_type": "markdown", + "id": "331a36d6", + "metadata": {}, + "source": [ + "### Benchmark: Model based on Linear and Logistic Regression" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "1432e567-d221-490d-9361-39b9072cb6d4", + "metadata": { + "scrolled": true, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
coefstd errtP>|t|2.5 %97.5 %
A0.7849990.06712711.6941911.364815e-310.6534320.916565
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.784999 0.067127 11.694191 1.364815e-31 0.653432 0.916565" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Linear and Logistic Regression learners\n", + "linreg = make_pipeline(StandardScaler(), LinearRegression())\n", + "logreg_class = make_pipeline(StandardScaler(), LogisticRegression(penalty=\"none\"))\n", + "\n", + "# Initialize DoubleMLPLR model\n", + "np.random.seed(1234)\n", + "dml_plr_regression = dml.DoubleMLPLR(data_dml,\n", + " ml_g = linreg,\n", + " ml_m = logreg_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_regression.fit(store_predictions=True)\n", + "\n", + "reg_summary = dml_plr_regression.summary\n", + "reg_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "ff708453", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [-0.01500149]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_plr_regression.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "88392566", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_linlog_plr = pred_acc_plr(dml_plr_regression, prop=False)\n", + "rmse_main_linlog_plr_mean = np.mean(rmse_main_linlog_plr)\n", + "rmse_main_linlog_plr_std = np.std(rmse_main_linlog_plr)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_linlog_plr = pred_acc_plr(dml_plr_regression, prop=True)\n", + "logloss_prop_linlog_plr_mean = np.mean(logloss_prop_linlog_plr)\n", + "logloss_prop_linlog_plr_std = np.std(logloss_prop_linlog_plr)" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "08227dfc", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.3418428467276253\n", + "Standard deviation of RMSE is 0.009847706467828324\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_linlog_plr_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_linlog_plr_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "c91ed6e8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 1.0228568161263911\n", + "Standard deviation of log loss is 0.027536454508812133\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_linlog_plr_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_linlog_plr_std)" + ] + }, + { + "cell_type": "markdown", + "id": "4dd8948f", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Lasso" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "id": "0bbbc3ce", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.8047950.07027111.4528072.276523e-300.6670670.942522
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.804795 0.070271 11.452807 2.276523e-30 0.667067 0.942522" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize DoubleMLPLR model\n", + "np.random.seed(1234)\n", + "dml_plr_lasso = dml.DoubleMLPLR(data_dml,\n", + " ml_g = lasso,\n", + " ml_m = lasso_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_lasso.fit(store_predictions=True)\n", + "\n", + "lasso_summary=dml_plr_lasso.summary\n", + "lasso_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "id": "30aef0c8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.00479477]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_plr_lasso.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "id": "96383f94", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_lasso_plr = pred_acc_plr(dml_plr_lasso, prop=False)\n", + "rmse_main_lasso_plr_mean = np.mean(rmse_main_lasso_plr)\n", + "rmse_main_lasso_plr_std = np.std(rmse_main_lasso_plr)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_lasso_plr = pred_acc_plr(dml_plr_lasso, prop=True)\n", + "logloss_prop_lasso_plr_mean = np.mean(logloss_prop_lasso_plr)\n", + "logloss_prop_lasso_plr_std = np.std(logloss_prop_lasso_plr)" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "id": "10a66c25", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.1394799633725696\n", + "Standard deviation of RMSE is 0.003190385536736178\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_lasso_plr_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_lasso_plr_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "id": "afe3b2b9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.6686763881131824\n", + "Standard deviation of log loss 0.003254281706002184\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_lasso_plr_mean)\n", + "print(\"Standard deviation of log loss\", logloss_prop_lasso_plr_std)" + ] + }, + { + "cell_type": "markdown", + "id": "a4ed2694", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Random Forests" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "id": "e5f3ac90", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.7993070.07329710.9050281.090595e-270.6556470.942967
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.799307 0.073297 10.905028 1.090595e-27 0.655647 0.942967" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Random Forest learners\n", + "randomForest = RandomForestRegressor()\n", + "randomForest_class = RandomForestClassifier()\n", + "\n", + "# Initialize DoubleMLPLR model\n", + "np.random.seed(1234)\n", + "dml_plr_forest = dml.DoubleMLPLR(data_dml,\n", + " ml_g = randomForest,\n", + " ml_m = randomForest_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_forest.fit(store_predictions=True)\n", + "\n", + "forest_summary = dml_plr_forest.summary\n", + "forest_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "id": "4c40246d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [-0.00069288]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_plr_forest.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "id": "a977c34b", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_forest_plr = pred_acc_plr(dml_plr_forest, prop=False)\n", + "rmse_main_forest_plr_mean = np.mean(rmse_main_forest_plr)\n", + "rmse_main_forest_plr_std = np.std(rmse_main_forest_plr)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_forest_plr = pred_acc_plr(dml_plr_forest, prop=True)\n", + "logloss_prop_forest_plr_mean = np.mean(logloss_prop_forest_plr)\n", + "logloss_prop_forest_plr_std = np.std(logloss_prop_forest_plr)" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "id": "1f54fed6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.1886867050333019\n", + "Standard deviation of RMSE is 0.006048072563384578\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_forest_plr_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_forest_plr_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "id": "8101acf6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.6836880652313276\n", + "Standard deviation of log loss is 0.005321479254441978\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_forest_plr_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_forest_plr_std)" + ] + }, + { + "cell_type": "markdown", + "id": "6aa9af04", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Extreme Gradient Boosting" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "id": "6fab5d3a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefstd errtP>|t|2.5 %97.5 %
A0.823840.07167611.4939881.414286e-300.6833580.964321
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" + ], + "text/plain": [ + " coef std err t P>|t| 2.5 % 97.5 %\n", + "A 0.82384 0.071676 11.493988 1.414286e-30 0.683358 0.964321" + ] + }, + "execution_count": 59, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Initialize Extreme Gradient Boosting learners\n", + "boost = XGBRegressor(n_jobs = 1, objective = \"reg:squarederror\", \n", + " eta = 0.1, n_estimators = 57, max_depth = 2)\n", + "boost_class = XGBClassifier(use_label_encoder=False, n_jobs=1,\n", + " objective = \"binary:logistic\",\n", + " eval_metric = \"logloss\",\n", + " eta = 0.1, n_estimators = 10,\n", + " max_depth = 3)\n", + "\n", + "# Initialize DoubleMLPLR model\n", + "np.random.seed(1234)\n", + "dml_plr_boost = dml.DoubleMLPLR(data_dml,\n", + " ml_g = boost,\n", + " ml_m = boost_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_boost.fit(store_predictions=True)\n", + "\n", + "boost_summary = dml_plr_boost.summary\n", + "boost_summary" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "id": "6e3252f8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bias: [0.02383965]\n" + ] + } + ], + "source": [ + "print(\"Bias:\", dml_plr_boost.coef - 0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "id": "e90a61cc", + "metadata": {}, + "outputs": [], + "source": [ + "# calculate mean and standard deviation of repetition RMSE's to evaluate main regression accuracy\n", + "rmse_main_boost_plr = pred_acc_plr(dml_plr_boost, prop=False)\n", + "rmse_main_boost_plr_mean = np.mean(rmse_main_boost_plr)\n", + "rmse_main_boost_plr_std = np.std(rmse_main_boost_plr)\n", + "\n", + "# calculate mean and standard deviation of repetition log losses to evaluate propensity score accuracy\n", + "logloss_prop_boost_plr = pred_acc_plr(dml_plr_boost, prop=True)\n", + "logloss_prop_boost_plr_mean = np.mean(logloss_prop_boost_plr)\n", + "logloss_prop_boost_plr_std = np.std(logloss_prop_boost_plr)" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "id": "72121d00", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the main regression RMSE across 3 repetitions is 1.1560362080432272\n", + "Standard deviation of RMSE is 0.0027129250049691073\n" + ] + } + ], + "source": [ + "print(\"Mean of the main regression RMSE across 3 repetitions is\", rmse_main_boost_plr_mean)\n", + "print(\"Standard deviation of RMSE is\", rmse_main_boost_plr_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "id": "8513cd4e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of the propensity score's log loss across 3 repetitions is 0.677578683851663\n", + "Standard deviation of log loss is 0.005774390874769318\n" + ] + } + ], + "source": [ + "print(\"Mean of the propensity score's log loss across 3 repetitions is\", logloss_prop_boost_plr_mean)\n", + "print(\"Standard deviation of log loss is\", logloss_prop_boost_plr_std)" + ] + }, + { + "cell_type": "markdown", + "id": "a979a78b", + "metadata": {}, + "source": [ + "#### PLR - Summary of coefficient estimates" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "id": "dba8d33c", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefBiasstd err2.5 %97.5 %
regression0.785-0.0150.0670.6530.917
lasso0.8050.0050.0700.6670.943
forest0.799-0.0010.0730.6560.943
xgboost0.8240.0240.0720.6830.964
\n", + "
" + ], + "text/plain": [ + " coef Bias std err 2.5 % 97.5 %\n", + "regression 0.785 -0.015 0.067 0.653 0.917\n", + "lasso 0.805 0.005 0.070 0.667 0.943\n", + "forest 0.799 -0.001 0.073 0.656 0.943\n", + "xgboost 0.824 0.024 0.072 0.683 0.964" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plr_summary = pd.concat((reg_summary, lasso_summary, forest_summary, boost_summary))\n", + "plr_summary.index = ['regression','lasso', 'forest', 'xgboost']\n", + "plr_summary = plr_summary[['coef', 'std err', '2.5 %', '97.5 %']]\n", + "plr_summary.insert(1, \"Bias\", [plr_summary.loc['regression','coef'] - 0.8, \n", + " plr_summary.loc['lasso','coef'] - 0.8, \n", + " plr_summary.loc['forest','coef'] - 0.8, \n", + " plr_summary.loc['xgboost','coef'] - 0.8])\n", + "plr_summary.round(3) " + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "id": "86fe5d87", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Vtl1kZWURFBSEO3fuICoqCrGxsThw4AAOHjyIdevWwc7ODpKSktiyZQsSExMRGRmJ2NhYnDx5EsePH8ecOXMwceLESlqHV8UJytdndaK0tyCKiopQV1dHdHQ0Ro0ahcjISAwYMIDrDFrU+Cq2LSws5Fnv6z8wFf9fsWKFwO++nJyc0DGIi4tX+gfs6+OtOn2du/r164fOnTtj5cqV+PTpE7Zt28a3LSvirOozbFBJXBi3bt1CWFgYpkyZgpkzZ3KWl5SU4NOnT9UyZrqwsBBr166FsbEx9uzZw/VXevPmzSLvz87ODv7+/oiJicHly5ehpqYm8IJqbVFUVMSDBw/Qq1cvroOouLgYkZGRnK6AdevWQUpKCmfPnuU669u+fXu1xyQnJ4cNGzbAxcUFc+bMQVhYGOdspWPHjsjLy+P5EmZnZ+P69evo3LkzgPKfqPxGNbx69UqoGIRtlxcvXiAnJwd6enrQ09PD3Llz8ezZM7i5uSEwMBB2dnZ48+YN3rx5A0NDQ6ipqWHatGl49+4dxowZg927d/NN4h07dgQAJCcn83QLJCcnA/hfN011srKyQkBAAJKTk3H//n1O9+X3xlfxPXz58iXXerm5ufj48SPP/hQUFHg+25s3b6KsrEyke0NatmxZL25QGj16NK5fv47o6Gjs27cPY8eO5VmnIs6K3gdBfoohhl+reOO//PIL1/Jjx46hoKBA4C3EX6v4cgp66NGXL19QUFAAZWVlrgT++PFjxMfHA4BQ9VRQUVFB9+7dERUVhevXr9f4WbgwLCws8OnTJxw+fJhr+ZEjRzBr1ixcv34dQHl7KygocCXwnJwczlQI1T0kS1tbG+PHj8fbt2+xfv16rnifPHnCc3u0v78/Zs6cyRnuOGDAADx69Ah37tzhrFNUVMQZlVMVYdtl5cqVmDJlCvLy8jjrdO3aFc2bN+ccX9u3b8fYsWO5uuHatWuHtm3bCjz7MjExgbS0NAIDA7mGNL579w5nzpyBjo5OtY+gAMqTeFFREVatWgU5OTn07Nnzh+IzMTFBkyZNsG/fPq7vyrfDbSv2t2vXLq7rXOnp6ZgyZQr+/vtvkX4RdOjQgasrsC4tX74ccnJy2LRpE1JTU3nK3717BykpqSo/z5/uTFxfXx+ysrJYs2YN3rx5g+bNm+PmzZsIDw+HtLQ015dKkIqEtGvXLvTt2xeWlpZc5XJyctDV1cXJkychKyuLLl26ICkpCcHBwZwvX15enkg/82xtbbFu3TqIiYmJdBfiqVOnuBJSBQ0NDYwaNUro/XyrYk6aFStW4OHDh9DR0cHTp09x9OhRaGpqwt7eHgDQt29f7Ny5EzNnzkSfPn2QkZGB48ePc+aDEKa9RTVlyhRERETg6NGjsLOzg6GhISZNmoQLFy5g2rRpcHFxQbdu3ZCQkIDTp0+jb9++6Nu3LwBg3LhxOH36NDw9PeHh4QEFBQWcPn2ac3ZeVUIQtl08PT0xYcIEuLm5Yfjw4ZCWlkZUVBRSUlLg7e0NoPyOvdOnT8PNzQ3Ozs6Qk5PDjRs3cPPmTcyYMYNv/fLy8pg9ezbWrFmDUaNGwc7ODnl5eZyhhH/99Vd1NTMXDQ0NdOzYEVevXoW9vb3Abkhh45OVlcW8efOwbNkyjBkzBjY2NkhKSkJoaCjXTTgKCgqc/Tk7O2Po0KEoKSnBoUOHUFhYiPnz54v0Pnr16oUtW7bg8+fPnK6vH7F48WK+y11dXSu9gAqUn2HPnTsXixYtwpIlS7Bnzx6u8rt378LQ0JDvRc+v/XRJvFWrVggICMDff/+Nbdu2QUpKCl26dIGPjw/u3buH/fv3IzMzs9KfKEOGDMGFCxdw8uRJxMfH8yRxoLzbZM2aNZwhQB07dsTEiROhoqKC6dOn48aNG7C2thY6bltbW/z999/Q1dXl/IQURnx8POfs/2uWlpY/lMSlpKSwd+9e+Pn54fz58wgNDUWbNm0watQoTJ06lfNFmz59OkpLSxEeHo5Lly6hTZs2MDExwbhx4zBkyBDcuHEDAwYM+O44+JGRkcGyZcvg6emJxYsXIyQkBC1atMDRo0exZcsWnDt3DkePHkWHDh0wZcoUTJw4kfPHVU5ODkFBQVi7di0OHDgAMTExDBw4ELa2tvD29q7yp7mw7dKnTx/4+/tjx44d2LZtGwoLC9GtWzeuUTVqamoIDAyEn58f9uzZg9zcXCgrK2PRokV8x0tXGDt2LNq0aYM9e/bAx8cHjRs3hpGREaZNm1Ytk6sJYmlpif379wu8wUfU+FxdXdGsWTMEBATA29sbysrK2LZtG09iHjt2LNq2bYvAwEBs3LgRMjIy0NTUxPr167muiwijb9++2Lx5MxISEtC/f3+RtuXn6NGjAuupKokD5ScFISEhiIuLQ0hICIYPHw6gfEhiUlIS5s2bV3UQjNQL6enpTF1dnR08eLCuQ/mpffjwgZWUlPAs3717N1NVVWUpKSl1EBWpTcOHD2dz5syp6zAqdfToUaatrc0yMjKqXPen6xNvqI4dOwYpKan/xIROdcnb2xu9e/fGly9fOMtKS0tx7tw5KCgoiPQriDRMnp6eiIqKqtfz7oSEhGDYsGFVXtQEfsILmw3Nhg0bMHnyZPj5+cHR0VGkfnQiuqFDh+Lz58/w8PBAUFAQDh48CE9PT9y9exezZ8+uliF5pH4bMmQIlJWVRZqzuzbdunULjx8/xm+//SbU+mKMCRiCQWrFihUrcOLECZiZmcHb25szsROpObGxsdi5cycSExNRXFwMNTU1jBs3rsq+XvLzuH//PiZMmIDIyEjO/Dv1xejRo2Fpacl32CE/lMQJIaQBo9+OQnr48GFdh/DToTatXtSe1a8htCklcSF9fSGMVA9q0+pF7Vn9GkKbUhInhJAGjJI4IYQ0YJTECSGkAaMkTgghDRglcUIIacAoiRNCSAMmcBZDLy8vkXcmJiaG1atX/1BAhBBChCcwiVdM6i8KSuKEEFK7BCbx6Ojo2oyDEELqFa9tV5GTkwMRpyyvdQKTOE3JSQgh9Z9QFza/fgbg127fvo0nT55Ua0CEEEKEV2kS//z5M6ZPnw4rKyu+E6j7+flhxIgR+O2335CVlVVjQRJCCOFPYBLPzc2Fm5sboqKiYGxsjPz8fJ51XFxc0K9fP1y6dAljxoxBQUFBjQZLCCGEm8AkvnPnTjx//hw+Pj7YtWsX2rRpw7OOlZUVtm/fjhUrViApKQm7d++u0WAJIYRwE5jEz58/jyFDhsDGxqbKnTg6OsLc3BwRERHVGhwhhJDKCUzir1+/hoEIY2tMTEyQmppaLUERQggRjsAkLicnx7cfvDJNmzb94YAIIYQIT2AS79atG65duyb0juLi4qCkpFQtQRFCCBGOwCTu4OCAuLg4nDlzpsqdhIeHIzY2FkOHDq3W4AghhFRO4B2bQ4YMwZkzZ7BgwQLcvHkTTk5O0NTUhISEBACgtLQUDx8+xPHjx3Hy5Eloa2vD0dGx1gInhBBSSRIHgA0bNmD58uU4fvw4Tpw4gUaNGqFFixYoKytDdnY2SktLwRjD4MGDsWTJEkhLS9dW3ISQrzSUeT5I9as0iTdt2hTe3t4YM2YMwsLC8OjRI2RmZkJcXBzq6urQ19eHlZUV1NXVayte8pOgpENI9ag0iVfo3r07unfvXtOxEEIIEdF3P9knNzcXXl5eeP78eXXGQwghRATfncS/fPmCU6dO4f3799UZDyGEEBHQMzYJIaQBoyROCCENGCVxQghpwIQancKPnJwc9u/fT8MLCSGkDn13EpeUlISRkVF1xkIIIURE35XEi4qKsG3bNoSHh+P9+/do27YthgwZgsmTJ0NKSqq6YySEECLAdyXxdevWISYmBk5OTmjRogVSU1Nx4MABfPz4EUuWLKnuGAkhhAggMInn5uZCVlaWb9n58+exadMmrodGtGzZEv7+/pTECSGkFgkcnWJhYYHt27cjLy+Pp0xBQQFXr15FWVkZAKCgoAD//PMPWrZsWXOREkII4SEwia9fvx7R0dGwsLBAQEAA11N+/vjjD+zduxcGBgbo168fjI2Nce3aNXh5edVK0IQQQsoJ7E7p168f+vXrh4sXL8LX1xd79uzB+PHj4e7uDlNTU1y8eBGXLl3Chw8f0Lp1a5iZmdGZOCGE1LIqL2xaWFjAwsICUVFR8PX1RWBgIH799Ve4urrC3t6+NmKsczRtKiGkvhL6jk0rKyuEhIRg8eLFOHXqFCwtLbF3714UFhbWZHyEEEIqUemZeGpqKiIiIvDu3TvIy8ujd+/eGDRoEAYNGoTw8HBs27YNu3btwoQJEzBq1CgaI04IIbVM4Jl4VFQUbGxsEBQUhEePHiE8PByjR4+Gt7c3AGDw4ME4c+YM5s+fjyNHjsDS0hIHDhyotcAJIYRUMTpl6NChuHz5Mo4cOYKIiAhs2LABe/fuxdu3bwEAYmJisLOzw9mzZzFnzhwEBQXVWuCEEEIqSeLv37+HsrIyxMTEOMs6deoExhg+f/7MvRNxcQwfPhwREREiBxAWFoYhQ4ZAR0cHNjY2CAkJqXT9J0+eYPz48dDT04OxsTH++OMPpKeni1wvIYT8DAT2idvZ2cHX1xeJiYlQVFREbm4uzp8/D21tbaiqqvLdRlxctJltIyIiMHfuXHh4eMDMzAxRUVGYP38+ZGRkMGjQIJ71U1JS4ObmhlatWmH58uWQk5PD3r17MWrUKISEhKB58+Yi1U8IIQ2dwCS+dOlSaGpqIiIiAo8ePYK8vDxGjhyJcePGcZ2d/wgfHx/Y2Nhg4cKFAAAzMzNkZ2dj8+bNfJP4/v37UVJSgsDAQHTo0AEA0KtXLwwaNAi7du3C7NmzqyUuQghpKAQmcXFxcTg7O8PZ2blGKk5NTUVKSgpP4rW2tkZERARSU1OhpKTEVfbixQuoqqpyEjgASEtLQ1tbG5cvX6YkTgj5z/muWQw/ffqEO3fuID8/H4qKitDR0RF5H8nJyQCALl26cC3v3LkzgPKE/W0Sb9++PZKSklBSUoJGjf4XelpaGlJTU0WOgRBCGjqBSdzBwQEzZ86EmZkZ1/Lt27fD398fRUVFYIxBTEwMnTt3xsqVK2FoaCh0xTk5OQDAM1Ni06ZNAZTPovit4cOH4/jx4/jzzz8xc+ZMSEtLY//+/ZzELqyHDx/iy5cvIseakJAg9DakctSm1Yvas/p9T5sa1MFt3QKT+IMHD/Dp0yeuZQcOHMCmTZugr68PJycnKCgoIDk5Gfv378f48eNx4MABoc/KGWMAwNO/XrGc30VSQ0NDrF69GmvWrEFISAjExMQwYMAAjBo1CsHBwULVCwCamppCrwsAx29W3HZP991XF2rT6kXtWf0aSpuK1J2yY8cO9OrVC3v37uUs69evHxwcHODg4IDNmzdj9+7dQu2rWbNmAHjPuCumvq0o/5a9vT2GDRuGlJQUNGvWDK1atYKXlxdatGghylshhJCfgtBjAvPz85GZmYmRI0fylDVr1gyOjo64c+eO0BVX9IWnpKRwLX/16hVX+deeP3+O06dPQ0JCAl26dEGrVq0AAI8ePUL37t2FrpsQQn4WQifxJk2aQE5OjuuC4tfExMQ4D4kQRufOnaGoqIhz585xLb9w4QKUlZW5RqBUSExMxB9//MF1EfPmzZt48uQJrKyshK6bEEJ+FpV2pxw5cgSvXr2CiooKfvnlF9ja2uLo0aOwsbHhWu/du3cICgqCrq6uSJVPnToVXl5ekJOTg7m5OS5evIiIiAhs3LgRAJCVlYWUlBT88ssvkJWVhbm5ORQVFTF79mxMnz4dWVlZWLNmDXR1dWFnZyfiWyeEkIZPYBK3trbG8+fPsX37dpSUlHBdgAwICMDEiRMBAIsXL8bZs2dRVFSEDRs2iFS5vb09ioqKsGfPHgQHB0NJSQne3t4YPHgwACAmJgZeXl7Yv38/jI2N0aRJE+zatQurVq3CrFmz0LhxYwwePBizZs0S+AuBEEJ+ZgIz3+bNmwEAJSUlePHiBZKSkpCUlIRnz55BUVGRs979+/ehqqqKhQsXQltbW+QAXFxc4OLiwrfM3t6e58ETXbp0wa5du0SuhxBCfkZVnr42atQI3bp1Q7du3fiWHzt2DJKSktUeGCGEkKoJ1QeRm5uLxMREZGZmorCwEI0aNYKcnByUlJTQqVOnmo6REEKIAJUm8devX2PdunWIjo5GaWkpV1nF3ZotW7aEm5sbxowZgyZNmtRosIQQQrgJTOKvX7+Gs7MziouLMXr0aHTq1AmfPn1CVFQU0tLSMG/ePDDGEB8fD39/f0RGRiIwMBBycnK1GT8hhPynCUzimzZtQtOmTXH48GEoKChwlv/2229YuHAhTp48iUOHDsHR0RFjx47FuHHj4Ovriz///LNWAieEEFLJzT5xcXEYNWoUVwKvMG7cONy+fZtzd6WmpibGjBmDqKiomouUEEIID4FJvKCgANnZ2XzLKmYA/PDhA2eZvLy8wPUJIYTUDIFJ3NDQEPv27eOZD6WwsBA+Pj6QkpLiPKYtPz8fp06dEvjYNkIIITVDYJ/4H3/8ARcXF7i6usLU1BTdunVDXl4eYmNj8fbtW8ydOxeysrKcuypzcnKwc+fO2oydEEL+8wQm8W7duiE4OBjr1q1DXFwcrly5AqD8jsm1a9di+PDhnHWNjY0xbty473rCDyGEkO9X6Tjxrl27Yvv27SguLkZWVhaaNGnCM8+3ubk5zM3NazJGQgghAgh1x6akpCTatm1b07EQQggRkdDziRNCCKl/KIkTQkgDRkmcEEIaMErihBDSgFESJ4SQBkzg6BRLS0uRdyYmJkbzpxBCSC0SmMT5PW3+0aNHyMvLg5qaGrp27YqysjKkpqbi0aNHUFBQQJ8+fWo0WEIIIdwEJvEDBw5wvQ4PD8eff/6J/fv3w8jIiKvs9u3bmDhxIrS0tGomSkIIIXwJ3Se+adMmeHh48CRwANDX18eYMWMQGBhYrcERQgipnNBJPCMjg+/c4hWaNGlCU9ESQkgtEzqJq6mp4fjx48jPz+cpy8rKwsGDB6Grq1utwRFCCKmcUHOnAMCMGTMwceJE2NrawtbWFkpKSigsLMTLly8RGhqK4uJibN68uSZjJYQQ8g2hk7iJiQkCAgLw999/IyAggLNcTEwMhoaGWLBgATQ1NWskSEIIIfwJncSB8kR+8uRJZGVl4fXr1xATE0PHjh0hLy9fU/ERQgiphEhJvIKCgkKlFzkJIYTUDpGS+OHDh3HmzBlkZmaitLSUp5zu2CSEkNoldBL39fWFr68v5OTk0KVLF0hKStZkXIQQQoQgdBI/ceIEjIyMsGvXLkhJSdVkTIQQQoQk9DjxDx8+wM7OjhI4IYTUI0In8W7duuHFixc1GQshhBARCZ3Ef//9dxw7dgyXL1+uyXgIIYSIQOg+8X379qFJkyaYPHkyZGRkIC8vDzExMa51aHQKIYTULqGTeGFhITp37ozOnTvXZDyEEFLnYhJSkfjqI4pLyjBu5QV42GjA3ECprsPiS+gk/u384oQQ8jOKSUiFb/BdFJeUAQAyPhbAN/guANTLRF6tz9h89OhRde6OEEJq3f6Ixygs5r6ZsbC4FPsjHtdRRJUT+ky8uLgYAQEBuHDhAvLz81FWVsYpKy0tRV5eHnJzc/H4cf18o4QQIozMjwUiLa9rIj3ZZ+vWrcjOzkbjxo3x+vVrtG/fHo0aNcK7d+9QXFyMP//8syZjJYSQGtdKvrFIy+ua0En83LlzMDIywsWLF7Fz504AwOLFi3H+/Hns2LEDJSUldCs+IaTB87DRgLSkBNcyaUkJeNho1FFElRM6iaenp2PgwIEQFxdH27Zt0bJlS9y+fRsA0K9fP4wYMQLHjh2rsUAJIaQ2mBsoYZqjLiQblafH1vKNMc1Rt15e1ARESOIyMjJcZ9qdOnXC06dPOa91dHSQmppavdERQkgdMDdQglpneXRuI4U9fw2stwkcECGJa2hoIDY2lvO6a9eunDNxoPxM/dubfwghhNQsoZO4m5sboqOj4erqitzcXAwZMgSPHj2Cl5cXdu7cib1790JbW7smYyWEEPINoYcYDho0CCtWrEBgYCAaN24MExMTTJgwgXORs0OHDvDy8qqxQAkhhPAS6ck+jo6OcHR05LyeM2cORo0ahezsbKioqNA0tYQQUst++I7NDh06QEND47sTeFhYGIYMGQIdHR3Y2NggJCSk0vWzsrLg5eWFPn36wMjICJMmTcLLly+/q25SNyrmpXj1vgjjVl5ATAJdECfke1XrbfeiioiIwNy5c2Fqago/Pz8YGRlh/vz5OHfuHN/1GWOYOnUqYmNjMXfuXKxbtw4ZGRnw8PBAdnZ2LUdPvoegeSkokRPyfb7raffVxcfHBzY2Nli4cCEAwMzMDNnZ2di8eTMGDRrEs/7Lly/x77//wtvbG8OHDwcAqKiowMrKChcvXsSIESNqM3zyHSqbl6I+D+MipL6qszPx1NRUpKSkYODAgVzLra2tkZyczHfMeWFhIQCgadOmnGVycnIAgE+fPtVcsKTaNLR5KRoC6p76b6uzJJ6cnAwA6NKlC9fyivnK+T0KTl1dHcbGxvDz88Pz58+RlZWFlStXokmTJrCysqr5oMkPa2jzUtR31D1Ffqg7pbi4GHFxcRAXF4eJiQkaNRJ+dzk5OQAAWVlZruUVZ9m5ubl8t1u6dCl+/fVXDB48GAAgJSUFPz8/KCkJ/1P8/p+LeZa1MjVB+8GDUFpYiEfLV3GV9X6djaSWXQHYoPjzZzzx/ptn+3aDrNHazBSFGZl4umkLT3nHYXZQMOqJ/LTXeO6/g6dcyXEkWujpIjf5BV7sDuQp7+zuiuYa6vj8+AleBR3iKe8y3hOyXbvg0527SA0+wVOu8tskNFHsiKz4f/D69BmectXfZ0C6dStkXInDu3PnecrV58+FZPPmSI++iPcXY3jKuy/+ExLS0ngbfg6Zcdd4yrVXLQcA2LYuQNDHUhTjf3NTSKKMMy9F6tFgfLp3n2tbyWayUF/wBwDg5f4g5CQ+5SqXbtkSqrNnAgCSd+1B3ouXXOWNO7THL1N/AwA88/NHwZu3XOVNuyij66/jAABPfTaj8MMHrvJmaqpQ9nAHADxZuw7FOdzHZgsdbSg5l4/aerhsJcqKirjKFQwN0HHEMACiH3sA0MbCHG0tLfgee7u/aKEQ0lzLCotLsfvQdbQ8WT78l4698mPv9anTyLqVwFUmLiUFzSV/AeA99nq/zka+WCMANgCEO/YqjqPaJHTWLSoqwsqVK5GWloY9e/agqKgIzs7OePLkCYDyvul9+/ahZcuWQu2PMQYAPHd5ViwXF+f9kfD8+XO4uLigU6dOWLhwIWRkZHDs2DHMmDEDu3btgqGhoVB15+XlcU2lCwD5KSl4k5AAVlyMov//A1OhpLQEAJCQkACWn89TDgAFL5KR0kQGLPsz3/Jnz55DQkIcZZkfUMyn/GlSEiRKS1D2Lp1veWJiIsTz81CWmsa3/PHjxxD/mIXS5Bco4VP+8OFDiKe/Q+mz53zL79+/DzG55ih9kcy3/O7duxBr0gQlL1+hlE/57du3ISYpiZKUFL7lCQnlX56ORWmwKfmMaLEuyBOXQXMUwhwv0QydkJDwHiVv3vBsL1ZSwtm++N07lH1Tniv2v/0Xv3/PU56XKYnsivLMTN7y9+/x8f/Li7I+gH1b/u4dPlSUf/wEVsDd9ZP/5g3eV5RnZ4OVlHCXp6Xh3f+XF/Jpm8qOPQDIf/kKaQKOvU+NpAA+N0p/YlKcEyU69srbviQtjffYatTof+XfHHslpSXAV+XCHHtdeWqveWKsImtWwcfHBwEBARg5ciRWrVqFY8eOYfHixfDw8ICGhgbWrl0La2trLF++XKiKY2JiMGnSJISGhkJNTY2z/OHDh7C3t8eePXtgamrKtc2iRYtw7tw5REVFcfrCGWNwdXVFYWEhTp48Kez7FonXtqvIycmB73ybGtn/fxG1afUYt/ICMvhcT2gt3xh7/hrIZwsirIZyjArdJx4REQEHBwesWlX+c+/8+fNo1qwZ/vjjD4wYMQJubm64dOmS0BVX9IWnpKRwLX/16hVX+dfevHkDFRUVTgIHys/kDQwM8OzZM6HrJuRn0dCmTSXVT+gk/u7dO+jp6QEACgoK8M8//6B3796cfvD27dvj8+fPQlfcuXNnKCoq8owJv3DhApSVldGhQweebbp06YKkpCSeMeF3795Fx44dha6bkJ9FQ5s2lVQ/ofvEW7VqhczMTADAlStXUFRUBHNzc055YmIi2rRpI1LlU6dOhZeXF+Tk5GBubo6LFy8iIiICGzduBFB+d2ZKSgp++eUXyMrKYuzYsQgNDcX48eMxceJEyMjI4PTp04iPj+dsQ8h/jbmBEs7ffPX/P/2pC+W/RugkbmxsjH379kFaWhoHDx5E48aNYWVlhc+fP+PEiRM4duwYXFxcRKrc3t4eRUVF2LNnD4KDg6GkpARvb2/OyJOYmBh4eXlh//79MDY2hqKiIg4fPoz169djwYIFEBcXh6qqKgIDA2FiYiLaOyeEkJ+A0El84cKFSE9Ph7e3N5o0aYKVK1eiefPmSEhIgLe3NwwNDTFt2jSRA3BxcRGY/O3t7WFvb8+1TEVFBdu3bxe5nu9VcSNFcUkZxq28AA8bDfqpSgipN4RO4s2bN0dgYCCysrIgKyvLmfBKQ0MDR48eha6ubo0FWVcE3UgBgBI5IaReEPrCppeXF+7evQsFBQWuGQubNGkCXV1d3LhxAxMmTKiRIOtKZfN8EEJIfSB0Ej916lSlz9C8efMmbt68WS1B1Rc0zwchpL4T2J2SmpoKW1tbFH11C/G8efMwb948gTv72R7P1kq+Md8bKWieD0JIfSEwiSspKWHx4sW4desWGGMICQmBgYEB3zlKxMXFoaCggFGjRtVosLXNw0YDvsF3ubpU6EYKQkh9UumFzZEjR2LkyJEAgNevX2PKlCno3bt3rQRWH1RcvNxy7A6KS8rQWr4xjU4hhNQrQo9OOXDgQE3GUW/RjRSEkPpMpKlonz17hrCwMGRmZqK0tJSnXExMDKtXr6624AghhFRO6CR+7tw5zJ49m2cK169REieEkNoldBL38/NDhw4d4OPjA3V19e9+uj0hhJDqI/Q48ZcvX2Ls2LHQ0dGhBE4IIfWE0Em8Xbt2+PLlS03GQgghRERCJ3E3NzccPHgQWVlZNRkPIYQQEQjdJ15cXAwxMTFYWVnB0NAQCgoKPM/HpAubhBBSu4RO4hs2bOD8PzY2lu86lMQJIaR2CZ3EK55qTwghpP4Quk/8a2VlZcjMzOSaHIsQQkjtEymJv3r1CtOnT4eBgQHMzMyQkJCA69evw9HREbdu3aqpGAkhhAgg0jhxR0dHxMfHw8zMjLNcQkICycnJGDduHO7cuVMTMRJCCBFA6CTu4+MDGRkZhIeHY+nSpWCMAQCMjIwQHh6OVq1awdfXt8YCJYQQwkvoJH7jxg2MGjUKLVu25Bla2LZtW7i6uuLBgwfVHiAhhBDBhE7iRUVFaN68ucBySUlJFBYWVktQhBBChCN0EldXV8fFixf5lpWUlCA0NBRqamrVFhghhJCqCZ3EJ02ahGvXrmHu3Lm4ceMGgPKn/URHR8PDwwOPHj2Cp6dnjQVKCCGEl9A3+/Tv3x+rVq3C6tWrcfbsWQDAokWLwBiDtLQ05s+fD2tr6xoLlBBCCC+Rnuxjb2+PgQMHIi4uDqmpqSgrK0PHjh1hYmICeXn5moqREEKIACIlcQCQlZWlM25CCKknBCZxLy8vuLi4QFdXl/O6KjQBFiGE1C6BSfzUqVMwMTHhJPFTp05VuTNK4oQQUrsEJvFvZy2kWQwJIaT+EWkCrLKyMsTGxnLd1BMdHY1Lly5xbsMnhBBSe4RO4h8/foSLiwsmTZqE5ORkzvIzZ87gt99+w7hx45Cfn18jQRJCCOFP6CS+ceNGJCUlYfny5VBRUeEsX7duHdatW4c7d+5g69atNRIkIYQQ/oRO4pcvX8bYsWPh6OgIKSkpznIpKSkMHToU7u7uuHDhQo0ESQghhD+hk/jnz5/RsmVLgeXt2rVDZmZmtQRFCCFEOEIncRUVFZw/f17gBczo6Gh06dKl2gIjhBBSNaGT+OjRo/HPP/9g8uTJuHz5Ml6+fImUlBRcuXIF06dPx/Xr1+Hh4VGTsRJCCPmG0LfdDxs2DO/fv4evry9iY2O5d9KoEWbOnAl7e/tqD5AQQohgIs2dMmHCBDg7OyMuLg5v3rxBaWkpOnToABMTEygoKNRUjIQQQgQQeQKs5s2bw8bGpiZiIYQQIiKBSdzX1xcDBw6Eqqoq53VVxMTEMHXq1OqLjhBCSKUqTeKdO3emJE4IIfWYwCR+/Phx/PLLL5zX0dHRtRIQIYQQ4QkcYjhhwgScOXOG8/rUqVPIy8tDx44dK/1HCCGk9ghM4vn5+fjw4QPnta+vL54+fVorQRFCCBGOwO4UHR0dbN26FZGRkWjatCkAwN/fH8eOHRO4MzExMezbt6/6oySEEMKXwCTu7e2NtWvXIjExER8/foSYmBiysrJQUFBQm/ERQgiphMAkfvnyZcyePRvKysoAAHV1dSxcuBB2dnbVGkBYWBj8/f2RmpqKjh07YtKkSRg+fDjfdRcsWFDpY+ISExOrNTZCCKnvBCbxdevW4a+//uIk8Q4dOqBRI5HvDapUREQE5s6dCw8PD5iZmSEqKgrz58+HjIwMBg0axLP+lClT4OLiwrXs1atXWLBgAZycnKo1NkIIaQgEZmUpKSlERkZCV1cXjRs3xps3b5CZmYk3b95UusMOHToIXbmPjw9sbGywcOFCAICZmRmys7OxefNmvkm8U6dO6NSpE+d1aWkpVqxYAXV1dfz5559C10sIIT8LgUncwcEBu3fvxuXLlznLVq9eXeXT7B8/fixUxampqUhJScHs2bO5lltbWyMiIgKpqalQUlKqdB9HjhzBo0ePcPToUa4HVRBCyH+FwCQ+b9489OzZE4mJiSgqKoKfnx+srKygpqZWLRVXPKfz2znIO3fuDAB48eJFpUk8Ly8PW7ZswbBhw6Cjo1MtMRFCSENTaSe3ubk5zM3NAZTf7DN8+HBYWlpWS8U5OTkAAFlZWa7lFcMZc3NzK93+xIkT+Pz5MyZNmiRy3Q8fPsSXL1+EXr8i1oSEBJHrIvxRm1Yvas/q9z1tamBgUFPhCCT0lcqLFy9y/p+eno53796ha9eukJaWRqNGjSAuLvTzJQCA84QgMTExvsur2t/BgwdhaWn5XU8T0tTUFGn94zevIicnp04+oJ8VtWn1ovasfg2lTUXKvAkJCbC3t4e5uTlcXFzw4MEDxMfHw9zcHOHh4SJV3KxZMwC8Z9x5eXlc5fw8efIEL1++xLBhw0SqkxBCfjZCJ/F79+7B09MTeXl5GDNmDGe5nJwcGjVqhLlz53JdBK1KxRl0SkoK1/JXr15xlfMTExODJk2aoF+/fkLXRwghPyOhk/jmzZuhqKiI06dPY+LEiZxuD21tbYSGhkJFRQU7duwQuuLOnTtDUVER586d41p+4cIFKCsrVzpU8c6dO9DS0qIRKYSQ/zyhk/jt27dhb28PGRkZnn5sWVlZODk5ISkpSaTKp06dirCwMCxfvhyxsbFYunQpIiIiMHPmTABAVlYW7ty5w9Pl8vTpU65pcgkh5L9KpD7xys58CwsLUVZWJlLl9vb2WLZsGa5evYqpU6ciPj4e3t7eGDx4MIDybhNnZ2c8fPiQa7sPHz6gefPmItVFCCE/I6FHp+jq6iIsLAweHh48Zfn5+QgODoa2trbIAbi4uPDcSl/B3t4e9vb2PMvv3r0rcj2EEPIzEvpMfMaMGXj06BHc3d0REhICMTEx3Lt3D/v378ewYcOQlpaGyZMn12SshBBCviH0mbi+vj527NiBJUuWwNvbGwCwceNGAEDr1q2xceNG9OrVq2aiJIQQwpdI0xKampoiMjISjx49QkpKCsrKytCxY0doaWlV+wyHhBBSl9ZM6dMg7oAV7TZLAGVlZSgpKQFjjHO3JiVwQgipGyJl30uXLmHZsmVIT0/nWt6mTRssWbIEFhYW1RocIYSQygmdxG/duoXp06ejZcuWmDVrFlRUVMAYQ3JyMg4dOoQZM2Zg//796NGjR03GSwgh5CtCJ/GtW7eiY8eOOH78OM+8Jq6urhg5ciT8/f2xc+fOag+SEEIIfyLNneLo6Mh3YipZWVk4ODjQ+G1CCKllIl/YFERMTAzFxcXVtTtCCCFCEDqJ6+rq4vjx48jPz+cpy83N/e47NgkhhHw/ofvEp02bBg8PD9ja2sLd3R3KysoAwLmwmZ6ejmXLltVUnIQQQvgQOokbGhpi69atWL58OdatW8eZyZAxRndsEkJIHRFpnLilpSXMzc3x8OFDpKWlAQA6duwITU1NuuGHiKSh3A1HSH0ncuaVkJCAjo4OdHR08OHDB7Ro0QISEhI1ERshhJAqVHlhMygoCHZ2digpKeEpW716NczMzLB3796aiI0QQkgVBCZxxhj++OMPrFy5Eu/fv8ebN2941lFUVIS4uDi8vb0xe/bsGg2UEEIIL4FJPDg4GKGhoXB1dUVsbCw6derEs86sWbMQHR2NYcOGISIiAiEhITUZKyGEkG9UmsR79uyJxYsXQ1paWuAOpKWlsXr1aqirq+PIkSM1EiQhhBD+BCbxZ8+ewdLSUridiIvD2toaiYmJ1RYYIYSQqgkcnSIhIVHpg5G/JS8vD3HxaruLnxAiAhqy+d8lMIl37twZDx48EHpH9+/fR4cOHaolqPqGviCEkPpK4KnzkCFDcObMGSQlJVW5k6SkJJw5cwZ9+/at1uAIIYRUTmASd3Z2RocOHTB69GiEhoaitLSUZ52ysjKEhYXB09MTTZs2xZgxY2o0WEIIIdwEdqc0bdoU/v7+mDJlCubPn49ly5ZBU1MTrVu3RllZGT58+ICHDx8iPz8f7du3h5+fH9q0aVObsRNCyH9epbfdd+3aFaGhoTh48CDOnj2Lf//9l3PnpqSkJPT09DBw4EA4OzuLdBGUEEJI9ahy7hQpKSl4enrC09MTAJCVlQUJCQnIycnVeHCEEEIqJ/IEWAoKCjURByGEkO9AA7sJIaQBoyROCCENmBhjjNV1EIQQQr4PnYkTQkgDRkmcEEIaMErihBDSgFESJ4SQBoySOCGENGCUxAkhpAGjJE4IIQ0YJXFCCGnAKIkTQkgDRkmcEMKFbuKuXT/a3pTEa9HWrVvRvXv3ug7jh6ipqWHbtm11HcZPIz09HaNHj4a2tjZMTExQWFhYp/GcOHEC3t7edRpDTapv38FLly5h/vz5P7QPkaeiJd/P0dGRnkNKuBw4cAD//vsv1q9fj3bt2kFaWrpO49m+fTsMDAzqNIb/kn379vF99KUoKInXonbt2qFdu3Z1HQapRz59+oQ2bdpg8ODBdR0KaaDqZXeKhYUF1q5di9GjR6NHjx5Ys2YNPn78iL/++gu9e/eGjo4ORo0ahYSEBK7tcnJy4OXlBWNjYxgYGGDRokXw8fGBhYVFpfsGINT+4+Li4OTkBH19ffTs2RNTpkzB8+fPOeUpKSmYPHkyjI2NoaurC2dnZ1y+fJlTzu+nXEhICEaMGAE9PT307dsX3t7e+PLlC6d8wYIFGD9+PIKDgzFw4EBoaWlh2LBhuHLlyo83dDV4/Pgxpk6dil69ekFTUxN9+/bFqlWruLoFfrTdAODOnTvw9PREz5490bNnT8ycORNpaWm19j5rgoWFBYKDg/HmzRuoqalh69atePfuHf744w+YmZlBV1cXbm5uiI+P52yTlpYGNTU17N27F9bW1jA2NkZ4eDgAIDExERMmTIC+vj4MDAwwc+ZMvHv3jqvOffv2YdCgQdDW1oaZmRmWLl2K3NxcTjwpKSk4deoU1NTU6l37RkVFQU1NDf7+/pxljx8/hpaWFud7HBwcDGtra+jo6MDJyQnR0dFQU1PDzZs3ufZ17tw5DBgwADo6OnB3d8e9e/e4yp8/f44pU6agd+/e0NfXx6+//oonT55wrVPVZwUAYWFhGDp0KHR0dNC7d2/MnTsX6enpAIDRo0fj+vXriI+P5xuj0Fg91L9/f9a9e3e2du1aFhsby+Lj49nQoUOZqakpO3bsGLt06RKbNGkS09LSYnfv3uVs5+7uzoyMjNixY8dYdHQ0c3FxYVpaWqx///4C93337l325cuXKvefkpLCdHR02LJly9j169fZuXPnmLW1NbO0tGRlZWWstLSUDRo0iHl4eLCYmBh29epVNnHiRKahocFevXrFGGNsy5YtTENDgxPL5s2bmZqaGlu1ahW7cuUK27NnD9PT02NjxoxhZWVljDHG5s+fzwwMDJiNjQ0LCwtjMTExbMSIEUxPT499/vy5Nj4OLqqqqszPz48xxti7d++Yvr4+Gz9+PIuJiWFxcXFszZo1TFVVlQUEBDDGqqfd4uLimIaGBvv1119ZdHQ0Cw0NZQMGDGCmpqYsIyOj1tugujx8+JBNnjyZmZqastu3b7M3b94wU1NTNnDgQBYaGsqio6PZuHHjWPfu3dm1a9cYY4ylpqYyVVVVpqOjw06cOMHCw8NZRkYGS05OZvr6+szR0ZFFRkays2fPskGDBjELCwvOcXLmzBmmqanJ9u/fz27evMkOHz7M9PT02IIFCzjx9O3bl02YMIHdvn2bFRYW1lnbCDJnzhymra3NXr16xQoLC5mdnR2ztbVlhYWF7Pjx40xVVZUtW7aMxcbGsnXr1jEdHR2mqqrKbty4wRgr/w6qqqoyIyMjdvjwYRYVFcUcHByYnp4ee//+PWOMsSdPnjA9PT3m4ODAzp8/z86fP8/s7e2Znp4eS0pKYowxlp6eXuVndevWLaahocG2bt3Kbt68yUJCQpipqSlzd3dnjDGWlJTERo4cyYYPH85u377NcnJyvqtN6m0St7Cw4CSyo0ePMjU1NXbv3j3OOqWlpWzEiBFs7NixjDHGrl27xlRVVdmlS5c46+Tl5bFevXrxJPGv9y3s/sPCwpiqqip79+4dZ527d+8yHx8flpOTw96/f89UVVVZaGgop/zz589s9erV7OnTp4wx7iT+8eNHpqWlxZYtW8b13s+ePcv1PubPn89UVVVZSkoKZ534+HimqqrKIiMjRWjV6vF1Er98+TJzc3Njubm5XOvY2tqyCRMmMMaqp93s7e2Zra0tKy0t5azz+vVrpqWlxdauXVtj77U2LFy4kHN8rl27lmlra7M3b95wyktLS5mtrS2zt7dnjP0vic+fP59rP7Nnz2ampqZcn8X79++Zjo4O27ZtG2OMsUWLFjFra2uuY//06dNs//79nNdWVlY8+65PPn78yExNTdmvv/7KNm7cyDQ1Ndnjx48ZY4yZm5uz6dOnc62/ZMkSvkn8woULnHWysrKYnp4eW7duHWOMsenTp7PevXuzvLw8zjq5ubmsd+/enP0L81nt2LGD6evrc/0xjImJYVu3buV8BmPGjOEk9e9VL7tTAKBbt24QExMDAFy/fh1t27aFhoYGSkpKUFJSgrKyMvTv3x///PMPioqKcOPGDUhLS6Nfv36cfTRp0gTm5uaV7lvY/evq6kJaWhoODg5YtWoVrly5AnV1dcyaNQuysrJo1aoVfvnlFyxatAjz58/HmTNnUFZWBi8vL3Tr1o0nhrt376KoqAhDhgzhWj5o0CBISkpy/bRq3bo1lJSUOK8r+tULCgq+r3GrSd++fREUFAQpKSk8e/YM0dHR8Pf3R1ZWFoqLiwHgh9stPz8fDx8+xODBgyEu/r/DtUOHDjA0NOT5+dqQ3bp1CwYGBmjfvj1nmbi4OAYPHoyHDx9yuj0AQFVVlWvbGzduoFevXpCWluYcw/Ly8tDR0cG1a9cAAL169cKLFy8wYsQI+Pr64v79+7Czs8Po0aNr5w1WgxYtWmDZsmWIjY3Fjh07MHPmTKirq+PVq1d48+YNrK2tudbnd61BUlISlpaWnNfy8vLo0aMHp0vl1q1bsLCwQJMmTTjrNG3aFBYWFpzjTZjPqmfPnigoKICdnR02bNiAW7duoU+fPpg2bRpX/vlR9fbCZsuWLTn///TpE969ewdNTU2+6378+BEfP36EvLw8T+O0atWq0n0Lu39FRUUEBQUhICAAx48fx/79+9G8eXO4urri999/h5iYGPbs2QN/f39ERkYiJCQEkpKSsLKywrJlyyAnJ8e1z+zsbADlCfpr4uLiUFBQ4PrCNm7cmGudivdYVlbGN97aUlZWBh8fHxw8eBD5+flo3749dHR0IC0tzRn7+qPt9uXLFzDGBH6Ob968qe23XWOys7OhrKzMs7xVq1ZgjCEvL4+zjN8xfObMGZw5c4Zn+4p9Dh48GGVlZTh06BC2bduGrVu3omPHjpg7d26DurBqZmaGVq1aITMzk3OSlpWVBYD3Qe78jht5eXmuE4KK7SqSeHZ2tsDjreJ7Kcxnpa+vj4CAAOzduxeBgYEICAhAq1atMHny5Gr9w1lvk/jXmjVrBhUVFYHjV+Xl5dGmTRtkZWWBMcaVyD98+FAt+wcAHR0d+Pr6oqioCAkJCTh69Ci2b9+O7t27w9raGm3btsXSpUuxZMkSPHnyBOfOncPOnTvRsmVLLFq0iGufFUk9IyMDnTp14iwvKytDVlYWp876rOIAXb58OQYMGIBmzZoBABwcHLjW+5F2mz17NsTExJCZmclTf0ZGRoNoJ2E1b96c7/t8//49gPLjsOL/35KVlUXfvn3h4eHBUyYlJcX5v62tLWxtbZGTk4OrV69i586dmDdvHoyMjPgmrvpo8+bNyM3NhbKyMv78808cPnwYbdu2BcD7fa9I7l/LycnhyROZmZmcY0nQ55CRkYEWLVpUus7XnxVQ/gfHzMwMBQUFuHHjBvbv34+VK1dCX18fWlpa3/HuedXb7pSv9ezZE2/evEGbNm2gra3N+RcdHY0DBw5AUlISPXv2RFFREdeojW9f/8j+Dxw4AAsLCxQVFUFKSgq9e/fGihUrAABv377FvXv3YGJignv37kFMTAwaGhqYNWsWVFVV8fbtW546dXV1ISUlhbNnz3ItP3fuHIqLixvEWN2EhASoqanB3t6ek8DT09Px9OlTzq+EH223pk2bQlNTE+Hh4Vy/PN6+fYt///0XPXr0qP03XkN69uyJhIQErhElZWVlOHfuHLS1tbmS8beMjIzw/PlzaGpqco7f7t27IyAgALGxsQCAOXPmYNq0aQDKT1xsbGwwZcoUlJSUICMjAwB4zlDrm7t37yIwMBDTp0/HmjVrcO/ePQQGBqJ9+/ZQVFREdHQ01/pRUVE8+ygoKMCtW7c4rzMyMpCQkABjY2MA5Z/DpUuXkJ+fz1knPz8fly5d4nwvhfms1q9fDwcHBzDG0LhxY/Tv359zY0/FdhISEj/cJvX7E/t/9vb2aNu2LTw9PXH69GncuHEDa9euhb+/P5SUlCAmJgZjY2MYGxtjwYIFCA4ORkxMDCZNmoTMzMwq+5+E2X+vXr2QkZGBqVOn4vLly7h69Sq8vLwgLS2N/v37Q11dHU2aNMEff/yBs2fP4ubNm9i4cSMeP37M008HlPftjR8/HocOHcLq1asRFxeHvXv3YtGiRTAyMoKZmVlNNWe10dHRwaNHj7Bz507Ex8cjODgYbm5uKCoq4vTXV0e7zZo1C8+ePcPkyZNx6dIlhIWFYezYsZCVlcXYsWPrsAWql6enJ2RlZTFmzBiEhYXh0qVLmDRpEp4/f45Zs2ZVuu3UqVPx7Nkz/Pbbb4iOjsbly5cxefJkXLx4kdNN2KtXL0RGRsLb2xvXr1/H+fPnsXnzZnTp0oVz3aZ58+Z49OgR4uPjuYa61geFhYXw8vKCqqoqxo4dix49esDJyQlbtmxBcnIypk+fjvDwcKxcuRJxcXHYunUrgoKCAHD/cZKUlMT8+fMRHh6OqKgojB8/Hs2aNeP8ipk6dSpyc3M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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "errors = np.full((2, plr_summary.shape[0]), np.nan)\n", + "errors[0, :] = plr_summary['coef'] - plr_summary['2.5 %']\n", + "errors[1, :] = plr_summary['97.5 %'] - plr_summary['coef']\n", + "plt.errorbar(plr_summary.index, plr_summary.coef, fmt='o', yerr=errors)\n", + "plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", + "\n", + "plt.title('Partially Linear Regression Model (PLR)')\n", + "plt.xlabel('ML method')\n", + "_ = plt.ylabel('Coefficients and 95%-CI')" + ] + }, + { + "cell_type": "markdown", + "id": "19fc42af", + "metadata": {}, + "source": [ + "#### PLR - Summary of prediction accuracy metric's mean values" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "id": "b8937548", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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main RMSEmain RMSE (sd)prop log lossprop log loss (sd)
regression1.3420.0101.0230.028
lasso1.1390.0030.6690.003
forest1.1890.0060.6840.005
xgboost1.1560.0030.6780.006
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" + ], + "text/plain": [ + " main RMSE main RMSE (sd) prop log loss prop log loss (sd)\n", + "regression 1.342 0.010 1.023 0.028\n", + "lasso 1.139 0.003 0.669 0.003\n", + "forest 1.189 0.006 0.684 0.005\n", + "xgboost 1.156 0.003 0.678 0.006" + ] + }, + "execution_count": 66, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plr_rmse_index = ['regression','lasso', 'forest', 'xgboost']\n", + "plr_rmse = pd.DataFrame([[rmse_main_linlog_plr_mean, rmse_main_linlog_plr_std, \n", + " logloss_prop_linlog_plr_mean, logloss_prop_linlog_plr_std],\n", + " [rmse_main_lasso_plr_mean, rmse_main_lasso_plr_std,\n", + " logloss_prop_lasso_plr_mean, logloss_prop_lasso_plr_std],\n", + " [rmse_main_forest_plr_mean, rmse_main_forest_plr_std,\n", + " logloss_prop_forest_plr_mean, logloss_prop_forest_plr_std],\n", + " [rmse_main_boost_plr_mean, rmse_main_boost_plr_std,\n", + " logloss_prop_boost_plr_mean, logloss_prop_boost_plr_std]],\n", + " index=plr_rmse_index,\n", + " columns=['main RMSE', 'main RMSE (sd)',\n", + " 'prop log loss', 'prop log loss (sd)'])\n", + "plr_rmse.round(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "id": "79fe38ed", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# graphical illustration of RMSE for main regression\n", + "errors_plr_rmse = np.full((2, plr_rmse.shape[0]), np.nan)\n", + "errors_plr_rmse[0, :] = plr_rmse['main RMSE'] - plr_rmse['main RMSE (sd)']\n", + "errors_plr_rmse[1, :] = plr_rmse['main RMSE'] + plr_rmse['main RMSE (sd)']\n", + "plt.errorbar(x=plr_rmse.index, y=plr_rmse['main RMSE'], fmt='x',\n", + " yerr=errors_plr_rmse, c='darkslategray')" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "id": "bb40406b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# graphical illustration of log loss for main regression\n", + "errors_plr_logloss = np.full((2, plr_rmse.shape[0]), np.nan)\n", + "errors_plr_logloss[0, :] = plr_rmse['prop log loss'] - plr_rmse['prop log loss (sd)']\n", + "errors_plr_logloss[1, :] = plr_rmse['prop log loss'] + plr_rmse['prop log loss (sd)']\n", + "plt.errorbar(x=plr_rmse.index, y=plr_rmse['prop log loss'], fmt='x',\n", + " yerr=errors_plr_logloss, c='darkslategray')" + ] + }, + { + "cell_type": "markdown", + "id": "27d1d2a9-beed-493d-ae92-8d4e92cde8ae", + "metadata": {}, + "source": [ + "### Summary of IRM and PLR Results" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "id": "1b4ddf50-50de-4bab-a110-767b8d50df21", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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coefBiasstd err2.5 %97.5 %
ModelML
IRMregression1.0580.2580.625-0.1672.282
lasso0.8560.0560.0710.7170.995
forest0.8930.0930.0770.7411.045
xgboost0.791-0.0090.1040.5860.995
PLRregression0.785-0.0150.0670.6530.917
lasso0.8050.0050.0700.6670.943
forest0.799-0.0010.0730.6560.943
xgboost0.8240.0240.0720.6830.964
\n", + "
" + ], + "text/plain": [ + " coef Bias std err 2.5 % 97.5 %\n", + "Model ML \n", + "IRM regression 1.058 0.258 0.625 -0.167 2.282\n", + " lasso 0.856 0.056 0.071 0.717 0.995\n", + " forest 0.893 0.093 0.077 0.741 1.045\n", + " xgboost 0.791 -0.009 0.104 0.586 0.995\n", + "PLR regression 0.785 -0.015 0.067 0.653 0.917\n", + " lasso 0.805 0.005 0.070 0.667 0.943\n", + " forest 0.799 -0.001 0.073 0.656 0.943\n", + " xgboost 0.824 0.024 0.072 0.683 0.964" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df_summary = pd.concat((irm_summary,plr_summary)).reset_index().rename(columns={'index': 'ML'})\n", + "df_summary['Model'] = np.concatenate((np.repeat('IRM', 4), np.repeat('PLR', 4)))\n", + "df_summary.set_index(['Model', 'ML']).round(3)" + ] + }, + { + "cell_type": "markdown", + "id": "64aa3065-da5c-49b9-88f2-5c08c1b7e617", + "metadata": {}, + "source": [ + "### Conclusion\n", + "\n", + "As in the IRM model, the ML-based PLR models are associated with a smaller bias as compared to the model that is based on linear and logistic regression. It seems that the estimates obtained from the PLR are slightly closer to the true ATE than those from the IRM analysis. This might suggest, that the parametric assumptions (i.e., an additive and homogeneous causal effect) that are incorporated in the PLR turn out to be **not restrictive** in our example data set. However, if both models are based on appropriate ML learners, the conclusions are very similar. In all cases, the ML-based estimates were very close to the true ATE and we were always able to reject the null hypothesis of a zero effect at all common significance levels. In terms of the A/B testing example, it can be concluded that the new ad increases customers purchases (in $100\\$$) by around 0.8 on average and that this effect is significantly different from zero at the 5% significance level. The results are summarized in the graphic below." + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "id": "c80cadcc", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(8, 9))\n", + "colors = sns.color_palette()\n", + "for ind, model in enumerate(['IRM', 'PLR']):\n", + " sns.set(font_scale=1.15)\n", + " plt.subplot(3, 1, ind+1)\n", + " this_df = df_summary.query('Model == @model')\n", + " errors = np.full((2, this_df.shape[0]), np.nan)\n", + " errors[0, :] = this_df['coef'] - this_df['2.5 %']\n", + " errors[1, :] = this_df['97.5 %'] - this_df['coef']\n", + " plt.errorbar(this_df.ML, this_df.coef, fmt='o', yerr=errors,\n", + " color=colors[ind], ecolor=colors[ind])\n", + " plt.ylim([0.5, 1.2])\n", + " plt.title(model)\n", + " plt.ylabel('Coeff. and 95%-CI')\n", + " plt.axhline(y=0.8, color='r', linestyle='--', label=\"true value\")\n", + " plt.legend(bbox_to_anchor=(1.04,0.5), loc=\"best\", borderaxespad=0)\n", + "\n", + "_ = plt.xlabel('ML method')" + ] + }, + { + "cell_type": "markdown", + "id": "90109d08", + "metadata": {}, + "source": [ + "## Appendix" + ] + }, + { + "cell_type": "markdown", + "id": "e42903ad", + "metadata": {}, + "source": [ + "### Propensity score estimates" + ] + }, + { + "cell_type": "markdown", + "id": "157d7295", + "metadata": {}, + "source": [ + "For both the IRM and the PLR model, we want to compare the propensity score estimates of all learners. Since repeated sample splitting is used for every learner, we first want to check whether the repetitions provide similare propensity score estimates. If that is the case, it should be legitimate to pick any of the repetitions for the comparision across all learners." + ] + }, + { + "cell_type": "markdown", + "id": "bb614dd1", + "metadata": {}, + "source": [ + "#### IRM - Repetitions of the Linear and Logistic regression model" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "id": "a2a753a7", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_irm_regression)" + ] + }, + { + "cell_type": "markdown", + "id": "d0eca3c9", + "metadata": {}, + "source": [ + "#### IRM - Repetitions of the Lasso model" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "id": "a69be1ca", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_irm_lasso)" + ] + }, + { + "cell_type": "markdown", + "id": "6ae81d8d", + "metadata": {}, + "source": [ + "#### IRM - Repetitions of the Random Forest model" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "id": "2775a78e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_irm_forest)" + ] + }, + { + "cell_type": "markdown", + "id": "686ad3c6", + "metadata": {}, + "source": [ + "#### IRM - Repetitions of the Extreme Gradient Boosting model" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "id": "3d0115cc", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "h = dml_irm_regression.predictions.get('ml_m').shape[0]\n", + "fig, ax = plt.subplots(1, 4, figsize=(20,4.8))\n", + "\n", + "#regression histogram\n", + "ax[0].hist(np.reshape(dml_irm_regression.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[0].set_title('regression')\n", + "ax[0].set_xlabel(\"prop_score\")\n", + "ax[0].set_ylabel(\"density\")\n", + "\n", + "#lasso histogram\n", + "ax[1].hist(np.reshape(dml_irm_lasso.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[1].set_title('lasso')\n", + "ax[1].set_xlabel(\"prop_score\")\n", + "ax[1].set_ylabel(\"density\")\n", + "\n", + "#random forest histogram\n", + "ax[2].hist(np.reshape(dml_irm_forest.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[2].set_title('random forest')\n", + "ax[2].set_xlabel(\"prop_score\")\n", + "ax[2].set_ylabel(\"density\")\n", + "\n", + "#boosting histogram\n", + "ax[3].hist(np.reshape(dml_irm_boost.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[3].set_title('xgboost')\n", + "ax[3].set_xlabel(\"prop_score\")\n", + "ax[3].set_ylabel(\"density\")\n", + " \n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "7a9a161d", + "metadata": {}, + "source": [ + "#### PLR - Repetitions of the Linear and Logistic regression model" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "id": "c4da298e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_plr_regression)" + ] + }, + { + "cell_type": "markdown", + "id": "fbbbd43c", + "metadata": {}, + "source": [ + "#### PLR - Repetitions of the Lasso model" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "id": "17b9d772", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_plr_lasso)" + ] + }, + { + "cell_type": "markdown", + "id": "768dabe2", + "metadata": {}, + "source": [ + "#### PLR - Repetitions of the Random Forest model" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "id": "7639ef46", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_plr_forest)" + ] + }, + { + "cell_type": "markdown", + "id": "99539929", + "metadata": {}, + "source": [ + "#### PLR - Repetitions of the Extreme Gradient Boosting model" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "id": "da73a9b4", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rep_propscore_plot(dml_plr_boost)" + ] + }, + { + "cell_type": "markdown", + "id": "70375158", + "metadata": {}, + "source": [ + "#### PLR - Propensity score estimates across learners" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "id": "1aeded78", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "h = dml_plr_regression.predictions.get('ml_m').shape[0]\n", + "fig, ax = plt.subplots(1, 4, figsize=(20,4.8))\n", + "\n", + "#regression histogram\n", + "ax[0].hist(np.reshape(dml_plr_regression.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[0].set_title('regression')\n", + "ax[0].set_xlabel(\"prop_score\")\n", + "ax[0].set_ylabel(\"density\")\n", + "\n", + "#lasso histogram\n", + "ax[1].hist(np.reshape(dml_plr_lasso.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[1].set_title('lasso')\n", + "ax[1].set_xlabel(\"prop_score\")\n", + "ax[1].set_ylabel(\"density\")\n", + "\n", + "#random forest histogram\n", + "ax[2].hist(np.reshape(dml_plr_forest.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[2].set_title('random forest')\n", + "ax[2].set_xlabel(\"prop_score\")\n", + "ax[2].set_ylabel(\"density\")\n", + "\n", + "#boosting histogram\n", + "ax[3].hist(np.reshape(dml_plr_boost.predictions.get('ml_m')[:,0], h), bins=25)\n", + "ax[3].set_title('xgboost')\n", + "ax[3].set_xlabel(\"prop_score\")\n", + "ax[3].set_ylabel(\"density\")\n", + " \n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "3aa8d603-0df5-48c6-ad62-ac5ffe3e8ada", + "metadata": {}, + "source": [ + "______\n", + "\n", + "**Notes and Acknowledgement**\n", + "\n", + "We would like to thank the organizers of the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge) for setting up this data challenge and making the numerous synthetic data examples publicly available. Although the data examples in the [ACIC 2019 Data Challenge](https://sites.google.com/view/acic2019datachallenge/data-challenge) do not explicitly adress A/B testing, we put the data example here in this context to give a tractable example on the use of causal machine learning in practice. The parameters for the random forests and extreme gradient boosting learners have been tuned externally. The corresponding tuning notebook will be uploaded in the [examples gallery](https://docs.doubleml.org/dev/examples/index.html) in the future." + ] + }, + { + "cell_type": "markdown", + "id": "egyptian-platform", + "metadata": {}, + "source": [ + "## References\n", + "\n", + "Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W. and Robins, J. (2018), Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21: C1-C68. doi:10.1111/ectj.12097." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 81fe64da6d1376e3373ebe8f08fbab94e97f4146 Mon Sep 17 00:00:00 2001 From: Philipp Bach Date: Wed, 1 Jun 2022 18:16:46 +0200 Subject: [PATCH 16/20] stage R version (code of main analysis), TODOs left for further progress --- doc/examples/R_double_ml_abtest.ipynb | 1047 +++++++++++++++++++++++++ 1 file changed, 1047 insertions(+) create mode 100644 doc/examples/R_double_ml_abtest.ipynb diff --git a/doc/examples/R_double_ml_abtest.ipynb b/doc/examples/R_double_ml_abtest.ipynb new file mode 100644 index 00000000..8fa176f7 --- /dev/null +++ b/doc/examples/R_double_ml_abtest.ipynb @@ -0,0 +1,1047 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "7a6837f6", + "metadata": {}, + "source": [ + "# R: A/B Testing with DoubleML" + ] + }, + { + "cell_type": "markdown", + "id": "476731d3", + "metadata": {}, + "source": [ + "\"An\n", + "\n", + "Image Source Freepik http://www.freepik.com, Designed by macrovector\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "15bef913", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Warning message:\n", + "\"package 'data.table' was built under R version 3.6.3\"\n" + ] + } + ], + "source": [ + "# Load required packages for this tutorial\n", + "library(DoubleML)\n", + "library(mlr3)\n", + "library(mlr3learners)\n", + "library(data.table)\n", + "library(ggplot2)\n", + "\n", + "# suppress messages during fitting\n", + "lgr::get_logger(\"mlr3\")$set_threshold(\"warn\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "dfdec0e0", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
  1. 1000
  2. 202
\n" + ], + "text/latex": [ + "\\begin{enumerate*}\n", + "\\item 1000\n", + "\\item 202\n", + "\\end{enumerate*}\n" + ], + "text/markdown": [ + "1. 1000\n", + "2. 202\n", + "\n", + "\n" + ], + "text/plain": [ + "[1] 1000 202" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Classes 'data.table' and 'data.frame':\t1000 obs. of 202 variables:\n", + " $ Y : num 7.36 8.33 7.47 6.5 7.04 ...\n", + " $ A : int 1 1 0 1 1 0 0 1 0 0 ...\n", + " $ V1 : int 10 12 14 0 12 8 10 9 11 15 ...\n", + " $ V2 : int 0 0 1 1 0 0 1 1 0 1 ...\n", + " $ V3 : int 0 1 1 0 0 1 1 1 1 1 ...\n", + " $ V4 : int 7 4 2 9 9 6 6 6 11 7 ...\n", + " $ V5 : num 193 200 194 202 201 ...\n", + " $ V6 : num 23.7 19.3 24.6 25.5 31.2 ...\n", + " $ V7 : int 8 7 5 4 6 9 2 4 7 2 ...\n", + " $ V8 : num 0.185 0.515 0.309 0.16 0.292 ...\n", + " $ V9 : num 15.85 9.24 10.79 22.64 25.79 ...\n", + " $ V10 : int 6 5 4 8 3 6 5 4 9 4 ...\n", + " $ V11 : int 1 0 1 0 1 1 1 1 1 1 ...\n", + " $ V12 : int 0 0 0 1 1 0 1 0 0 1 ...\n", + " $ V13 : num 0.201 0.223 0.175 0.149 0.138 ...\n", + " $ V14 : num 1.17 -1.537 -1.285 0.348 0.345 ...\n", + " $ V15 : num 1.22 1.12 1.27 1.14 1.3 ...\n", + " $ V16 : num -16.8 -15.1 -27.8 -15.8 -30.3 ...\n", + " $ V17 : num 8.07 4.48 6.19 4.75 7.79 ...\n", + " $ V18 : int 1 0 1 0 0 0 1 0 0 1 ...\n", + " $ V19 : num 1.04 -0.542 1.021 1.227 1.655 ...\n", + " $ V20 : int 30 -1 59 25 8 25 -1 -9 43 41 ...\n", + " $ V21 : int 0 0 0 1 1 0 1 1 0 0 ...\n", + " $ V22 : num 0.279 0.256 0.75 0.537 0.737 ...\n", + " $ V23 : num -1.421 2.789 -0.647 4.633 -3.566 ...\n", + " $ V24 : num 0.05559 0.01498 0.00637 0.05703 0.03166 ...\n", + " $ V25 : num 0.0403 0.0484 0.0693 0.1223 0.1016 ...\n", + " $ V26 : num 7.90e-05 8.59e-03 2.61e-05 8.09e-03 1.20e-03 ...\n", + " $ V27 : num -59 -20.4 -50.8 -58.7 -12.7 ...\n", + " $ V28 : int 20 7 16 27 14 10 23 10 19 18 ...\n", + " $ V29 : num 16.6 46.5 14.5 13.7 18.5 ...\n", + " $ V30 : num 34.7 21.7 25 25.5 28.6 ...\n", + " $ V31 : num 4.95 7.37 14.16 7.71 8.43 ...\n", + " $ V32 : num 0.175 0.431 0.826 -0.775 -0.961 ...\n", + " $ V33 : num 0.232 1.926 6.007 32.186 0.476 ...\n", + " $ V34 : num 2.07 1.83 1.77 1.87 1.39 ...\n", + " $ V35 : int 0 1 0 0 0 0 0 0 0 0 ...\n", + " $ V36 : num 20.06 28.06 11.85 20.51 9.66 ...\n", + " $ V37 : num 0.00044 0.00077 0.0018 0.00269 0.0024 ...\n", + " $ V38 : int 1 0 0 0 0 1 1 1 1 1 ...\n", + " $ V39 : num 0.481 2.161 1.018 2.384 0.241 ...\n", + " $ V40 : num 1.244 1.012 1.227 0.664 1.195 ...\n", + " $ V41 : int 5 12 8 15 8 7 17 8 16 25 ...\n", + " $ V42 : num 21.3 12.1 15.1 29.7 34.2 ...\n", + " $ V43 : int 1 0 0 0 1 1 0 1 1 0 ...\n", + " $ V44 : int 27 27 26 23 28 31 33 30 22 26 ...\n", + " $ V45 : int 1 1 0 1 0 0 0 0 1 0 ...\n", + " $ V46 : int 1 0 1 1 0 1 0 0 0 0 ...\n", + " $ V47 : num 20.79 24.43 19.13 6.96 20.87 ...\n", + " $ V48 : int 0 0 0 0 0 0 0 0 0 0 ...\n", + " $ V49 : int 1 0 1 1 1 0 1 0 1 1 ...\n", + " $ V50 : int 1 1 0 1 1 1 1 1 1 0 ...\n", + " $ V51 : num 0.5835 -0.8916 1.5197 -0.2097 -0.0912 ...\n", + " $ V52 : num 3.59 2.6 4.51 2.15 4.61 ...\n", + " $ V53 : int 1 1 1 1 1 1 1 1 0 1 ...\n", + " $ V54 : int 0 0 0 0 0 0 0 0 0 0 ...\n", + " $ V55 : int 0 1 1 0 1 0 0 0 0 0 ...\n", + " $ V56 : num 2.14 2.39 2.11 2.28 2.08 ...\n", + " $ V57 : int 0 1 1 0 0 0 0 0 1 0 ...\n", + " $ V58 : num -4.576 -0.215 -4.02 -4.183 -3.193 ...\n", + " $ V59 : num -2.339 0.591 2.002 -0.896 -0.636 ...\n", + " $ V60 : int 1 1 0 1 0 1 1 0 0 1 ...\n", + " $ V61 : num 1.14e-03 1.37e-05 2.30e-02 1.22e-03 8.93e-04 ...\n", + " $ V62 : num 11.5 11.3 10.7 12.1 10.8 ...\n", + " $ V63 : int 0 0 0 1 0 0 0 1 0 1 ...\n", + " $ V64 : int 4 2 2 5 0 2 6 1 1 2 ...\n", + " $ V65 : int 1 1 1 1 1 1 1 1 1 1 ...\n", + " $ V66 : int 1 0 0 0 0 0 0 1 0 0 ...\n", + " $ V67 : num 3.9 6.47 4.8 2.62 5.2 ...\n", + " $ V68 : num 177.5 70.2 28.4 19.8 55.4 ...\n", + " $ V69 : num -0.97783 -0.00815 -0.09309 0.29349 -0.32934 ...\n", + " $ V70 : num -15.66 2.43 -4.63 -12.2 -19.63 ...\n", + " $ V71 : num -0.3391 0.2509 0.4934 -0.32 -0.0074 ...\n", + " $ V72 : num -4.86 -4.88 -2.58 -4.52 -3.06 ...\n", + " $ V73 : num 46.8 44.3 59.1 11.2 12.2 ...\n", + " $ V74 : int 7 4 3 3 5 9 8 4 15 6 ...\n", + " $ V75 : num 27.4 23 21.7 25.3 23.3 ...\n", + " $ V76 : num -2.203 -0.976 -0.786 -0.288 0.368 ...\n", + " $ V77 : int 0 0 0 0 0 0 0 0 1 0 ...\n", + " $ V78 : int 6 7 11 14 7 5 11 11 14 12 ...\n", + " $ V79 : int 1 0 0 0 0 0 0 0 0 0 ...\n", + " $ V80 : num -0.9566 -0.9183 -0.9225 0.0593 -0.0718 ...\n", + " $ V81 : num 0.0563 0.0879 0.0654 0.1113 0.0547 ...\n", + " $ V82 : int 29 24 22 13 16 34 9 36 5 24 ...\n", + " $ V83 : int 0 0 0 0 0 0 1 0 0 0 ...\n", + " $ V84 : num 0.0374 0.0372 0.031 0.0354 0.0278 ...\n", + " $ V85 : num -0.15724 -0.13814 0.99698 -2.0978 0.00798 ...\n", + " $ V86 : num -0.195 1.19 -4.1359 -0.0292 0.5086 ...\n", + " $ V87 : int 0 0 0 0 0 0 0 0 0 0 ...\n", + " $ V88 : int 0 1 1 0 0 1 1 0 0 1 ...\n", + " $ V89 : int 17 17 22 8 14 11 18 20 11 20 ...\n", + " $ V90 : num 1.08 1.26 2.44 1.04 1.84 ...\n", + " $ V91 : int 1 1 0 0 1 0 0 1 1 0 ...\n", + " $ V92 : num 1.2526 -0.4946 -0.1259 1.0655 -0.0294 ...\n", + " $ V93 : int 0 0 0 0 0 0 0 0 0 0 ...\n", + " $ V94 : num 0.976 0.976 0.981 0.982 0.988 ...\n", + " $ V95 : int 5 6 6 4 4 5 5 3 6 7 ...\n", + " $ V96 : num 2.21 5.38 3.87 2.46 3.04 ...\n", + " $ V97 : num 1.27 1.25 1.28 1.29 1.16 ...\n", + " [list output truncated]\n", + " - attr(*, \".internal.selfref\")= \n" + ] + } + ], + "source": [ + "library(data.table)\n", + "\n", + "# Load data set from url (internet connection required)\n", + "url = \"https://raw.githubusercontent.com/DoubleML/doubleml-docs/p-add-ACIC-dataset/doc/examples/data/high42.CSV\"\n", + "df = fread(url)\n", + "\n", + "dim(df)\n", + "\n", + "# TODO: Add info on types of variables\n", + "str(df)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "d95977a0", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + 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A data.table: 6 × 202
YAV1V2V3V4V5V6V7V8...V191V192V193V194V195V196V197V198V199V200
<dbl><int><int><int><int><int><dbl><dbl><int><dbl>...<dbl><int><dbl><int><int><dbl><dbl><int><int><dbl>
7.358185110007192.793823.6769580.18544294...1.46283711627.274004.683956 0.5656669030.02433804
8.333672112014199.653619.2812770.51484172...1.33052211661.484106.766661-0.3954021040.05651780
7.472758014112194.207824.5893350.30919878...1.38415111658.939005.647794 1.1127661000.01344207
6.5023191 0109201.838025.5139240.16016010...1.22030311650.802005.370363-0.3058420040.03463235
7.043758112009201.360431.1606460.29197555...1.17009411676.819003.446532 2.4406606010.01751381
5.6583370 8016193.219520.4656490.05673076...1.80294511634.093105.294410 1.0869714100.04712806
\n" + ], + "text/latex": [ + "A data.table: 6 × 202\n", + "\\begin{tabular}{lllllllllllllllllllll}\n", + " Y & A & V1 & V2 & V3 & V4 & V5 & V6 & V7 & V8 & ... & V191 & V192 & V193 & V194 & V195 & V196 & V197 & V198 & V199 & V200\\\\\n", + " & & & & & & & & & & ... & & & & & & & & & & \\\\\n", + "\\hline\n", + "\t 7.358185 & 1 & 10 & 0 & 0 & 7 & 192.7938 & 23.67695 & 8 & 0.18544294 & ... & 1.462837 & 1 & 1627.274 & 0 & 0 & 4.683956 & 0.5656669 & 0 & 3 & 0.02433804\\\\\n", + "\t 8.333672 & 1 & 12 & 0 & 1 & 4 & 199.6536 & 19.28127 & 7 & 0.51484172 & ... & 1.330522 & 1 & 1661.484 & 1 & 0 & 6.766661 & -0.3954021 & 0 & 4 & 0.05651780\\\\\n", + "\t 7.472758 & 0 & 14 & 1 & 1 & 2 & 194.2078 & 24.58933 & 5 & 0.30919878 & ... & 1.384151 & 1 & 1658.939 & 0 & 0 & 5.647794 & 1.1127661 & 0 & 0 & 0.01344207\\\\\n", + "\t 6.502319 & 1 & 0 & 1 & 0 & 9 & 201.8380 & 25.51392 & 4 & 0.16016010 & ... & 1.220303 & 1 & 1650.802 & 0 & 0 & 5.370363 & -0.3058420 & 0 & 4 & 0.03463235\\\\\n", + "\t 7.043758 & 1 & 12 & 0 & 0 & 9 & 201.3604 & 31.16064 & 6 & 0.29197555 & ... & 1.170094 & 1 & 1676.819 & 0 & 0 & 3.446532 & 2.4406606 & 0 & 1 & 0.01751381\\\\\n", + "\t 5.658337 & 0 & 8 & 0 & 1 & 6 & 193.2195 & 20.46564 & 9 & 0.05673076 & ... & 1.802945 & 1 & 1634.093 & 1 & 0 & 5.294410 & 1.0869714 & 1 & 0 & 0.04712806\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.table: 6 × 202\n", + "\n", + "| Y <dbl> | A <int> | V1 <int> | V2 <int> | V3 <int> | V4 <int> | V5 <dbl> | V6 <dbl> | V7 <int> | V8 <dbl> | ... ... | V191 <dbl> | V192 <int> | V193 <dbl> | V194 <int> | V195 <int> | V196 <dbl> | V197 <dbl> | V198 <int> | V199 <int> | V200 <dbl> |\n", + "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n", + "| 7.358185 | 1 | 10 | 0 | 0 | 7 | 192.7938 | 23.67695 | 8 | 0.18544294 | ... | 1.462837 | 1 | 1627.274 | 0 | 0 | 4.683956 | 0.5656669 | 0 | 3 | 0.02433804 |\n", + "| 8.333672 | 1 | 12 | 0 | 1 | 4 | 199.6536 | 19.28127 | 7 | 0.51484172 | ... | 1.330522 | 1 | 1661.484 | 1 | 0 | 6.766661 | -0.3954021 | 0 | 4 | 0.05651780 |\n", + "| 7.472758 | 0 | 14 | 1 | 1 | 2 | 194.2078 | 24.58933 | 5 | 0.30919878 | ... | 1.384151 | 1 | 1658.939 | 0 | 0 | 5.647794 | 1.1127661 | 0 | 0 | 0.01344207 |\n", + "| 6.502319 | 1 | 0 | 1 | 0 | 9 | 201.8380 | 25.51392 | 4 | 0.16016010 | ... | 1.220303 | 1 | 1650.802 | 0 | 0 | 5.370363 | -0.3058420 | 0 | 4 | 0.03463235 |\n", + "| 7.043758 | 1 | 12 | 0 | 0 | 9 | 201.3604 | 31.16064 | 6 | 0.29197555 | ... | 1.170094 | 1 | 1676.819 | 0 | 0 | 3.446532 | 2.4406606 | 0 | 1 | 0.01751381 |\n", + "| 5.658337 | 0 | 8 | 0 | 1 | 6 | 193.2195 | 20.46564 | 9 | 0.05673076 | ... | 1.802945 | 1 | 1634.093 | 1 | 0 | 5.294410 | 1.0869714 | 1 | 0 | 0.04712806 |\n", + "\n" + ], + "text/plain": [ + " Y A V1 V2 V3 V4 V5 V6 V7 V8 ... V191 V192\n", + "1 7.358185 1 10 0 0 7 192.7938 23.67695 8 0.18544294 ... 1.462837 1 \n", + "2 8.333672 1 12 0 1 4 199.6536 19.28127 7 0.51484172 ... 1.330522 1 \n", + "3 7.472758 0 14 1 1 2 194.2078 24.58933 5 0.30919878 ... 1.384151 1 \n", + "4 6.502319 1 0 1 0 9 201.8380 25.51392 4 0.16016010 ... 1.220303 1 \n", + "5 7.043758 1 12 0 0 9 201.3604 31.16064 6 0.29197555 ... 1.170094 1 \n", + "6 5.658337 0 8 0 1 6 193.2195 20.46564 9 0.05673076 ... 1.802945 1 \n", + " V193 V194 V195 V196 V197 V198 V199 V200 \n", + "1 1627.274 0 0 4.683956 0.5656669 0 3 0.02433804\n", + "2 1661.484 1 0 6.766661 -0.3954021 0 4 0.05651780\n", + "3 1658.939 0 0 5.647794 1.1127661 0 0 0.01344207\n", + "4 1650.802 0 0 5.370363 -0.3058420 0 4 0.03463235\n", + "5 1676.819 0 0 3.446532 2.4406606 0 1 0.01751381\n", + "6 1634.093 1 0 5.294410 1.0869714 1 0 0.04712806" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "head(df)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "e8698562", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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PIaTO77jD/tZe4/Dl9d+EMvNpyaP12FVBdYXoPJfZ+260gvf3fnT1ch1QWW12By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\nSc5i/5Lfz8N/7Pzj9uElmTjqxMPdvaHJbn0b+TC51OlujJ13ZLw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+ "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 420, + "width": 420 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "hist_A = ggplot(df, aes(x = A, fill = factor(A))) +\n", + " geom_bar() + theme_minimal() +\n", + " ggtitle(\"Treatment\") + xlab(\"A\") +\n", + " theme(legend.position = \"bottom\", plot.title = element_text(hjust = 0.5),\n", + " text = element_text(size = 20))\n", + "hist_A" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "9aa1164a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
A data.table: 2 × 2
AV1
<int><dbl>
17.953744
06.836141
\n" + ], + "text/latex": [ + "A data.table: 2 × 2\n", + "\\begin{tabular}{ll}\n", + " A & V1\\\\\n", + " & \\\\\n", + "\\hline\n", + "\t 1 & 7.953744\\\\\n", + "\t 0 & 6.836141\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.table: 2 × 2\n", + "\n", + "| A <int> | V1 <dbl> |\n", + "|---|---|\n", + "| 1 | 7.953744 |\n", + "| 0 | 6.836141 |\n", + "\n" + ], + "text/plain": [ + " A V1 \n", + "1 1 7.953744\n", + "2 0 6.836141" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "1.11760295064719" + ], + "text/latex": [ + "1.11760295064719" + ], + "text/markdown": [ + "1.11760295064719" + ], + "text/plain": [ + "[1] 1.117603" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Unconditional ATE\n", + "df[, mean(Y), by = A]\n", + "\n", + "ATE_uncond = df[A == 1, mean(Y)] - df[A==0, mean(Y)]\n", + "ATE_uncond" + ] + }, + { + "cell_type": "markdown", + "id": "479cd6f7", + "metadata": {}, + "source": [ + "### `DoubleMLData`\n" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "ea2df013", + "metadata": {}, + "outputs": [], + "source": [ + "features_base = colnames(df)[grep(\"V\", colnames(df))]\n", + "data_dml = DoubleMLData$new(df,\n", + " y_col = \"Y\",\n", + " d_cols = \"A\",\n", + " x_cols = features_base)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "c98e3ec1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "================= DoubleMLData Object ==================\n", + "\n", + "\n", + "------------------ Data summary ------------------\n", + "Outcome variable: Y\n", + "Treatment variable(s): A\n", + "Covariates: V1, V2, V3, V4, V5, V6, V7, V8, V9, V10, V11, V12, V13, V14, V15, V16, V17, V18, V19, V20, V21, V22, V23, V24, V25, V26, V27, V28, V29, V30, V31, V32, V33, V34, V35, V36, V37, V38, V39, V40, V41, V42, V43, V44, V45, V46, V47, V48, V49, V50, V51, V52, V53, V54, V55, V56, V57, V58, V59, V60, V61, V62, V63, V64, V65, V66, V67, V68, V69, V70, V71, V72, V73, V74, V75, V76, V77, V78, V79, V80, V81, V82, V83, V84, V85, V86, V87, V88, V89, V90, V91, V92, V93, V94, V95, V96, V97, V98, V99, V100, V101, V102, V103, V104, V105, V106, V107, V108, V109, V110, V111, V112, V113, V114, V115, V116, V117, V118, V119, V120, V121, V122, V123, V124, V125, V126, V127, V128, V129, V130, V131, V132, V133, V134, V135, V136, V137, V138, V139, V140, V141, V142, V143, V144, V145, V146, V147, V148, V149, V150, V151, V152, V153, V154, V155, V156, V157, V158, V159, V160, V161, V162, V163, V164, V165, V166, V167, V168, V169, V170, V171, V172, V173, V174, V175, V176, V177, V178, V179, V180, V181, V182, V183, V184, V185, V186, V187, V188, V189, V190, V191, V192, V193, V194, V195, V196, V197, V198, V199, V200\n", + "Instrument(s): \n", + "No. Observations: 1000\n" + ] + } + ], + "source": [ + "print(data_dml)" + ] + }, + { + "cell_type": "markdown", + "id": "b56ad806", + "metadata": {}, + "source": [ + "### IRM\n" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "df43c333", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: helper function for prediction of nuisance\n", + "\n", + "pred_acc_irm = function() {\n", + " \n", + "}" + ] + }, + { + "cell_type": "markdown", + "id": "03501b58", + "metadata": {}, + "source": [ + "### Benchmark: Model based on Linear and Logistic Regression" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "98545886", + "metadata": {}, + "outputs": [ + { + "ename": "ERROR", + "evalue": "Error in sort(assert_subset(properties, mlr_reflections$learner_properties[[task_type]])): Assertion on 'properties' failed: Must be a subset of {'featureless','missings','weights','importance','selected_features','oob_error'}, but is {'weights','loglik'}.\n", + "output_type": "error", + "traceback": [ + "Error in sort(assert_subset(properties, mlr_reflections$learner_properties[[task_type]])): Assertion on 'properties' failed: Must be a subset of {'featureless','missings','weights','importance','selected_features','oob_error'}, but is {'weights','loglik'}.\nTraceback:\n", + "1. lrn(\"regr.lm\")", + "2. dictionary_sugar_get(mlr_learners, .key, ...)", + "3. dictionary_get(dict, .key)", + "4. dictionary_initialize_item(key, obj, dots)", + "5. do.call(constructor$new, cargs)", + "6. (function (...) \n . {\n . inherit <- get_inherit()\n . if (!is.null(inherit)) {\n . if (!inherits(inherit, \"R6ClassGenerator\")) \n . stop(\"`inherit` must be a R6ClassGenerator.\")\n . if (!identical(portable, inherit$portable)) \n . stop(\"Sub and superclass must both be portable or non-portable.\")\n . recursive_merge <- function(obj, which) {\n . if (is.null(obj)) \n . return(NULL)\n . merge_vectors(recursive_merge(obj$get_inherit(), \n . which), obj[[which]])\n . }\n . public_fields <- merge_vectors(recursive_merge(inherit, \n . \"public_fields\"), public_fields)\n . private_fields <- merge_vectors(recursive_merge(inherit, \n . \"private_fields\"), private_fields)\n . }\n . if (class) {\n . classes <- c(classname, get_superclassnames(inherit), \n . \"R6\")\n . }\n . else {\n . classes <- NULL\n . }\n . has_priv <- has_private()\n . if (portable) {\n . if (has_priv) \n . private_bind_env <- new.env(parent = emptyenv(), \n . hash = FALSE)\n . else private_bind_env <- NULL\n . public_bind_env <- new.env(parent = emptyenv(), hash = FALSE)\n . enclos_env <- new.env(parent = parent_env, hash = FALSE)\n . }\n . else {\n . if (has_priv) {\n . private_bind_env <- new.env(parent = parent_env, \n . hash = FALSE)\n . public_bind_env <- new.env(parent = private_bind_env, \n . hash = FALSE)\n . }\n . else {\n . private_bind_env <- NULL\n . public_bind_env <- new.env(parent = parent_env, hash = FALSE)\n . }\n . enclos_env <- public_bind_env\n . }\n . enclos_env$self <- public_bind_env\n . if (has_priv) \n . enclos_env$private <- private_bind_env\n . public_methods <- assign_func_envs(public_methods, enclos_env)\n . if (has_priv) \n . private_methods <- assign_func_envs(private_methods, \n . enclos_env)\n . if (!is.null(active)) \n . active <- assign_func_envs(active, enclos_env)\n . if (length(debug_names) > 0) {\n . lapply(public_methods[names(public_methods) %in% debug_names], \n . base::debug)\n . lapply(private_methods[names(private_methods) %in% debug_names], \n . base::debug)\n . lapply(active[names(active) %in% debug_names], base::debug)\n . }\n . if (!is.null(inherit)) {\n . if (portable) {\n . super_struct <- create_super_env(inherit, public_bind_env, \n . private_bind_env, portable = TRUE, cloneable = cloneable)\n . }\n . else {\n . super_struct <- create_super_env(inherit, public_bind_env, \n . portable = FALSE, cloneable = cloneable)\n . }\n . enclos_env$super <- super_struct$bind_env\n . public_methods <- merge_vectors(super_struct$public_methods, \n . public_methods)\n . private_methods <- merge_vectors(super_struct$private_methods, \n . private_methods)\n . active <- merge_vectors(super_struct$active, active)\n . }\n . list2env2(public_methods, envir = public_bind_env)\n . list2env2(public_fields, envir = public_bind_env)\n . if (has_priv) {\n . list2env2(private_methods, envir = private_bind_env)\n . list2env2(private_fields, envir = private_bind_env)\n . }\n . if (!is.null(active)) {\n . for (name in names(active)) {\n . makeActiveBinding(name, active[[name]], public_bind_env)\n . }\n . enclos_env$.__active__ <- active\n . }\n . public_bind_env$.__enclos_env__ <- enclos_env\n . if (lock_objects) {\n . if (has_priv) \n . lockEnvironment(private_bind_env)\n . lockEnvironment(public_bind_env)\n . }\n . if (has_priv) {\n . for (name in names(private_methods)) lockBinding(name, \n . private_bind_env)\n . }\n . for (name in names(public_methods)) lockBinding(name, public_bind_env)\n . class(public_bind_env) <- classes\n . initialize <- .subset2(public_bind_env, \"initialize\")\n . if (is.function(initialize)) {\n . initialize(...)\n . }\n . else if (length(list(...)) != 0) {\n . stop(\"Called new() with arguments, but there is no initialize method.\")\n . }\n . if (is.function(.subset2(public_bind_env, \"finalize\"))) {\n . finalizer_wrapper <- function(e) {\n . .subset2(e, \"finalize\")()\n . }\n . environment(finalizer_wrapper) <- baseenv()\n . reg.finalizer(public_bind_env, finalizer_wrapper, onexit = TRUE)\n . }\n . if (has_priv) {\n . if (is.function(.subset2(private_bind_env, \"finalize\"))) {\n . finalizer_wrapper <- function(e) {\n . .subset2(e, \".__enclos_env__\")$private$finalize()\n . }\n . environment(finalizer_wrapper) <- baseenv()\n . reg.finalizer(public_bind_env, finalizer_wrapper, \n . onexit = TRUE)\n . }\n . }\n . public_bind_env\n . })()", + "7. initialize(...)", + "8. .__LearnerRegrLM__initialize(self = self, private = private, \n . super = super)", + "9. super$initialize(id = \"regr.lm\", param_set = ps, predict_types = c(\"response\", \n . \"se\"), feature_types = c(\"logical\", \"integer\", \"numeric\", \n . \"factor\", \"character\"), properties = c(\"weights\", \"loglik\"), \n . packages = \"stats\", man = \"mlr3learners::mlr_learners_regr.lm\")", + "10. .__LearnerRegr__initialize(self = self, private = private, super = super, \n . id = id, param_set = param_set, predict_types = predict_types, \n . feature_types = feature_types, properties = properties, data_formats = data_formats, \n . packages = packages, man = man)", + "11. super$initialize(id = id, task_type = \"regr\", param_set = param_set, \n . feature_types = feature_types, predict_types = predict_types, \n . properties = properties, data_formats = data_formats, packages = packages, \n . man = man)", + "12. .__Learner__initialize(self = self, private = private, super = super, \n . id = id, task_type = task_type, param_set = param_set, predict_types = predict_types, \n . feature_types = feature_types, properties = properties, data_formats = data_formats, \n . packages = packages, man = man)", + "13. sort(assert_subset(properties, mlr_reflections$learner_properties[[task_type]]))", + "14. assert_subset(properties, mlr_reflections$learner_properties[[task_type]])", + "15. makeAssertion(x, res, .var.name, add)", + "16. mstop(\"Assertion on '%s' failed: %s.\", var.name, res, call. = sys.call(-2L))" + ] + } + ], + "source": [ + "linreg = lrn(\"regr.lm\")\n", + "logreg_class = lrn(\"classif.log_reg\")\n", + "\n", + "set.seed(1234)\n", + "dml_irm_regression = DoubleMLIRM$new(data_dml,\n", + " ml_g = linreg,\n", + " ml_m = logreg_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_irm_regression$fit(store_predictions = TRUE)\n", + "dml_irm_regression$summary()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "883562c1", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Calculate Bias\n", + "# TODO: Summary for predictive accuracy\n", + "# TODO: Print RMSE mean and sd for ml_g and log_loss for ml_m" + ] + }, + { + "cell_type": "markdown", + "id": "560d5fc5", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Lasso\n" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "a7c55597", + "metadata": {}, + "outputs": [ + { + "ename": "ERROR", + "evalue": "Error in checkClass(x, classes, ordered, null.ok): Objekt 'data_dml' nicht gefunden\n", + "output_type": "error", + "traceback": [ + "Error in checkClass(x, classes, ordered, null.ok): Objekt 'data_dml' nicht gefunden\nTraceback:\n", + "1. DoubleMLIRM$new(data_dml, ml_g = lasso, ml_m = lasso_class, trimming_threshold = 0.025, \n . n_folds = 3, n_rep = 3)", + "2. initialize(...)", + "3. super$initialize_double_ml(data, n_folds, n_rep, score, dml_procedure, \n . draw_sample_splitting, apply_cross_fitting)", + "4. assert_class(data, \"DoubleMLData\")", + "5. checkClass(x, classes, ordered, null.ok)" + ] + } + ], + "source": [ + "lasso = lrn(\"regr.cv_glmnet\", nfolds = 5, s = \"lambda.min\")\n", + "lasso_class = lrn(\"classif.cv_glmnet\", nfolds = 5, s = \"lambda.min\")\n", + "\n", + "set.seed(1234)\n", + "dml_irm_lasso = DoubleMLIRM$new(data_dml,\n", + " ml_g = lasso,\n", + " ml_m = lasso_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_irm_lasso$fit(store_predictions = TRUE)\n", + "\n", + "dml_irm_lasso$summary()" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "15c8afb3", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Calculate Bias\n", + "# TODO: Summary for predictive accuracy\n", + "# TODO: Print RMSE mean and sd for ml_g and log_loss for ml_m" + ] + }, + { + "cell_type": "markdown", + "id": "e5099672", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Random Forest\n" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "6c3530e5", + "metadata": {}, + "outputs": [ + { + "ename": "ERROR", + "evalue": "Error in checkClass(x, classes, ordered, null.ok): Objekt 'data_dml' nicht gefunden\n", + "output_type": "error", + "traceback": [ + "Error in checkClass(x, classes, ordered, null.ok): Objekt 'data_dml' nicht gefunden\nTraceback:\n", + "1. DoubleMLIRM$new(data_dml, ml_g = randomForest, ml_m = randomForest_class, \n . trimming_threshold = 0.025, n_folds = 3, n_rep = 3)", + "2. initialize(...)", + "3. super$initialize_double_ml(data, n_folds, n_rep, score, dml_procedure, \n . draw_sample_splitting, apply_cross_fitting)", + "4. assert_class(data, \"DoubleMLData\")", + "5. checkClass(x, classes, ordered, null.ok)" + ] + } + ], + "source": [ + "randomForest = lrn(\"regr.ranger\")\n", + "randomForest_class = lrn(\"classif.ranger\")\n", + "\n", + "set.seed(1234)\n", + "dml_irm_forest = DoubleMLIRM$new(data_dml,\n", + " ml_g = randomForest,\n", + " ml_m = randomForest_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "# Set nuisance-part specific parameters\n", + "dml_irm_forest$set_ml_nuisance_params(\"ml_g0\", \"A\",\n", + " list(\"mtry\" = 200,\n", + " \"num.trees\" = 250))\n", + "dml_irm_forest$set_ml_nuisance_params(\"ml_g1\", \"A\",\n", + " list(\"mtry\" = 200,\n", + " \"num.trees\" = 250))\n", + "dml_irm_forest$set_ml_nuisance_params(\"ml_m\", \"A\",\n", + " list(\"mtry\" = 200,\n", + " \"num.trees\" = 250))\n", + "\n", + "dml_irm_forest$fit(store_predictions = TRUE)\n", + "dml_irm_forest$summary()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6c63aae2", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Calculate Bias\n", + "# TODO: Summary for predictive accuracy\n", + "# TODO: Print RMSE mean and sd for ml_g and log_loss for ml_m" + ] + }, + { + "cell_type": "markdown", + "id": "98447b3b", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Extreme Gradient Boosting" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3991105c", + "metadata": {}, + "outputs": [], + "source": [ + "boost = lrn(\"regr.xgboost\",\n", + " objective = \"reg:squarederror\")\n", + "boost_class = lrn(\"classif.xgboost\",\n", + " objective = \"binary:logistic\",\n", + " eval_metric = \"logloss\")\n", + "\n", + "set.seed(1234)\n", + "dml_irm_boost = DoubleMLIRM$new(data_dml,\n", + " ml_g = boost,\n", + " ml_m = boost_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_irm_boost$set_ml_nuisance_params(\"ml_g0\", \"A\",\n", + " list(\"nrounds\" = 30,\n", + " \"eta\" = 0.2))\n", + "dml_irm_boost$set_ml_nuisance_params(\"ml_g1\", \"A\",\n", + " list(\"nrounds\" = 30,\n", + " \"eta\" = 0.2))\n", + "dml_irm_boost$set_ml_nuisance_params(\"ml_m\", \"A\",\n", + " list(\"nrounds\" = 15,\n", + " \"eta\" = 0.2))\n", + "\n", + "dml_irm_boost$fit(store_predictions = TRUE)\n", + "dml_irm_boost$summary()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2193503d", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Calculate Bias\n", + "# TODO: Summary for predictive accuracy\n", + "# TODO: Print RMSE mean and sd for ml_g and log_loss for ml_m" + ] + }, + { + "cell_type": "markdown", + "id": "f2214f23", + "metadata": {}, + "source": [ + "#### IRM - Summary of coefficient estimates\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "3f805daa", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Add summary of results" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ae0d545f", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Add visualization of summary" + ] + }, + { + "cell_type": "markdown", + "id": "9ee7a793", + "metadata": {}, + "source": [ + "#### IRM - Summary of prediction assessment metric's mean values" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "c1a10e33", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Add comparison/summary for predictive accuracy (nuisance)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "97b9a1c8", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Add visualization of summary" + ] + }, + { + "cell_type": "markdown", + "id": "29e91c0b", + "metadata": {}, + "source": [ + "### Inspection of the benchmark model\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3cc70b60", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Function for propensity score visualiztation\n", + "\n", + "rep_propscore_plot = function() {\n", + " \n", + "}" + ] + }, + { + "cell_type": "markdown", + "id": "c05e662c", + "metadata": {}, + "source": [ + "## 2. Partially Linear Regression Model (PLR)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fb1157a1", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Function for calculation of prediction accuracy PLR\n", + "\n", + "pred_acc_plr = function() {\n", + " \n", + "}" + ] + }, + { + "cell_type": "markdown", + "id": "d103856e", + "metadata": {}, + "source": [ + "### Benchmark: Model based on Linear and Logistic Regression" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6f60eac3", + "metadata": {}, + "outputs": [], + "source": [ + "linreg = lrn(\"regr.lm\")\n", + "logreg_class = lrn(\"classif.log_reg\")\n", + "\n", + "set.seed(1234)\n", + "dml_plr_regression = DoubleMLPLR$new(data_dml,\n", + " ml_g = linreg,\n", + " ml_m = logreg_class,\n", + " trimming_threshold = 0.025,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_regression$fit(store_predictions = TRUE)\n", + "dml_plr_regression$summary()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5a418036", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Calculate Bias\n", + "# TODO: Summary for predictive accuracy\n", + "# TODO: Print RMSE mean and sd for ml_g and log_loss for ml_m" + ] + }, + { + "cell_type": "markdown", + "id": "8a7e424f", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Lasso" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "094dfed2", + "metadata": {}, + "outputs": [ + { + "ename": "ERROR", + "evalue": "Error in checkClass(x, classes, ordered, null.ok): Objekt 'data_dml' nicht gefunden\n", + "output_type": "error", + "traceback": [ + "Error in checkClass(x, classes, ordered, null.ok): Objekt 'data_dml' nicht gefunden\nTraceback:\n", + "1. DoubleMLPLR$new(data_dml, ml_g = lasso, ml_m = lasso_class, n_folds = 3, \n . n_rep = 3)", + "2. initialize(...)", + "3. super$initialize_double_ml(data, n_folds, n_rep, score, dml_procedure, \n . draw_sample_splitting, apply_cross_fitting)", + "4. assert_class(data, \"DoubleMLData\")", + "5. checkClass(x, classes, ordered, null.ok)" + ] + } + ], + "source": [ + "lasso = lrn(\"regr.cv_glmnet\", nfolds = 5, s = \"lambda.min\")\n", + "lasso_class = lrn(\"classif.cv_glmnet\", nfolds = 5, s = \"lambda.min\")\n", + "\n", + "set.seed(1234)\n", + "dml_plr_lasso = DoubleMLPLR$new(data_dml,\n", + " ml_g = lasso,\n", + " ml_m = lasso_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_lasso$fit(store_predictions = TRUE)\n", + "\n", + "dml_plr_lasso$summary()\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dd4ae562", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Calculate Bias\n", + "# TODO: Summary for predictive accuracy\n", + "# TODO: Print RMSE mean and sd for ml_g and log_loss for ml_m" + ] + }, + { + "cell_type": "markdown", + "id": "4fbbead6", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Random Forests" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a11f82d7", + "metadata": {}, + "outputs": [], + "source": [ + "randomForest = lrn(\"regr.ranger\")\n", + "randomForest_class = lrn(\"classif.ranger\")\n", + "\n", + "set.seed(1234)\n", + "dml_plr_forest = DoubleMLPLR$new(data_dml,\n", + " ml_g = randomForest,\n", + " ml_m = randomForest_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "\n", + "dml_plr_forest$fit(store_predictions = TRUE)\n", + "dml_plr_forest$summary()" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "480064a1", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Calculate Bias\n", + "# TODO: Summary for predictive accuracy\n", + "# TODO: Print RMSE mean and sd for ml_g and log_loss for ml_m" + ] + }, + { + "cell_type": "markdown", + "id": "b9ed9bcb", + "metadata": {}, + "source": [ + "### Double Machine Learning based on Extreme Gradient Boosting" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b63e2bd8", + "metadata": {}, + "outputs": [], + "source": [ + "boost = lrn(\"regr.xgboost\",\n", + " objective = \"reg:squarederror\",\n", + " eta = 0.1, nrounds = 57, max_depth = 2)\n", + "\n", + "boost_class = lrn(\"classif.xgboost\",\n", + " objective = \"binary:logistic\",\n", + " eval_metric = \"logloss\",\n", + " eta = 0.1, nrounds = 10, max_depth = 3)\n", + "\n", + "set.seed(1234)\n", + "dml_plr_boost = DoubleMLPLR$new(data_dml,\n", + " ml_g = boost,\n", + " ml_m = boost_class,\n", + " n_folds = 3,\n", + " n_rep = 3)\n", + "\n", + "dml_plr_boost$fit(store_predictions = TRUE)\n", + "dml_plr_boost$summary()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8a75616e", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Calculate Bias\n", + "# TODO: Summary for predictive accuracy\n", + "# TODO: Print RMSE mean and sd for ml_g and log_loss for ml_m" + ] + }, + { + "cell_type": "markdown", + "id": "4c1076db", + "metadata": {}, + "source": [ + "#### PLR - Summary of coefficient estimates" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "53aba28d", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Summary" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a9534744", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2137028e", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "R", + "language": "R", + "name": "ir" + }, + "language_info": { + "codemirror_mode": "r", + "file_extension": ".r", + "mimetype": "text/x-r-source", + "name": "R", + "pygments_lexer": "r", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 5ea0ed1a08b2988aea14802d9793b6cdfcab4616 Mon Sep 17 00:00:00 2001 From: Philipp Bach Date: Wed, 1 Jun 2022 18:17:55 +0200 Subject: [PATCH 17/20] latest version of Py notebook --- doc/examples/py_double_ml_abtest.ipynb | 21 ++++----------------- 1 file changed, 4 insertions(+), 17 deletions(-) diff --git a/doc/examples/py_double_ml_abtest.ipynb b/doc/examples/py_double_ml_abtest.ipynb index 014e07d0..46d9cb25 100644 --- a/doc/examples/py_double_ml_abtest.ipynb +++ b/doc/examples/py_double_ml_abtest.ipynb @@ -753,24 +753,11 @@ ] }, { - "cell_type": "code", - "execution_count": 8, - "id": "57392f09", + "cell_type": "raw", + "id": "9aafbdb3", "metadata": { "scrolled": true }, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], "source": [ "_ = sns.displot(df, x=\"Y\", hue=\"A\", col=\"A\",\n", " kind=\"kde\", rug = True, fill=True)" @@ -2466,7 +2453,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 81, "id": "1432e567-d221-490d-9361-39b9072cb6d4", "metadata": { "scrolled": true, @@ -2521,7 +2508,7 @@ "A 0.784999 0.067127 11.694191 1.364815e-31 0.653432 0.916565" ] }, - "execution_count": 44, + "execution_count": 81, "metadata": {}, "output_type": "execute_result" } From e7cc4801de40ac3d3f77d6ad415a4d05f885c2da Mon Sep 17 00:00:00 2001 From: Philipp Bach Date: Thu, 2 Jun 2022 15:32:52 +0200 Subject: [PATCH 18/20] upd link to master branch --- doc/examples/R_double_ml_abtest.ipynb | 558 +++++-------------------- doc/examples/py_double_ml_abtest.ipynb | 2 +- 2 files changed, 112 insertions(+), 448 deletions(-) diff --git a/doc/examples/R_double_ml_abtest.ipynb b/doc/examples/R_double_ml_abtest.ipynb index 8fa176f7..fdebcb84 100644 --- a/doc/examples/R_double_ml_abtest.ipynb +++ b/doc/examples/R_double_ml_abtest.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "7a6837f6", + "id": "9f13f4be", "metadata": {}, "source": [ "# R: A/B Testing with DoubleML" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "476731d3", + "id": "ac8c0bac", "metadata": {}, "source": [ "\"An\n", @@ -20,14 +20,16 @@ }, { "cell_type": "code", - "execution_count": 14, - "id": "15bef913", + "execution_count": 1, + "id": "5fe422a9", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ + "Warning message:\n", + "\"package 'mlr3' was built under R version 4.1.0\"\n", "Warning message:\n", "\"package 'data.table' was built under R version 3.6.3\"\n" ] @@ -47,153 +49,15 @@ }, { "cell_type": "code", - "execution_count": 15, - "id": "dfdec0e0", + "execution_count": null, + "id": "edbdeffd", "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "
  1. 1000
  2. 202
\n" - ], - "text/latex": [ - "\\begin{enumerate*}\n", - "\\item 1000\n", - "\\item 202\n", - "\\end{enumerate*}\n" - ], - "text/markdown": [ - "1. 1000\n", - "2. 202\n", - "\n", - "\n" - ], - "text/plain": [ - "[1] 1000 202" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Classes 'data.table' and 'data.frame':\t1000 obs. of 202 variables:\n", - " $ Y : num 7.36 8.33 7.47 6.5 7.04 ...\n", - " $ A : int 1 1 0 1 1 0 0 1 0 0 ...\n", - " $ V1 : int 10 12 14 0 12 8 10 9 11 15 ...\n", - " $ V2 : int 0 0 1 1 0 0 1 1 0 1 ...\n", - " $ V3 : int 0 1 1 0 0 1 1 1 1 1 ...\n", - " $ V4 : int 7 4 2 9 9 6 6 6 11 7 ...\n", - " $ V5 : num 193 200 194 202 201 ...\n", - " $ V6 : num 23.7 19.3 24.6 25.5 31.2 ...\n", - " $ V7 : int 8 7 5 4 6 9 2 4 7 2 ...\n", - " $ V8 : num 0.185 0.515 0.309 0.16 0.292 ...\n", - " $ V9 : num 15.85 9.24 10.79 22.64 25.79 ...\n", - " $ V10 : int 6 5 4 8 3 6 5 4 9 4 ...\n", - " $ V11 : int 1 0 1 0 1 1 1 1 1 1 ...\n", - " $ V12 : int 0 0 0 1 1 0 1 0 0 1 ...\n", - " $ V13 : num 0.201 0.223 0.175 0.149 0.138 ...\n", - " $ V14 : num 1.17 -1.537 -1.285 0.348 0.345 ...\n", - " $ V15 : num 1.22 1.12 1.27 1.14 1.3 ...\n", - " $ V16 : num -16.8 -15.1 -27.8 -15.8 -30.3 ...\n", - " $ V17 : num 8.07 4.48 6.19 4.75 7.79 ...\n", - " $ V18 : int 1 0 1 0 0 0 1 0 0 1 ...\n", - " $ V19 : num 1.04 -0.542 1.021 1.227 1.655 ...\n", - " $ V20 : int 30 -1 59 25 8 25 -1 -9 43 41 ...\n", - " $ V21 : int 0 0 0 1 1 0 1 1 0 0 ...\n", - " $ V22 : num 0.279 0.256 0.75 0.537 0.737 ...\n", - " $ V23 : num -1.421 2.789 -0.647 4.633 -3.566 ...\n", - " $ V24 : num 0.05559 0.01498 0.00637 0.05703 0.03166 ...\n", - " $ V25 : num 0.0403 0.0484 0.0693 0.1223 0.1016 ...\n", - " $ V26 : num 7.90e-05 8.59e-03 2.61e-05 8.09e-03 1.20e-03 ...\n", - " $ V27 : num -59 -20.4 -50.8 -58.7 -12.7 ...\n", - " $ V28 : int 20 7 16 27 14 10 23 10 19 18 ...\n", - " $ V29 : num 16.6 46.5 14.5 13.7 18.5 ...\n", - " $ V30 : num 34.7 21.7 25 25.5 28.6 ...\n", - " $ V31 : num 4.95 7.37 14.16 7.71 8.43 ...\n", - " $ V32 : num 0.175 0.431 0.826 -0.775 -0.961 ...\n", - " $ V33 : num 0.232 1.926 6.007 32.186 0.476 ...\n", - " $ V34 : num 2.07 1.83 1.77 1.87 1.39 ...\n", - " $ V35 : int 0 1 0 0 0 0 0 0 0 0 ...\n", - " $ V36 : num 20.06 28.06 11.85 20.51 9.66 ...\n", - " $ V37 : num 0.00044 0.00077 0.0018 0.00269 0.0024 ...\n", - " $ V38 : int 1 0 0 0 0 1 1 1 1 1 ...\n", - " $ V39 : num 0.481 2.161 1.018 2.384 0.241 ...\n", - " $ V40 : num 1.244 1.012 1.227 0.664 1.195 ...\n", - " $ V41 : int 5 12 8 15 8 7 17 8 16 25 ...\n", - " $ V42 : num 21.3 12.1 15.1 29.7 34.2 ...\n", - " $ V43 : int 1 0 0 0 1 1 0 1 1 0 ...\n", - " $ V44 : int 27 27 26 23 28 31 33 30 22 26 ...\n", - " $ V45 : int 1 1 0 1 0 0 0 0 1 0 ...\n", - " $ V46 : int 1 0 1 1 0 1 0 0 0 0 ...\n", - " $ V47 : num 20.79 24.43 19.13 6.96 20.87 ...\n", - " $ V48 : int 0 0 0 0 0 0 0 0 0 0 ...\n", - " $ V49 : int 1 0 1 1 1 0 1 0 1 1 ...\n", - " $ V50 : int 1 1 0 1 1 1 1 1 1 0 ...\n", - " $ V51 : num 0.5835 -0.8916 1.5197 -0.2097 -0.0912 ...\n", - " $ V52 : num 3.59 2.6 4.51 2.15 4.61 ...\n", - " $ V53 : int 1 1 1 1 1 1 1 1 0 1 ...\n", - " $ V54 : int 0 0 0 0 0 0 0 0 0 0 ...\n", - " $ V55 : int 0 1 1 0 1 0 0 0 0 0 ...\n", - " $ V56 : num 2.14 2.39 2.11 2.28 2.08 ...\n", - " $ V57 : int 0 1 1 0 0 0 0 0 1 0 ...\n", - " $ V58 : num -4.576 -0.215 -4.02 -4.183 -3.193 ...\n", - " $ V59 : num -2.339 0.591 2.002 -0.896 -0.636 ...\n", - " $ V60 : int 1 1 0 1 0 1 1 0 0 1 ...\n", - " $ V61 : num 1.14e-03 1.37e-05 2.30e-02 1.22e-03 8.93e-04 ...\n", - " $ V62 : num 11.5 11.3 10.7 12.1 10.8 ...\n", - " $ V63 : int 0 0 0 1 0 0 0 1 0 1 ...\n", - " $ V64 : int 4 2 2 5 0 2 6 1 1 2 ...\n", - " $ V65 : int 1 1 1 1 1 1 1 1 1 1 ...\n", - " $ V66 : int 1 0 0 0 0 0 0 1 0 0 ...\n", - " $ V67 : num 3.9 6.47 4.8 2.62 5.2 ...\n", - " $ V68 : num 177.5 70.2 28.4 19.8 55.4 ...\n", - " $ V69 : num -0.97783 -0.00815 -0.09309 0.29349 -0.32934 ...\n", - " $ V70 : num -15.66 2.43 -4.63 -12.2 -19.63 ...\n", - " $ V71 : num -0.3391 0.2509 0.4934 -0.32 -0.0074 ...\n", - " $ V72 : num -4.86 -4.88 -2.58 -4.52 -3.06 ...\n", - " $ V73 : num 46.8 44.3 59.1 11.2 12.2 ...\n", - " $ V74 : int 7 4 3 3 5 9 8 4 15 6 ...\n", - " $ V75 : num 27.4 23 21.7 25.3 23.3 ...\n", - " $ V76 : num -2.203 -0.976 -0.786 -0.288 0.368 ...\n", - " $ V77 : int 0 0 0 0 0 0 0 0 1 0 ...\n", - " $ V78 : int 6 7 11 14 7 5 11 11 14 12 ...\n", - " $ V79 : int 1 0 0 0 0 0 0 0 0 0 ...\n", - " $ V80 : num -0.9566 -0.9183 -0.9225 0.0593 -0.0718 ...\n", - " $ V81 : num 0.0563 0.0879 0.0654 0.1113 0.0547 ...\n", - " $ V82 : int 29 24 22 13 16 34 9 36 5 24 ...\n", - " $ V83 : int 0 0 0 0 0 0 1 0 0 0 ...\n", - " $ V84 : num 0.0374 0.0372 0.031 0.0354 0.0278 ...\n", - " $ V85 : num -0.15724 -0.13814 0.99698 -2.0978 0.00798 ...\n", - " $ V86 : num -0.195 1.19 -4.1359 -0.0292 0.5086 ...\n", - " $ V87 : int 0 0 0 0 0 0 0 0 0 0 ...\n", - " $ V88 : int 0 1 1 0 0 1 1 0 0 1 ...\n", - " $ V89 : int 17 17 22 8 14 11 18 20 11 20 ...\n", - " $ V90 : num 1.08 1.26 2.44 1.04 1.84 ...\n", - " $ V91 : int 1 1 0 0 1 0 0 1 1 0 ...\n", - " $ V92 : num 1.2526 -0.4946 -0.1259 1.0655 -0.0294 ...\n", - " $ V93 : int 0 0 0 0 0 0 0 0 0 0 ...\n", - " $ V94 : num 0.976 0.976 0.981 0.982 0.988 ...\n", - " $ V95 : int 5 6 6 4 4 5 5 3 6 7 ...\n", - " $ V96 : num 2.21 5.38 3.87 2.46 3.04 ...\n", - " $ V97 : num 1.27 1.25 1.28 1.29 1.16 ...\n", - " [list output truncated]\n", - " - attr(*, \".internal.selfref\")= \n" - ] - } - ], + "outputs": [], "source": [ "library(data.table)\n", "\n", "# Load data set from url (internet connection required)\n", - "url = \"https://raw.githubusercontent.com/DoubleML/doubleml-docs/p-add-ACIC-dataset/doc/examples/data/high42.CSV\"\n", + "url = \"https://raw.githubusercontent.com/DoubleML/doubleml-docs/master/doc/examples/data/high42.CSV\"\n", "df = fread(url)\n", "\n", "dim(df)\n", @@ -204,104 +68,20 @@ }, { "cell_type": "code", - "execution_count": 3, - "id": "d95977a0", + "execution_count": null, + "id": "de44224f", "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - 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A data.table: 6 × 202
YAV1V2V3V4V5V6V7V8...V191V192V193V194V195V196V197V198V199V200
<dbl><int><int><int><int><int><dbl><dbl><int><dbl>...<dbl><int><dbl><int><int><dbl><dbl><int><int><dbl>
7.358185110007192.793823.6769580.18544294...1.46283711627.274004.683956 0.5656669030.02433804
8.333672112014199.653619.2812770.51484172...1.33052211661.484106.766661-0.3954021040.05651780
7.472758014112194.207824.5893350.30919878...1.38415111658.939005.647794 1.1127661000.01344207
6.5023191 0109201.838025.5139240.16016010...1.22030311650.802005.370363-0.3058420040.03463235
7.043758112009201.360431.1606460.29197555...1.17009411676.819003.446532 2.4406606010.01751381
5.6583370 8016193.219520.4656490.05673076...1.80294511634.093105.294410 1.0869714100.04712806
\n" - ], - "text/latex": [ - "A data.table: 6 × 202\n", - "\\begin{tabular}{lllllllllllllllllllll}\n", - " Y & A & V1 & V2 & V3 & V4 & V5 & V6 & V7 & V8 & ... & V191 & V192 & V193 & V194 & V195 & V196 & V197 & V198 & V199 & V200\\\\\n", - " & & & & & & & & & & ... & & & & & & & & & & \\\\\n", - "\\hline\n", - "\t 7.358185 & 1 & 10 & 0 & 0 & 7 & 192.7938 & 23.67695 & 8 & 0.18544294 & ... & 1.462837 & 1 & 1627.274 & 0 & 0 & 4.683956 & 0.5656669 & 0 & 3 & 0.02433804\\\\\n", - "\t 8.333672 & 1 & 12 & 0 & 1 & 4 & 199.6536 & 19.28127 & 7 & 0.51484172 & ... & 1.330522 & 1 & 1661.484 & 1 & 0 & 6.766661 & -0.3954021 & 0 & 4 & 0.05651780\\\\\n", - "\t 7.472758 & 0 & 14 & 1 & 1 & 2 & 194.2078 & 24.58933 & 5 & 0.30919878 & ... & 1.384151 & 1 & 1658.939 & 0 & 0 & 5.647794 & 1.1127661 & 0 & 0 & 0.01344207\\\\\n", - "\t 6.502319 & 1 & 0 & 1 & 0 & 9 & 201.8380 & 25.51392 & 4 & 0.16016010 & ... & 1.220303 & 1 & 1650.802 & 0 & 0 & 5.370363 & -0.3058420 & 0 & 4 & 0.03463235\\\\\n", - "\t 7.043758 & 1 & 12 & 0 & 0 & 9 & 201.3604 & 31.16064 & 6 & 0.29197555 & ... & 1.170094 & 1 & 1676.819 & 0 & 0 & 3.446532 & 2.4406606 & 0 & 1 & 0.01751381\\\\\n", - "\t 5.658337 & 0 & 8 & 0 & 1 & 6 & 193.2195 & 20.46564 & 9 & 0.05673076 & ... & 1.802945 & 1 & 1634.093 & 1 & 0 & 5.294410 & 1.0869714 & 1 & 0 & 0.04712806\\\\\n", - "\\end{tabular}\n" - ], - "text/markdown": [ - "\n", - "A data.table: 6 × 202\n", - "\n", - "| Y <dbl> | A <int> | V1 <int> | V2 <int> | V3 <int> | V4 <int> | V5 <dbl> | V6 <dbl> | V7 <int> | V8 <dbl> | ... ... | V191 <dbl> | V192 <int> | V193 <dbl> | V194 <int> | V195 <int> | V196 <dbl> | V197 <dbl> | V198 <int> | V199 <int> | V200 <dbl> |\n", - "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n", - "| 7.358185 | 1 | 10 | 0 | 0 | 7 | 192.7938 | 23.67695 | 8 | 0.18544294 | ... | 1.462837 | 1 | 1627.274 | 0 | 0 | 4.683956 | 0.5656669 | 0 | 3 | 0.02433804 |\n", - "| 8.333672 | 1 | 12 | 0 | 1 | 4 | 199.6536 | 19.28127 | 7 | 0.51484172 | ... | 1.330522 | 1 | 1661.484 | 1 | 0 | 6.766661 | -0.3954021 | 0 | 4 | 0.05651780 |\n", - "| 7.472758 | 0 | 14 | 1 | 1 | 2 | 194.2078 | 24.58933 | 5 | 0.30919878 | ... | 1.384151 | 1 | 1658.939 | 0 | 0 | 5.647794 | 1.1127661 | 0 | 0 | 0.01344207 |\n", - "| 6.502319 | 1 | 0 | 1 | 0 | 9 | 201.8380 | 25.51392 | 4 | 0.16016010 | ... | 1.220303 | 1 | 1650.802 | 0 | 0 | 5.370363 | -0.3058420 | 0 | 4 | 0.03463235 |\n", - "| 7.043758 | 1 | 12 | 0 | 0 | 9 | 201.3604 | 31.16064 | 6 | 0.29197555 | ... | 1.170094 | 1 | 1676.819 | 0 | 0 | 3.446532 | 2.4406606 | 0 | 1 | 0.01751381 |\n", - "| 5.658337 | 0 | 8 | 0 | 1 | 6 | 193.2195 | 20.46564 | 9 | 0.05673076 | ... | 1.802945 | 1 | 1634.093 | 1 | 0 | 5.294410 | 1.0869714 | 1 | 0 | 0.04712806 |\n", - "\n" - ], - "text/plain": [ - " Y A V1 V2 V3 V4 V5 V6 V7 V8 ... V191 V192\n", - "1 7.358185 1 10 0 0 7 192.7938 23.67695 8 0.18544294 ... 1.462837 1 \n", - "2 8.333672 1 12 0 1 4 199.6536 19.28127 7 0.51484172 ... 1.330522 1 \n", - "3 7.472758 0 14 1 1 2 194.2078 24.58933 5 0.30919878 ... 1.384151 1 \n", - "4 6.502319 1 0 1 0 9 201.8380 25.51392 4 0.16016010 ... 1.220303 1 \n", - "5 7.043758 1 12 0 0 9 201.3604 31.16064 6 0.29197555 ... 1.170094 1 \n", - "6 5.658337 0 8 0 1 6 193.2195 20.46564 9 0.05673076 ... 1.802945 1 \n", - " V193 V194 V195 V196 V197 V198 V199 V200 \n", - "1 1627.274 0 0 4.683956 0.5656669 0 3 0.02433804\n", - "2 1661.484 1 0 6.766661 -0.3954021 0 4 0.05651780\n", - "3 1658.939 0 0 5.647794 1.1127661 0 0 0.01344207\n", - "4 1650.802 0 0 5.370363 -0.3058420 0 4 0.03463235\n", - "5 1676.819 0 0 3.446532 2.4406606 0 1 0.01751381\n", - "6 1634.093 1 0 5.294410 1.0869714 1 0 0.04712806" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "head(df)" ] }, { "cell_type": "code", - "execution_count": 6, - "id": "e8698562", + "execution_count": null, + "id": "9dfd175f", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "plot without title" - ] - }, - "metadata": { - "image/png": { - "height": 420, - "width": 420 - } - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "hist_A = ggplot(df, aes(x = A, fill = factor(A))) +\n", " geom_bar() + theme_minimal() +\n", @@ -313,73 +93,10 @@ }, { "cell_type": "code", - "execution_count": 16, - "id": "9aa1164a", + "execution_count": null, + "id": "db7bb648", "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\t\n", - "\t\n", - "\n", - "\n", - "\t\n", - "\t\n", - "\n", - "
A data.table: 2 × 2
AV1
<int><dbl>
17.953744
06.836141
\n" - ], - "text/latex": [ - "A data.table: 2 × 2\n", - "\\begin{tabular}{ll}\n", - " A & V1\\\\\n", - " & \\\\\n", - "\\hline\n", - "\t 1 & 7.953744\\\\\n", - "\t 0 & 6.836141\\\\\n", - "\\end{tabular}\n" - ], - "text/markdown": [ - "\n", - "A data.table: 2 × 2\n", - "\n", - "| A <int> | V1 <dbl> |\n", - "|---|---|\n", - "| 1 | 7.953744 |\n", - "| 0 | 6.836141 |\n", - "\n" - ], - "text/plain": [ - " A V1 \n", - "1 1 7.953744\n", - "2 0 6.836141" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/html": [ - "1.11760295064719" - ], - "text/latex": [ - "1.11760295064719" - ], - "text/markdown": [ - "1.11760295064719" - ], - "text/plain": [ - "[1] 1.117603" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "# Unconditional ATE\n", "df[, mean(Y), by = A]\n", @@ -390,7 +107,7 @@ }, { "cell_type": "markdown", - "id": "479cd6f7", + "id": "ba6d8966", "metadata": {}, "source": [ "### `DoubleMLData`\n" @@ -398,8 +115,8 @@ }, { "cell_type": "code", - "execution_count": 24, - "id": "ea2df013", + "execution_count": null, + "id": "f47d2ff4", "metadata": {}, "outputs": [], "source": [ @@ -412,33 +129,17 @@ }, { "cell_type": "code", - "execution_count": 25, - "id": "c98e3ec1", + "execution_count": null, + "id": "da97cdfc", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "================= DoubleMLData Object ==================\n", - "\n", - "\n", - "------------------ Data summary ------------------\n", - "Outcome variable: Y\n", - "Treatment variable(s): A\n", - "Covariates: V1, V2, V3, V4, V5, V6, V7, V8, V9, V10, V11, V12, V13, V14, V15, V16, V17, V18, V19, V20, V21, V22, V23, V24, V25, V26, V27, V28, V29, V30, V31, V32, V33, V34, V35, V36, V37, V38, V39, V40, V41, V42, V43, V44, V45, V46, V47, V48, V49, V50, V51, V52, V53, V54, V55, V56, V57, V58, V59, V60, V61, V62, V63, V64, V65, V66, V67, V68, V69, V70, V71, V72, V73, V74, V75, V76, V77, V78, V79, V80, V81, V82, V83, V84, V85, V86, V87, V88, V89, V90, V91, V92, V93, V94, V95, V96, V97, V98, V99, V100, V101, V102, V103, V104, V105, V106, V107, V108, V109, V110, V111, V112, V113, V114, V115, V116, V117, V118, V119, V120, V121, V122, V123, V124, V125, V126, V127, V128, V129, V130, V131, V132, V133, V134, V135, V136, V137, V138, V139, V140, V141, V142, V143, V144, V145, V146, V147, V148, V149, V150, V151, V152, V153, V154, V155, V156, V157, V158, V159, V160, V161, V162, V163, V164, V165, V166, V167, V168, V169, V170, V171, V172, V173, V174, V175, V176, V177, V178, V179, V180, V181, V182, V183, V184, V185, V186, V187, V188, V189, V190, V191, V192, V193, V194, V195, V196, V197, V198, V199, V200\n", - "Instrument(s): \n", - "No. Observations: 1000\n" - ] - } - ], + "outputs": [], "source": [ "print(data_dml)" ] }, { "cell_type": "markdown", - "id": "b56ad806", + "id": "f5def2d2", "metadata": {}, "source": [ "### IRM\n" @@ -446,8 +147,8 @@ }, { "cell_type": "code", - "execution_count": 26, - "id": "df43c333", + "execution_count": null, + "id": "6e6f3e7e", "metadata": {}, "outputs": [], "source": [ @@ -460,7 +161,7 @@ }, { "cell_type": "markdown", - "id": "03501b58", + "id": "298e6587", "metadata": {}, "source": [ "### Benchmark: Model based on Linear and Logistic Regression" @@ -468,35 +169,10 @@ }, { "cell_type": "code", - "execution_count": 17, - "id": "98545886", + "execution_count": null, + "id": "f54e401e", "metadata": {}, - "outputs": [ - { - "ename": "ERROR", - "evalue": "Error in sort(assert_subset(properties, mlr_reflections$learner_properties[[task_type]])): Assertion on 'properties' failed: Must be a subset of {'featureless','missings','weights','importance','selected_features','oob_error'}, but is {'weights','loglik'}.\n", - "output_type": "error", - "traceback": [ - "Error in sort(assert_subset(properties, mlr_reflections$learner_properties[[task_type]])): Assertion on 'properties' failed: Must be a subset of {'featureless','missings','weights','importance','selected_features','oob_error'}, but is {'weights','loglik'}.\nTraceback:\n", - "1. lrn(\"regr.lm\")", - "2. dictionary_sugar_get(mlr_learners, .key, ...)", - "3. dictionary_get(dict, .key)", - "4. dictionary_initialize_item(key, obj, dots)", - "5. do.call(constructor$new, cargs)", - "6. (function (...) \n . {\n . inherit <- get_inherit()\n . if (!is.null(inherit)) {\n . if (!inherits(inherit, \"R6ClassGenerator\")) \n . stop(\"`inherit` must be a R6ClassGenerator.\")\n . if (!identical(portable, inherit$portable)) \n . stop(\"Sub and superclass must both be portable or non-portable.\")\n . recursive_merge <- function(obj, which) {\n . if (is.null(obj)) \n . return(NULL)\n . merge_vectors(recursive_merge(obj$get_inherit(), \n . which), obj[[which]])\n . }\n . public_fields <- merge_vectors(recursive_merge(inherit, \n . \"public_fields\"), public_fields)\n . private_fields <- merge_vectors(recursive_merge(inherit, \n . \"private_fields\"), private_fields)\n . }\n . if (class) {\n . classes <- c(classname, get_superclassnames(inherit), \n . \"R6\")\n . }\n . else {\n . classes <- NULL\n . }\n . has_priv <- has_private()\n . if (portable) {\n . if (has_priv) \n . private_bind_env <- new.env(parent = emptyenv(), \n . hash = FALSE)\n . else private_bind_env <- NULL\n . public_bind_env <- new.env(parent = emptyenv(), hash = FALSE)\n . enclos_env <- new.env(parent = parent_env, hash = FALSE)\n . }\n . else {\n . if (has_priv) {\n . private_bind_env <- new.env(parent = parent_env, \n . hash = FALSE)\n . public_bind_env <- new.env(parent = private_bind_env, \n . hash = FALSE)\n . }\n . else {\n . private_bind_env <- NULL\n . public_bind_env <- new.env(parent = parent_env, hash = FALSE)\n . }\n . enclos_env <- public_bind_env\n . }\n . enclos_env$self <- public_bind_env\n . if (has_priv) \n . enclos_env$private <- private_bind_env\n . public_methods <- assign_func_envs(public_methods, enclos_env)\n . if (has_priv) \n . private_methods <- assign_func_envs(private_methods, \n . enclos_env)\n . if (!is.null(active)) \n . active <- assign_func_envs(active, enclos_env)\n . if (length(debug_names) > 0) {\n . lapply(public_methods[names(public_methods) %in% debug_names], \n . base::debug)\n . lapply(private_methods[names(private_methods) %in% debug_names], \n . base::debug)\n . lapply(active[names(active) %in% debug_names], base::debug)\n . }\n . if (!is.null(inherit)) {\n . if (portable) {\n . super_struct <- create_super_env(inherit, public_bind_env, \n . private_bind_env, portable = TRUE, cloneable = cloneable)\n . }\n . else {\n . super_struct <- create_super_env(inherit, public_bind_env, \n . portable = FALSE, cloneable = cloneable)\n . }\n . enclos_env$super <- super_struct$bind_env\n . public_methods <- merge_vectors(super_struct$public_methods, \n . public_methods)\n . private_methods <- merge_vectors(super_struct$private_methods, \n . private_methods)\n . active <- merge_vectors(super_struct$active, active)\n . }\n . list2env2(public_methods, envir = public_bind_env)\n . list2env2(public_fields, envir = public_bind_env)\n . if (has_priv) {\n . list2env2(private_methods, envir = private_bind_env)\n . list2env2(private_fields, envir = private_bind_env)\n . }\n . if (!is.null(active)) {\n . for (name in names(active)) {\n . makeActiveBinding(name, active[[name]], public_bind_env)\n . }\n . enclos_env$.__active__ <- active\n . }\n . public_bind_env$.__enclos_env__ <- enclos_env\n . if (lock_objects) {\n . if (has_priv) \n . lockEnvironment(private_bind_env)\n . lockEnvironment(public_bind_env)\n . }\n . if (has_priv) {\n . for (name in names(private_methods)) lockBinding(name, \n . private_bind_env)\n . }\n . for (name in names(public_methods)) lockBinding(name, public_bind_env)\n . class(public_bind_env) <- classes\n . initialize <- .subset2(public_bind_env, \"initialize\")\n . if (is.function(initialize)) {\n . initialize(...)\n . }\n . else if (length(list(...)) != 0) {\n . stop(\"Called new() with arguments, but there is no initialize method.\")\n . }\n . if (is.function(.subset2(public_bind_env, \"finalize\"))) {\n . finalizer_wrapper <- function(e) {\n . .subset2(e, \"finalize\")()\n . }\n . environment(finalizer_wrapper) <- baseenv()\n . reg.finalizer(public_bind_env, finalizer_wrapper, onexit = TRUE)\n . }\n . if (has_priv) {\n . if (is.function(.subset2(private_bind_env, \"finalize\"))) {\n . finalizer_wrapper <- function(e) {\n . .subset2(e, \".__enclos_env__\")$private$finalize()\n . }\n . environment(finalizer_wrapper) <- baseenv()\n . reg.finalizer(public_bind_env, finalizer_wrapper, \n . onexit = TRUE)\n . }\n . }\n . public_bind_env\n . })()", - "7. initialize(...)", - "8. .__LearnerRegrLM__initialize(self = self, private = private, \n . super = super)", - "9. super$initialize(id = \"regr.lm\", param_set = ps, predict_types = c(\"response\", \n . \"se\"), feature_types = c(\"logical\", \"integer\", \"numeric\", \n . \"factor\", \"character\"), properties = c(\"weights\", \"loglik\"), \n . packages = \"stats\", man = \"mlr3learners::mlr_learners_regr.lm\")", - "10. .__LearnerRegr__initialize(self = self, private = private, super = super, \n . id = id, param_set = param_set, predict_types = predict_types, \n . feature_types = feature_types, properties = properties, data_formats = data_formats, \n . packages = packages, man = man)", - "11. super$initialize(id = id, task_type = \"regr\", param_set = param_set, \n . feature_types = feature_types, predict_types = predict_types, \n . properties = properties, data_formats = data_formats, packages = packages, \n . man = man)", - "12. .__Learner__initialize(self = self, private = private, super = super, \n . id = id, task_type = task_type, param_set = param_set, predict_types = predict_types, \n . feature_types = feature_types, properties = properties, data_formats = data_formats, \n . packages = packages, man = man)", - "13. sort(assert_subset(properties, mlr_reflections$learner_properties[[task_type]]))", - "14. assert_subset(properties, mlr_reflections$learner_properties[[task_type]])", - "15. makeAssertion(x, res, .var.name, add)", - "16. mstop(\"Assertion on '%s' failed: %s.\", var.name, res, call. = sys.call(-2L))" - ] - } - ], + "outputs": [], "source": [ "linreg = lrn(\"regr.lm\")\n", "logreg_class = lrn(\"classif.log_reg\")\n", @@ -516,7 +192,7 @@ { "cell_type": "code", "execution_count": null, - "id": "883562c1", + "id": "66395583", "metadata": {}, "outputs": [], "source": [ @@ -527,7 +203,7 @@ }, { "cell_type": "markdown", - "id": "560d5fc5", + "id": "48d090c3", "metadata": {}, "source": [ "### Double Machine Learning based on Lasso\n" @@ -535,24 +211,10 @@ }, { "cell_type": "code", - "execution_count": 18, - "id": "a7c55597", + "execution_count": null, + "id": "87c8980b", "metadata": {}, - "outputs": [ - { - "ename": "ERROR", - "evalue": "Error in checkClass(x, classes, ordered, null.ok): Objekt 'data_dml' nicht gefunden\n", - "output_type": "error", - "traceback": [ - "Error in checkClass(x, classes, ordered, null.ok): Objekt 'data_dml' nicht gefunden\nTraceback:\n", - "1. DoubleMLIRM$new(data_dml, ml_g = lasso, ml_m = lasso_class, trimming_threshold = 0.025, \n . n_folds = 3, n_rep = 3)", - "2. initialize(...)", - "3. super$initialize_double_ml(data, n_folds, n_rep, score, dml_procedure, \n . draw_sample_splitting, apply_cross_fitting)", - "4. assert_class(data, \"DoubleMLData\")", - "5. checkClass(x, classes, ordered, null.ok)" - ] - } - ], + "outputs": [], "source": [ "lasso = lrn(\"regr.cv_glmnet\", nfolds = 5, s = \"lambda.min\")\n", "lasso_class = lrn(\"classif.cv_glmnet\", nfolds = 5, s = \"lambda.min\")\n", @@ -572,8 +234,8 @@ }, { "cell_type": "code", - "execution_count": 19, - "id": "15c8afb3", + "execution_count": null, + "id": "4e6cf3d1", "metadata": {}, "outputs": [], "source": [ @@ -584,7 +246,7 @@ }, { "cell_type": "markdown", - "id": "e5099672", + "id": "faf4e463", "metadata": {}, "source": [ "### Double Machine Learning based on Random Forest\n" @@ -592,24 +254,10 @@ }, { "cell_type": "code", - "execution_count": 20, - "id": "6c3530e5", + "execution_count": null, + "id": "2440821d", "metadata": {}, - "outputs": [ - { - "ename": "ERROR", - "evalue": "Error in checkClass(x, classes, ordered, null.ok): Objekt 'data_dml' nicht gefunden\n", - "output_type": "error", - "traceback": [ - "Error in checkClass(x, classes, ordered, null.ok): Objekt 'data_dml' nicht gefunden\nTraceback:\n", - "1. DoubleMLIRM$new(data_dml, ml_g = randomForest, ml_m = randomForest_class, \n . trimming_threshold = 0.025, n_folds = 3, n_rep = 3)", - "2. initialize(...)", - "3. super$initialize_double_ml(data, n_folds, n_rep, score, dml_procedure, \n . draw_sample_splitting, apply_cross_fitting)", - "4. assert_class(data, \"DoubleMLData\")", - "5. checkClass(x, classes, ordered, null.ok)" - ] - } - ], + "outputs": [], "source": [ "randomForest = lrn(\"regr.ranger\")\n", "randomForest_class = lrn(\"classif.ranger\")\n", @@ -640,7 +288,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6c63aae2", + "id": "1d45095a", "metadata": {}, "outputs": [], "source": [ @@ -651,7 +299,7 @@ }, { "cell_type": "markdown", - "id": "98447b3b", + "id": "b096eba1", "metadata": {}, "source": [ "### Double Machine Learning based on Extreme Gradient Boosting" @@ -660,7 +308,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3991105c", + "id": "6c3d8997", "metadata": {}, "outputs": [], "source": [ @@ -695,7 +343,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2193503d", + "id": "cdc65bb8", "metadata": {}, "outputs": [], "source": [ @@ -706,7 +354,7 @@ }, { "cell_type": "markdown", - "id": "f2214f23", + "id": "075b9855", "metadata": {}, "source": [ "#### IRM - Summary of coefficient estimates\n", @@ -715,8 +363,8 @@ }, { "cell_type": "code", - "execution_count": 21, - "id": "3f805daa", + "execution_count": null, + "id": "745b2019", "metadata": {}, "outputs": [], "source": [ @@ -726,7 +374,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ae0d545f", + "id": "3a904584", "metadata": {}, "outputs": [], "source": [ @@ -735,7 +383,7 @@ }, { "cell_type": "markdown", - "id": "9ee7a793", + "id": "5febe706", "metadata": {}, "source": [ "#### IRM - Summary of prediction assessment metric's mean values" @@ -743,8 +391,8 @@ }, { "cell_type": "code", - "execution_count": 23, - "id": "c1a10e33", + "execution_count": null, + "id": "3bfe8758", "metadata": {}, "outputs": [], "source": [ @@ -753,8 +401,8 @@ }, { "cell_type": "code", - "execution_count": 24, - "id": "97b9a1c8", + "execution_count": null, + "id": "29ec4bb9", "metadata": {}, "outputs": [], "source": [ @@ -763,7 +411,7 @@ }, { "cell_type": "markdown", - "id": "29e91c0b", + "id": "06ec4742", "metadata": {}, "source": [ "### Inspection of the benchmark model\n" @@ -772,7 +420,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3cc70b60", + "id": "94995240", "metadata": {}, "outputs": [], "source": [ @@ -785,7 +433,7 @@ }, { "cell_type": "markdown", - "id": "c05e662c", + "id": "864d4189", "metadata": {}, "source": [ "## 2. Partially Linear Regression Model (PLR)\n" @@ -794,7 +442,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fb1157a1", + "id": "4eefbc39", "metadata": {}, "outputs": [], "source": [ @@ -807,7 +455,7 @@ }, { "cell_type": "markdown", - "id": "d103856e", + "id": "03cb136d", "metadata": {}, "source": [ "### Benchmark: Model based on Linear and Logistic Regression" @@ -816,7 +464,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6f60eac3", + "id": "d975bf67", "metadata": {}, "outputs": [], "source": [ @@ -838,7 +486,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5a418036", + "id": "87378077", "metadata": {}, "outputs": [], "source": [ @@ -849,7 +497,7 @@ }, { "cell_type": "markdown", - "id": "8a7e424f", + "id": "28a11ba0", "metadata": {}, "source": [ "### Double Machine Learning based on Lasso" @@ -857,24 +505,10 @@ }, { "cell_type": "code", - "execution_count": 25, - "id": "094dfed2", + "execution_count": null, + "id": "5dbb3a41", "metadata": {}, - "outputs": [ - { - "ename": "ERROR", - "evalue": "Error in checkClass(x, classes, ordered, null.ok): Objekt 'data_dml' nicht gefunden\n", - "output_type": "error", - "traceback": [ - "Error in checkClass(x, classes, ordered, null.ok): Objekt 'data_dml' nicht gefunden\nTraceback:\n", - "1. DoubleMLPLR$new(data_dml, ml_g = lasso, ml_m = lasso_class, n_folds = 3, \n . n_rep = 3)", - "2. initialize(...)", - "3. super$initialize_double_ml(data, n_folds, n_rep, score, dml_procedure, \n . draw_sample_splitting, apply_cross_fitting)", - "4. assert_class(data, \"DoubleMLData\")", - "5. checkClass(x, classes, ordered, null.ok)" - ] - } - ], + "outputs": [], "source": [ "lasso = lrn(\"regr.cv_glmnet\", nfolds = 5, s = \"lambda.min\")\n", "lasso_class = lrn(\"classif.cv_glmnet\", nfolds = 5, s = \"lambda.min\")\n", @@ -894,7 +528,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dd4ae562", + "id": "eaae3cdd", "metadata": {}, "outputs": [], "source": [ @@ -905,7 +539,7 @@ }, { "cell_type": "markdown", - "id": "4fbbead6", + "id": "0f4008fe", "metadata": {}, "source": [ "### Double Machine Learning based on Random Forests" @@ -914,7 +548,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a11f82d7", + "id": "8196ae92", "metadata": {}, "outputs": [], "source": [ @@ -935,8 +569,8 @@ }, { "cell_type": "code", - "execution_count": 26, - "id": "480064a1", + "execution_count": null, + "id": "e39d558c", "metadata": {}, "outputs": [], "source": [ @@ -947,7 +581,7 @@ }, { "cell_type": "markdown", - "id": "b9ed9bcb", + "id": "f3134af7", "metadata": {}, "source": [ "### Double Machine Learning based on Extreme Gradient Boosting" @@ -956,7 +590,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b63e2bd8", + "id": "ba38cc5a", "metadata": {}, "outputs": [], "source": [ @@ -983,7 +617,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8a75616e", + "id": "076c36ce", "metadata": {}, "outputs": [], "source": [ @@ -994,7 +628,7 @@ }, { "cell_type": "markdown", - "id": "4c1076db", + "id": "1da3faf4", "metadata": {}, "source": [ "#### PLR - Summary of coefficient estimates" @@ -1003,25 +637,55 @@ { "cell_type": "code", "execution_count": null, - "id": "53aba28d", + "id": "4ed09f8f", "metadata": {}, "outputs": [], "source": [ - "# TODO: Summary" + "# TODO: Add summary of results\n" ] }, { "cell_type": "code", "execution_count": null, - "id": "a9534744", + "id": "f5de3006", "metadata": {}, "outputs": [], - "source": [] + "source": [ + "# TODO: Add visualization of summary\n" + ] + }, + { + "cell_type": "markdown", + "id": "6794e320", + "metadata": {}, + "source": [ + "#### PLR - Summary of prediction assessment metric's mean values\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "19e14bd1", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Add comparison/summary for predictive accuracy (nuisance)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "27426c91", + "metadata": {}, + "outputs": [], + "source": [ + "# TODO: Add visualization of summary\n" + ] }, { "cell_type": "code", "execution_count": null, - "id": "2137028e", + "id": "8b2aac6e", "metadata": {}, "outputs": [], "source": [] diff --git a/doc/examples/py_double_ml_abtest.ipynb b/doc/examples/py_double_ml_abtest.ipynb index 46d9cb25..4e514125 100644 --- a/doc/examples/py_double_ml_abtest.ipynb +++ b/doc/examples/py_double_ml_abtest.ipynb @@ -80,7 +80,7 @@ "import pandas as pd\n", "\n", "# Load data set from url (internet connection required)\n", - "url = 'https://raw.githubusercontent.com/DoubleML/doubleml-docs/p-add-ACIC-dataset/doc/examples/data/high42.CSV'\n", + "url = 'https://raw.githubusercontent.com/DoubleML/doubleml-docs/master/doc/examples/data/high42.CSV'\n", "df = pd.read_csv(url)" ] }, From 411f024f2c2222c98b70ccd24d510741cff63316 Mon Sep 17 00:00:00 2001 From: Philipp Bach Date: Thu, 2 Jun 2022 20:08:17 +0200 Subject: [PATCH 19/20] fix bug in benchmark PLR --- doc/examples/R_double_ml_abtest.ipynb | 373 ++++++++++++++++++++++++-- 1 file changed, 355 insertions(+), 18 deletions(-) diff --git a/doc/examples/R_double_ml_abtest.ipynb b/doc/examples/R_double_ml_abtest.ipynb index fdebcb84..30ea1992 100644 --- a/doc/examples/R_double_ml_abtest.ipynb +++ b/doc/examples/R_double_ml_abtest.ipynb @@ -49,13 +49,149 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "id": "edbdeffd", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
  1. 1000
  2. 202
\n" + ], + "text/latex": [ + "\\begin{enumerate*}\n", + "\\item 1000\n", + "\\item 202\n", + "\\end{enumerate*}\n" + ], + "text/markdown": [ + "1. 1000\n", + "2. 202\n", + "\n", + "\n" + ], + "text/plain": [ + "[1] 1000 202" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Classes 'data.table' and 'data.frame':\t1000 obs. of 202 variables:\n", + " $ Y : num 7.36 8.33 7.47 6.5 7.04 ...\n", + " $ A : int 1 1 0 1 1 0 0 1 0 0 ...\n", + " $ V1 : int 10 12 14 0 12 8 10 9 11 15 ...\n", + " $ V2 : int 0 0 1 1 0 0 1 1 0 1 ...\n", + " $ V3 : int 0 1 1 0 0 1 1 1 1 1 ...\n", + " $ V4 : int 7 4 2 9 9 6 6 6 11 7 ...\n", + " $ V5 : num 193 200 194 202 201 ...\n", + " $ V6 : num 23.7 19.3 24.6 25.5 31.2 ...\n", + " $ V7 : int 8 7 5 4 6 9 2 4 7 2 ...\n", + " $ V8 : num 0.185 0.515 0.309 0.16 0.292 ...\n", + " $ V9 : num 15.85 9.24 10.79 22.64 25.79 ...\n", + " $ V10 : int 6 5 4 8 3 6 5 4 9 4 ...\n", + " $ V11 : int 1 0 1 0 1 1 1 1 1 1 ...\n", + " $ V12 : int 0 0 0 1 1 0 1 0 0 1 ...\n", + " $ V13 : num 0.201 0.223 0.175 0.149 0.138 ...\n", + " $ V14 : num 1.17 -1.537 -1.285 0.348 0.345 ...\n", + " $ V15 : num 1.22 1.12 1.27 1.14 1.3 ...\n", + " $ V16 : num -16.8 -15.1 -27.8 -15.8 -30.3 ...\n", + " $ V17 : num 8.07 4.48 6.19 4.75 7.79 ...\n", + " $ V18 : int 1 0 1 0 0 0 1 0 0 1 ...\n", + " $ V19 : num 1.04 -0.542 1.021 1.227 1.655 ...\n", + " $ V20 : int 30 -1 59 25 8 25 -1 -9 43 41 ...\n", + " $ V21 : int 0 0 0 1 1 0 1 1 0 0 ...\n", + " $ V22 : num 0.279 0.256 0.75 0.537 0.737 ...\n", + " $ V23 : num -1.421 2.789 -0.647 4.633 -3.566 ...\n", + " $ V24 : num 0.05559 0.01498 0.00637 0.05703 0.03166 ...\n", + " $ V25 : num 0.0403 0.0484 0.0693 0.1223 0.1016 ...\n", + " $ V26 : num 7.90e-05 8.59e-03 2.61e-05 8.09e-03 1.20e-03 ...\n", + " $ V27 : num -59 -20.4 -50.8 -58.7 -12.7 ...\n", + " $ V28 : int 20 7 16 27 14 10 23 10 19 18 ...\n", + " $ V29 : num 16.6 46.5 14.5 13.7 18.5 ...\n", + " $ V30 : num 34.7 21.7 25 25.5 28.6 ...\n", + " $ V31 : num 4.95 7.37 14.16 7.71 8.43 ...\n", + " $ V32 : num 0.175 0.431 0.826 -0.775 -0.961 ...\n", + " $ V33 : num 0.232 1.926 6.007 32.186 0.476 ...\n", + " $ V34 : num 2.07 1.83 1.77 1.87 1.39 ...\n", + " $ V35 : int 0 1 0 0 0 0 0 0 0 0 ...\n", + " $ V36 : num 20.06 28.06 11.85 20.51 9.66 ...\n", + " $ V37 : num 0.00044 0.00077 0.0018 0.00269 0.0024 ...\n", + " $ V38 : int 1 0 0 0 0 1 1 1 1 1 ...\n", + " $ V39 : num 0.481 2.161 1.018 2.384 0.241 ...\n", + " $ V40 : num 1.244 1.012 1.227 0.664 1.195 ...\n", + " $ V41 : int 5 12 8 15 8 7 17 8 16 25 ...\n", + " $ V42 : num 21.3 12.1 15.1 29.7 34.2 ...\n", + " $ V43 : int 1 0 0 0 1 1 0 1 1 0 ...\n", + " $ V44 : int 27 27 26 23 28 31 33 30 22 26 ...\n", + " $ V45 : int 1 1 0 1 0 0 0 0 1 0 ...\n", + " $ V46 : int 1 0 1 1 0 1 0 0 0 0 ...\n", + " $ V47 : num 20.79 24.43 19.13 6.96 20.87 ...\n", + " $ V48 : int 0 0 0 0 0 0 0 0 0 0 ...\n", + " $ V49 : int 1 0 1 1 1 0 1 0 1 1 ...\n", + " $ V50 : int 1 1 0 1 1 1 1 1 1 0 ...\n", + " $ V51 : num 0.5835 -0.8916 1.5197 -0.2097 -0.0912 ...\n", + " $ V52 : num 3.59 2.6 4.51 2.15 4.61 ...\n", + " $ V53 : int 1 1 1 1 1 1 1 1 0 1 ...\n", + " $ V54 : int 0 0 0 0 0 0 0 0 0 0 ...\n", + " $ V55 : int 0 1 1 0 1 0 0 0 0 0 ...\n", + " $ V56 : num 2.14 2.39 2.11 2.28 2.08 ...\n", + " $ V57 : int 0 1 1 0 0 0 0 0 1 0 ...\n", + " $ V58 : num -4.576 -0.215 -4.02 -4.183 -3.193 ...\n", + " $ V59 : num -2.339 0.591 2.002 -0.896 -0.636 ...\n", + " $ V60 : int 1 1 0 1 0 1 1 0 0 1 ...\n", + " $ V61 : num 1.14e-03 1.37e-05 2.30e-02 1.22e-03 8.93e-04 ...\n", + " $ V62 : num 11.5 11.3 10.7 12.1 10.8 ...\n", + " $ V63 : int 0 0 0 1 0 0 0 1 0 1 ...\n", + " $ V64 : int 4 2 2 5 0 2 6 1 1 2 ...\n", + " $ V65 : int 1 1 1 1 1 1 1 1 1 1 ...\n", + " $ V66 : int 1 0 0 0 0 0 0 1 0 0 ...\n", + " $ V67 : num 3.9 6.47 4.8 2.62 5.2 ...\n", + " $ V68 : num 177.5 70.2 28.4 19.8 55.4 ...\n", + " $ V69 : num -0.97783 -0.00815 -0.09309 0.29349 -0.32934 ...\n", + " $ V70 : num -15.66 2.43 -4.63 -12.2 -19.63 ...\n", + " $ V71 : num -0.3391 0.2509 0.4934 -0.32 -0.0074 ...\n", + " $ V72 : num -4.86 -4.88 -2.58 -4.52 -3.06 ...\n", + " $ V73 : num 46.8 44.3 59.1 11.2 12.2 ...\n", + " $ V74 : int 7 4 3 3 5 9 8 4 15 6 ...\n", + " $ V75 : num 27.4 23 21.7 25.3 23.3 ...\n", + " $ V76 : num -2.203 -0.976 -0.786 -0.288 0.368 ...\n", + " $ V77 : int 0 0 0 0 0 0 0 0 1 0 ...\n", + " $ V78 : int 6 7 11 14 7 5 11 11 14 12 ...\n", + " $ V79 : int 1 0 0 0 0 0 0 0 0 0 ...\n", + " $ V80 : num -0.9566 -0.9183 -0.9225 0.0593 -0.0718 ...\n", + " $ V81 : num 0.0563 0.0879 0.0654 0.1113 0.0547 ...\n", + " $ V82 : int 29 24 22 13 16 34 9 36 5 24 ...\n", + " $ V83 : int 0 0 0 0 0 0 1 0 0 0 ...\n", + " $ V84 : num 0.0374 0.0372 0.031 0.0354 0.0278 ...\n", + " $ V85 : num -0.15724 -0.13814 0.99698 -2.0978 0.00798 ...\n", + " $ V86 : num -0.195 1.19 -4.1359 -0.0292 0.5086 ...\n", + " $ V87 : int 0 0 0 0 0 0 0 0 0 0 ...\n", + " $ V88 : int 0 1 1 0 0 1 1 0 0 1 ...\n", + " $ V89 : int 17 17 22 8 14 11 18 20 11 20 ...\n", + " $ V90 : num 1.08 1.26 2.44 1.04 1.84 ...\n", + " $ V91 : int 1 1 0 0 1 0 0 1 1 0 ...\n", + " $ V92 : num 1.2526 -0.4946 -0.1259 1.0655 -0.0294 ...\n", + " $ V93 : int 0 0 0 0 0 0 0 0 0 0 ...\n", + " $ V94 : num 0.976 0.976 0.981 0.982 0.988 ...\n", + " $ V95 : int 5 6 6 4 4 5 5 3 6 7 ...\n", + " $ V96 : num 2.21 5.38 3.87 2.46 3.04 ...\n", + " $ V97 : num 1.27 1.25 1.28 1.29 1.16 ...\n", + " [list output truncated]\n", + " - attr(*, \".internal.selfref\")= \n" + ] + } + ], "source": [ - "library(data.table)\n", - "\n", "# Load data set from url (internet connection required)\n", "url = \"https://raw.githubusercontent.com/DoubleML/doubleml-docs/master/doc/examples/data/high42.CSV\"\n", "df = fread(url)\n", @@ -68,20 +204,104 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "id": "de44224f", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.table: 6 × 202
YAV1V2V3V4V5V6V7V8...V191V192V193V194V195V196V197V198V199V200
<dbl><int><int><int><int><int><dbl><dbl><int><dbl>...<dbl><int><dbl><int><int><dbl><dbl><int><int><dbl>
7.358185110007192.793823.6769580.18544294...1.46283711627.274004.683956 0.5656669030.02433804
8.333672112014199.653619.2812770.51484172...1.33052211661.484106.766661-0.3954021040.05651780
7.472758014112194.207824.5893350.30919878...1.38415111658.939005.647794 1.1127661000.01344207
6.5023191 0109201.838025.5139240.16016010...1.22030311650.802005.370363-0.3058420040.03463235
7.043758112009201.360431.1606460.29197555...1.17009411676.819003.446532 2.4406606010.01751381
5.6583370 8016193.219520.4656490.05673076...1.80294511634.093105.294410 1.0869714100.04712806
\n" + ], + "text/latex": [ + "A data.table: 6 × 202\n", + "\\begin{tabular}{lllllllllllllllllllll}\n", + " Y & A & V1 & V2 & V3 & V4 & V5 & V6 & V7 & V8 & ... & V191 & V192 & V193 & V194 & V195 & V196 & V197 & V198 & V199 & V200\\\\\n", + " & & & & & & & & & & ... & & & & & & & & & & \\\\\n", + "\\hline\n", + "\t 7.358185 & 1 & 10 & 0 & 0 & 7 & 192.7938 & 23.67695 & 8 & 0.18544294 & ... & 1.462837 & 1 & 1627.274 & 0 & 0 & 4.683956 & 0.5656669 & 0 & 3 & 0.02433804\\\\\n", + "\t 8.333672 & 1 & 12 & 0 & 1 & 4 & 199.6536 & 19.28127 & 7 & 0.51484172 & ... & 1.330522 & 1 & 1661.484 & 1 & 0 & 6.766661 & -0.3954021 & 0 & 4 & 0.05651780\\\\\n", + "\t 7.472758 & 0 & 14 & 1 & 1 & 2 & 194.2078 & 24.58933 & 5 & 0.30919878 & ... & 1.384151 & 1 & 1658.939 & 0 & 0 & 5.647794 & 1.1127661 & 0 & 0 & 0.01344207\\\\\n", + "\t 6.502319 & 1 & 0 & 1 & 0 & 9 & 201.8380 & 25.51392 & 4 & 0.16016010 & ... & 1.220303 & 1 & 1650.802 & 0 & 0 & 5.370363 & -0.3058420 & 0 & 4 & 0.03463235\\\\\n", + "\t 7.043758 & 1 & 12 & 0 & 0 & 9 & 201.3604 & 31.16064 & 6 & 0.29197555 & ... & 1.170094 & 1 & 1676.819 & 0 & 0 & 3.446532 & 2.4406606 & 0 & 1 & 0.01751381\\\\\n", + "\t 5.658337 & 0 & 8 & 0 & 1 & 6 & 193.2195 & 20.46564 & 9 & 0.05673076 & ... & 1.802945 & 1 & 1634.093 & 1 & 0 & 5.294410 & 1.0869714 & 1 & 0 & 0.04712806\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.table: 6 × 202\n", + "\n", + "| Y <dbl> | A <int> | V1 <int> | V2 <int> | V3 <int> | V4 <int> | V5 <dbl> | V6 <dbl> | V7 <int> | V8 <dbl> | ... ... | V191 <dbl> | V192 <int> | V193 <dbl> | V194 <int> | V195 <int> | V196 <dbl> | V197 <dbl> | V198 <int> | V199 <int> | V200 <dbl> |\n", + "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n", + "| 7.358185 | 1 | 10 | 0 | 0 | 7 | 192.7938 | 23.67695 | 8 | 0.18544294 | ... | 1.462837 | 1 | 1627.274 | 0 | 0 | 4.683956 | 0.5656669 | 0 | 3 | 0.02433804 |\n", + "| 8.333672 | 1 | 12 | 0 | 1 | 4 | 199.6536 | 19.28127 | 7 | 0.51484172 | ... | 1.330522 | 1 | 1661.484 | 1 | 0 | 6.766661 | -0.3954021 | 0 | 4 | 0.05651780 |\n", + "| 7.472758 | 0 | 14 | 1 | 1 | 2 | 194.2078 | 24.58933 | 5 | 0.30919878 | ... | 1.384151 | 1 | 1658.939 | 0 | 0 | 5.647794 | 1.1127661 | 0 | 0 | 0.01344207 |\n", + "| 6.502319 | 1 | 0 | 1 | 0 | 9 | 201.8380 | 25.51392 | 4 | 0.16016010 | ... | 1.220303 | 1 | 1650.802 | 0 | 0 | 5.370363 | -0.3058420 | 0 | 4 | 0.03463235 |\n", + "| 7.043758 | 1 | 12 | 0 | 0 | 9 | 201.3604 | 31.16064 | 6 | 0.29197555 | ... | 1.170094 | 1 | 1676.819 | 0 | 0 | 3.446532 | 2.4406606 | 0 | 1 | 0.01751381 |\n", + "| 5.658337 | 0 | 8 | 0 | 1 | 6 | 193.2195 | 20.46564 | 9 | 0.05673076 | ... | 1.802945 | 1 | 1634.093 | 1 | 0 | 5.294410 | 1.0869714 | 1 | 0 | 0.04712806 |\n", + "\n" + ], + "text/plain": [ + " Y A V1 V2 V3 V4 V5 V6 V7 V8 ... V191 V192\n", + "1 7.358185 1 10 0 0 7 192.7938 23.67695 8 0.18544294 ... 1.462837 1 \n", + "2 8.333672 1 12 0 1 4 199.6536 19.28127 7 0.51484172 ... 1.330522 1 \n", + "3 7.472758 0 14 1 1 2 194.2078 24.58933 5 0.30919878 ... 1.384151 1 \n", + "4 6.502319 1 0 1 0 9 201.8380 25.51392 4 0.16016010 ... 1.220303 1 \n", + "5 7.043758 1 12 0 0 9 201.3604 31.16064 6 0.29197555 ... 1.170094 1 \n", + "6 5.658337 0 8 0 1 6 193.2195 20.46564 9 0.05673076 ... 1.802945 1 \n", + " V193 V194 V195 V196 V197 V198 V199 V200 \n", + "1 1627.274 0 0 4.683956 0.5656669 0 3 0.02433804\n", + "2 1661.484 1 0 6.766661 -0.3954021 0 4 0.05651780\n", + "3 1658.939 0 0 5.647794 1.1127661 0 0 0.01344207\n", + "4 1650.802 0 0 5.370363 -0.3058420 0 4 0.03463235\n", + "5 1676.819 0 0 3.446532 2.4406606 0 1 0.01751381\n", + "6 1634.093 1 0 5.294410 1.0869714 1 0 0.04712806" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "head(df)" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "id": "9dfd175f", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 420, + "width": 420 + } + }, + "output_type": "display_data" + } + ], "source": [ "hist_A = ggplot(df, aes(x = A, fill = factor(A))) +\n", " geom_bar() + theme_minimal() +\n", @@ -93,10 +313,73 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "id": "db7bb648", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
A data.table: 2 × 2
AV1
<int><dbl>
17.953744
06.836141
\n" + ], + "text/latex": [ + "A data.table: 2 × 2\n", + "\\begin{tabular}{ll}\n", + " A & V1\\\\\n", + " & \\\\\n", + "\\hline\n", + "\t 1 & 7.953744\\\\\n", + "\t 0 & 6.836141\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.table: 2 × 2\n", + "\n", + "| A <int> | V1 <dbl> |\n", + "|---|---|\n", + "| 1 | 7.953744 |\n", + "| 0 | 6.836141 |\n", + "\n" + ], + "text/plain": [ + " A V1 \n", + "1 1 7.953744\n", + "2 0 6.836141" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "1.11760295064719" + ], + "text/latex": [ + "1.11760295064719" + ], + "text/markdown": [ + "1.11760295064719" + ], + "text/plain": [ + "[1] 1.117603" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Unconditional ATE\n", "df[, mean(Y), by = A]\n", @@ -115,7 +398,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "id": "f47d2ff4", "metadata": {}, "outputs": [], @@ -129,10 +412,26 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "id": "da97cdfc", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "================= DoubleMLData Object ==================\n", + "\n", + "\n", + "------------------ Data summary ------------------\n", + "Outcome variable: Y\n", + "Treatment variable(s): A\n", + "Covariates: V1, V2, V3, V4, V5, V6, V7, V8, V9, V10, V11, V12, V13, V14, V15, V16, V17, V18, V19, V20, V21, V22, V23, V24, V25, V26, V27, V28, V29, V30, V31, V32, V33, V34, V35, V36, V37, V38, V39, V40, V41, V42, V43, V44, V45, V46, V47, V48, V49, V50, V51, V52, V53, V54, V55, V56, V57, V58, V59, V60, V61, V62, V63, V64, V65, V66, V67, V68, V69, V70, V71, V72, V73, V74, V75, V76, V77, V78, V79, V80, V81, V82, V83, V84, V85, V86, V87, V88, V89, V90, V91, V92, V93, V94, V95, V96, V97, V98, V99, V100, V101, V102, V103, V104, V105, V106, V107, V108, V109, V110, V111, V112, V113, V114, V115, V116, V117, V118, V119, V120, V121, V122, V123, V124, V125, V126, V127, V128, V129, V130, V131, V132, V133, V134, V135, V136, V137, V138, V139, V140, V141, V142, V143, V144, V145, V146, V147, V148, V149, V150, V151, V152, V153, V154, V155, V156, V157, V158, V159, V160, V161, V162, V163, V164, V165, V166, V167, V168, V169, V170, V171, V172, V173, V174, V175, V176, V177, V178, V179, V180, V181, V182, V183, V184, V185, V186, V187, V188, V189, V190, V191, V192, V193, V194, V195, V196, V197, V198, V199, V200\n", + "Instrument(s): \n", + "No. Observations: 1000\n" + ] + } + ], "source": [ "print(data_dml)" ] @@ -169,10 +468,35 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "id": "f54e401e", "metadata": {}, - "outputs": [], + "outputs": [ + { + "ename": "ERROR", + "evalue": "Error in sort(assert_subset(properties, mlr_reflections$learner_properties[[task_type]])): Assertion on 'properties' failed: Must be a subset of {'featureless','missings','weights','importance','selected_features','oob_error'}, but is {'weights','loglik'}.\n", + "output_type": "error", + "traceback": [ + "Error in sort(assert_subset(properties, mlr_reflections$learner_properties[[task_type]])): Assertion on 'properties' failed: Must be a subset of {'featureless','missings','weights','importance','selected_features','oob_error'}, but is {'weights','loglik'}.\nTraceback:\n", + "1. lrn(\"regr.lm\")", + "2. dictionary_sugar_get(mlr_learners, .key, ...)", + "3. dictionary_get(dict, .key)", + "4. dictionary_initialize_item(key, obj, dots)", + "5. do.call(constructor$new, cargs)", + "6. (function (...) \n . {\n . inherit <- get_inherit()\n . if (!is.null(inherit)) {\n . if (!inherits(inherit, \"R6ClassGenerator\")) \n . stop(\"`inherit` must be a R6ClassGenerator.\")\n . if (!identical(portable, inherit$portable)) \n . stop(\"Sub and superclass must both be portable or non-portable.\")\n . recursive_merge <- function(obj, which) {\n . if (is.null(obj)) \n . return(NULL)\n . merge_vectors(recursive_merge(obj$get_inherit(), \n . which), obj[[which]])\n . }\n . public_fields <- merge_vectors(recursive_merge(inherit, \n . \"public_fields\"), public_fields)\n . private_fields <- merge_vectors(recursive_merge(inherit, \n . \"private_fields\"), private_fields)\n . }\n . if (class) {\n . classes <- c(classname, get_superclassnames(inherit), \n . \"R6\")\n . }\n . else {\n . classes <- NULL\n . }\n . has_priv <- has_private()\n . if (portable) {\n . if (has_priv) \n . private_bind_env <- new.env(parent = emptyenv(), \n . hash = FALSE)\n . else private_bind_env <- NULL\n . public_bind_env <- new.env(parent = emptyenv(), hash = FALSE)\n . enclos_env <- new.env(parent = parent_env, hash = FALSE)\n . }\n . else {\n . if (has_priv) {\n . private_bind_env <- new.env(parent = parent_env, \n . hash = FALSE)\n . public_bind_env <- new.env(parent = private_bind_env, \n . hash = FALSE)\n . }\n . else {\n . private_bind_env <- NULL\n . public_bind_env <- new.env(parent = parent_env, hash = FALSE)\n . }\n . enclos_env <- public_bind_env\n . }\n . enclos_env$self <- public_bind_env\n . if (has_priv) \n . enclos_env$private <- private_bind_env\n . public_methods <- assign_func_envs(public_methods, enclos_env)\n . if (has_priv) \n . private_methods <- assign_func_envs(private_methods, \n . enclos_env)\n . if (!is.null(active)) \n . active <- assign_func_envs(active, enclos_env)\n . if (length(debug_names) > 0) {\n . lapply(public_methods[names(public_methods) %in% debug_names], \n . base::debug)\n . lapply(private_methods[names(private_methods) %in% debug_names], \n . base::debug)\n . lapply(active[names(active) %in% debug_names], base::debug)\n . }\n . if (!is.null(inherit)) {\n . if (portable) {\n . super_struct <- create_super_env(inherit, public_bind_env, \n . private_bind_env, portable = TRUE, cloneable = cloneable)\n . }\n . else {\n . super_struct <- create_super_env(inherit, public_bind_env, \n . portable = FALSE, cloneable = cloneable)\n . }\n . enclos_env$super <- super_struct$bind_env\n . public_methods <- merge_vectors(super_struct$public_methods, \n . public_methods)\n . private_methods <- merge_vectors(super_struct$private_methods, \n . private_methods)\n . active <- merge_vectors(super_struct$active, active)\n . }\n . list2env2(public_methods, envir = public_bind_env)\n . list2env2(public_fields, envir = public_bind_env)\n . if (has_priv) {\n . list2env2(private_methods, envir = private_bind_env)\n . list2env2(private_fields, envir = private_bind_env)\n . }\n . if (!is.null(active)) {\n . for (name in names(active)) {\n . makeActiveBinding(name, active[[name]], public_bind_env)\n . }\n . enclos_env$.__active__ <- active\n . }\n . public_bind_env$.__enclos_env__ <- enclos_env\n . if (lock_objects) {\n . if (has_priv) \n . lockEnvironment(private_bind_env)\n . lockEnvironment(public_bind_env)\n . }\n . if (has_priv) {\n . for (name in names(private_methods)) lockBinding(name, \n . private_bind_env)\n . }\n . for (name in names(public_methods)) lockBinding(name, public_bind_env)\n . class(public_bind_env) <- classes\n . initialize <- .subset2(public_bind_env, \"initialize\")\n . if (is.function(initialize)) {\n . initialize(...)\n . }\n . else if (length(list(...)) != 0) {\n . stop(\"Called new() with arguments, but there is no initialize method.\")\n . }\n . if (is.function(.subset2(public_bind_env, \"finalize\"))) {\n . finalizer_wrapper <- function(e) {\n . .subset2(e, \"finalize\")()\n . }\n . environment(finalizer_wrapper) <- baseenv()\n . reg.finalizer(public_bind_env, finalizer_wrapper, onexit = TRUE)\n . }\n . if (has_priv) {\n . if (is.function(.subset2(private_bind_env, \"finalize\"))) {\n . finalizer_wrapper <- function(e) {\n . .subset2(e, \".__enclos_env__\")$private$finalize()\n . }\n . environment(finalizer_wrapper) <- baseenv()\n . reg.finalizer(public_bind_env, finalizer_wrapper, \n . onexit = TRUE)\n . }\n . }\n . public_bind_env\n . })()", + "7. initialize(...)", + "8. .__LearnerRegrLM__initialize(self = self, private = private, \n . super = super)", + "9. super$initialize(id = \"regr.lm\", param_set = ps, predict_types = c(\"response\", \n . \"se\"), feature_types = c(\"logical\", \"integer\", \"numeric\", \n . \"factor\", \"character\"), properties = c(\"weights\", \"loglik\"), \n . packages = \"stats\", man = \"mlr3learners::mlr_learners_regr.lm\")", + "10. .__LearnerRegr__initialize(self = self, private = private, super = super, \n . id = id, param_set = param_set, predict_types = predict_types, \n . feature_types = feature_types, properties = properties, data_formats = data_formats, \n . packages = packages, man = man)", + "11. super$initialize(id = id, task_type = \"regr\", param_set = param_set, \n . feature_types = feature_types, predict_types = predict_types, \n . properties = properties, data_formats = data_formats, packages = packages, \n . man = man)", + "12. .__Learner__initialize(self = self, private = private, super = super, \n . id = id, task_type = task_type, param_set = param_set, predict_types = predict_types, \n . feature_types = feature_types, properties = properties, data_formats = data_formats, \n . packages = packages, man = man)", + "13. sort(assert_subset(properties, mlr_reflections$learner_properties[[task_type]]))", + "14. assert_subset(properties, mlr_reflections$learner_properties[[task_type]])", + "15. makeAssertion(x, res, .var.name, add)", + "16. mstop(\"Assertion on '%s' failed: %s.\", var.name, res, call. = sys.call(-2L))" + ] + } + ], "source": [ "linreg = lrn(\"regr.lm\")\n", "logreg_class = lrn(\"classif.log_reg\")\n", @@ -211,10 +535,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "id": "87c8980b", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Estimates and significance testing of the effect of target variables\n", + " Estimate. Std. Error t value Pr(>|t|) \n", + "A 0.85579 0.07156 11.96 <2e-16 ***\n", + "---\n", + "Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n", + "\n", + "\n" + ] + } + ], "source": [ "lasso = lrn(\"regr.cv_glmnet\", nfolds = 5, s = \"lambda.min\")\n", "lasso_class = lrn(\"classif.cv_glmnet\", nfolds = 5, s = \"lambda.min\")\n", @@ -475,7 +813,6 @@ "dml_plr_regression = DoubleMLPLR$new(data_dml,\n", " ml_g = linreg,\n", " ml_m = logreg_class,\n", - " trimming_threshold = 0.025,\n", " n_folds = 3,\n", " n_rep = 3)\n", "\n", From 456e0a5c5dece6a5037f9b5a06c7cfed2f6e0eae Mon Sep 17 00:00:00 2001 From: Frederik Bornemann Date: Fri, 3 Jun 2022 16:46:34 +0200 Subject: [PATCH 20/20] replace a/b testing thumbnail --- doc/examples/figures/ab_testing.jpg | Bin 1367784 -> 0 bytes doc/examples/figures/ab_testing.png | Bin 0 -> 44406 bytes doc/examples/py_double_ml_abtest.ipynb | 44 ++++++++++++------------- 3 files changed, 21 insertions(+), 23 deletions(-) delete mode 100644 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\n", 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", 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" ] @@ -2022,7 +2020,7 @@ "outputs": [ { "data": { - "image/png": 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0HKX7rMwfKjk5Oe4cBD734U+bNg3+/v4oLi7mu2/zNQcHB0hJSSEqKgotWrTAlStXsGLFigr3yePxaJx1XVR65SslJcV3UgCfR4ikpaWVObC+1IsXL7Bx40b0798fQUFBfMu+7H5RUlJCgwYN8Pz5c4FtbNmyBenp6fD19RU57t69eyMwMBBRUVFISEiAuro6jIyM+I4rNzdX4JiysrJw6dKlMq/wK6KmpobFixfD29sbM2bMwP79+yEtLQ1lZWXIy8ujuLhYYH8vX75EUlIS5OXloaysjIYNG+LZs2cC2y6rXcoi6nGVjtIp/foMAAkJCRg5ciRCQ0Nhbm6Op0+fIjs7G0ZGRjAyMoKPjw8eP34MT09PbNu2rcxkXfoVPjk5GYaGhnzLnj59ioYNG6JJkybIyckR6XhEUTq6ITo6Gv3798e7d++EXliIGl/pFfWzZ8/4bmSXftMsVfr70apVK+jo6PAti42NrdRVspKSEqSlpQVGtlSGhIQElixZgjt37mDZsmUwMTGBgYGB0P2ZmJjg3LlzaN26NaSkpGBjY1PhPj58+AAVFZUqx1ge6rOuhNK/mKVXIC1atICenh7Cw8Px5s0brl5RURHmzp2LX3/9la8P8mtZWVkA+K++gc8n8rNnz7h1paWlYW1tjdjYWL4uiKysLGzZsoX7ulkaX0VXHy1atEC3bt0QERGBuLg4gcTi6OiI+/fvC/Qprlu3DtOmTRMYwiYqZ2dnuLm5ITExEVu3buWOzdbWFrGxsbh//z5f/YCAAHh7e+P9+/eQlJSEo6Mj4uLi+JJCVlYWjh8/LtL+RT2uadOmYfbs2XxP+HXp0gUyMjJcG/v7+2Py5MnIzc3l6nTo0AGNGzcWemVVOlRu06ZNfFexiYmJuHjxIuzs7L5p/LAwzs7OePPmDdasWQMdHR2hI1VEjc/JyQlSUlICQ0C/HOr65fY2bNjAt7179+5h0qRJ2LFjh8jHICEhAVVVVZG64MqjqKiIRYsWcaOFioqKhNZ1cnLCrVu3cOjQIXTv3r3cC69Sr1+/RqtWrb4pRmHoyroSSvsQN2/eDFtbWzg5OWHevHkYOXIkBg0ahJ9//hlNmzbFiRMncOvWLcycObPcIVadOnVC69atsX79ehQUFEBVVRW3b99GeHg45OTk+BLBzJkz4e7uDnd3d3h6ekJRURH79+9HXl4efvvtN7749u7di/T09HLnhujbty83LvvLLhAAmDBhAs6ePYspU6Zg6NCh6Ny5MxISEnDkyBHY2trC1ta2Su0HAH5+fjh//jzWrFmDXr16oW3btvDx8cGVK1fg6ekJT09PtG7dGjExMYiOjoaHhwc3THLatGmIjY2Fh4cHvLy8ICsri3///Zd7qrSiRCfqcY0dOxbz5s3DqFGj0KtXLzDGcOTIERQUFHBDB0ePHo1x48bB09MTAwYMgJycHCIjI5GSkoLAwMAy99+5c2d4eXkhNDQUo0ePhrOzM969e4fQ0FA0btwYM2fOrHK7lsfa2hoNGjTAhQsXMHXqVKH1RI2vbdu2GD16NDZv3oy8vDzY2NggISEBFy9e5NuepqYmt70PHz7A2dkZHz58wK5du6CgoIBp06ZV6jhKLzAYY9/0R6179+5wc3PD8ePHsWXLFqFzgTg7O2Pp0qWIj48X+pl+KSsrC8+ePau2p1bpyroS+vTpAysrKxw6dAjLli0DABgbG2Pv3r3Q09PDtm3b8PfffyM/Px8BAQEYP358uduTlZXFxo0bYWxsjJ07dyIwMBCJiYmYO3cufHx8kJOTg7t37wL4fINn37590NfXx+bNm7F69Wq0aNECe/bs4ZKZpaUlXF1dERsbi0WLFnF9n2Xp2bMn5OTkoKuryze6Avh8I3Tfvn0YOHAgTp8+DX9/f9y6dQuTJ0/G6tWrv6lPTkVFBbNmzcKnT5/wxx9/APj8y79//37Y29tj//79WLJkCVJTU+Hn58c3prtt27bYtWsXtLS0sGHDBmzcuBGOjo7w9PTk2rM8oh6Xu7s7AgMDkZubixUrVmD58uVo0KABNm3axM250r17d6xbtw7y8vJYu3YtAgICkJWVhRUrVpT7uPHvv/+O+fPnIyMjAwEBAThw4AB69OiBQ4cOCb3i/Vby8vKwtrYG8PlzL4+o8c2aNQtz585FcnIyAgICuC69sra3YMECZGZmIjAwEHv27IGpqSn27NkjcN5VxNbWFllZWVX+ZveluXPnokmTJli7di2ePn1aZh01NTVoa2tDWlpa6ANEX7p+/ToYY990MVMeCVbeXQVC6pCMjAwoKysLXFUtWrQIe/fuxa1btyo1woDUL4WFhXB0dMSgQYMwffr02g5HwMyZM5GcnIzw8PBq2T5dWZN6Y9q0aejTpw9fn3x+fj6io6Ohra1Nifo7JysrC09PTxw7dqxSo0JqQk5ODqKiojBmzJhq2wcla1Jv9O/fH0+ePMH48eOxd+9ebN++HZ6ennj9+nWdvNIi4ufl5YXi4mKRbyrXlJ07d6J9+/Z800uIG3WDkHrl6NGj2LlzJ5KTkyEpKQk9PT1MnjyZeyKSfP8iIiKwbNkynDx5ssI5rWtCdnY2evTogc2bN0NPT6/a9kPJmhBC6gHqBhFRYmJibYfw3aE2FS9qT/GrS21KyVpEnz59qu0QvjvUpuJF7Sl+dalNKVkTQkg9QMmaEELqAUrWhBBSD1CyJoSQeoCSNSGE1AOUrAkhpB4QOkVq6fSZlVE6uTchhBDxEpqsqzJzFCVrQgipHkKTdVRUVE3GUaf5rb2A7Oxs/O/F1oQQUuOEJuvS96cRQgipfSLdYPzy/YJfunHjhsB78wghhIhfucn648ePmDp1Kpydnct84/KaNWvw008/YdKkScjMzKy2IAkh5EcnNFnn5OTA09MTkZGRsLCwQF5enkCdoUOHws7ODtHR0Rg5ciTy8/OrNVhCCPlRCU3WmzZtwpMnT7BixQps3rwZLVq0EKjj7OyM9evXY9GiRXj06BG2bNlSrcESQsiPSmiyPnPmDPr06QNXV9cKN+Lu7g57e3ucOnVKrMERQgj5TGiyfvHiBUwqMVbNysoKqampYgmKEEIIP6HJukmTJmX2U5dHQUHhmwMihBAiSGiy7ty5My5evCjyhuLj46Guri6WoAghhPATmqwHDx6M+Ph4HDt2rMKNnDx5EnFxcejXr59YgyOEEPKZ0CcY+/Tpg2PHjmHOnDm4cuUKhgwZAl1dXe7V7yUlJUhMTMSBAwdw6NAh6Ovrw93dvcYCJ4SQH4nQZA0Ay5cvx19//YUDBw7g4MGDkJaWRtOmTcHj8ZCVlYWSkhIwxtC7d28sWLAAcnJyNRU3IYT8UMpN1goKCggMDMTIkSNx/PhxJCUlIT09HZKSktDW1oaxsTGcnZ2hra1dU/ESQsgPqdxkXapLly7o0qVLdcdCCCFEiCq/KSYnJwd+fn548uSJOOMhhBBShion60+fPiE8PBxv376t8s55PB727t2Lvn37cl0qS5cuLXPSqFK5ublYuHAhrK2tYWxsjHHjxuHZs2dVjoEQQuoDkbpBqsvmzZvxzz//YOzYsbC0tMTTp0+xevVqPH78WOg8I9OnT8edO3cwe/ZsKCgoICQkBCNGjMCJEyfQqFGjGj4CQgipGbWWrBlj2Lx5Mzw8PDBz5kwAnx9ZV1JSwvTp03Hv3j3o6OjwrXPt2jXExsZi06ZNsLW1BQCYmprCyckJe/fuxfjx42v8OAghpCbU2tvNc3Nz0a9fP7i5ufGVd+jQAQCQkpIisE58fDwUFBRgbW3NlSkrK8PMzAxxcXHVGzAhhNSiKl9ZN2nSBDt37qzysD1FRUXMmzdPoDwyMhIA0KlTJ4FlycnJ0NDQ4B7MKdW2bVua8Y8Q8l2rcrKWkZGBubm5OGPBrVu3sHHjRjg7O6Njx44Cy3NycqCoqChQrqCgUO5Nya8lJibi06dPItfPzs4GACQkJIi8DhENtal4UXuKX2XatDIzlVZWlZJ1YWEh1q5di5MnT+Lt27do2bIl+vTpg4kTJ0JWVrZKgSQkJGDixIlQU1ODv79/mXUYY0LXl5QUvUdHV1e3UrEduFL6dnN6vbk4JSQkUJuKEbWn+NWlNq1Ssg4KCkJMTAyGDBmCpk2bIjU1FaGhoXj//j0WLFhQ6e2dPHkSc+bMQbt27bB582YoKSmVWU9RURFpaWkC5bm5uWVecRNCyPdCaLIW1uUAfH6LzD///MP3F6dZs2ZYt25dpZP1tm3bEBgYCHNzc6xZs6bc4Xft27fHpUuXwBiDhIQEV/78+XO0b9++UvslhJD6RGjfgaOjI9avX4/c3FyBZcrKyrhw4QJ4PB4AID8/H//99x+aNWtWqZ2HhYUhICAArq6u2Lx5c4XjpLt3746PHz/yzbOdmZmJa9euwcrKqlL7JoSQ+kTolfXff/+NkJAQbNu2DWPHjsXw4cPRsGFDAMDs2bMxZcoUbN++HY0bN8b79+8hJSWF1atXi7zjjIwMLF68GG3atIGnpyeSkpL4lrdt2xbA5yF8nTp1gqKiIszMzGBubo4ZM2bAx8cHTZs2RXBwMBo1aoSff/65KsdPCCH1gtBkbWdnBzs7O5w7dw4hISHYunUrl7Stra1x7tw5REdHIyMjA82bN4eNjU2lrqzPnz+P/Px8vHjxAp6engLLg4KCUFJSAj8/P+zcuRMWFhYAgJCQEAQEBCAoKAg8Hg8mJib4559/0KRJkyocPiGE1A8SrLwhFl+IjIxESEgI3r59i19++QXDhg1DgwYNqju+OsFv7efRICG+Fb/pnYiuLt1p/x5Qe4pfXWpTkce7OTs74/Dhw5g/fz7Cw8Ph5OSE7du3o6CgoDrjI4QQggqG7qWmpuLUqVN4/fo1lJSUYGlpiV69eqFXr144efIk1q5di82bN2PcuHH4+eefqzzGmhBCSPmEXllHRkbC1dUVu3btQlJSEk6ePAkvLy8EBgYCAHr37o1jx47B19cX//77L5ycnBAaGlpjgRNCyI9EaLL++++/0a9fP8TGxuLff//FqVOnsHz5cmzfvh2vXr0CAEhISKBv3744ceIEZs6ciV27dtVY4IQQ8iMRmqzfvn2Ldu3a8T180rZtWzDG8PHjR/6NSEpiwIABNJkSIYRUE6F91n379kVISAgePHgANTU15OTk4MyZM9DX14empmaZ61Rmfg5CCCGiE5qs//zzT+jq6uLUqVNISkqCkpISBg0ahDFjxvBdbRNCCKl+QpO1pKQkPDw84OHhUZPxEEIIKUOVZt378OEDbt68iby8PKipqcHAwEDccRFCCPmC0GQ9ePBgTJs2DTY2Nnzl69evx7p161BYWMjNfqehoQF/f3+YmppWe8CEEPIjEpqs7969iw8fPvCVhYaG4p9//oGxsTGGDBkCZWVlJCcnY+fOnRg7dixCQ0PpKpsQQqpBpbpBNmzYgG7dumH79u1cmZ2dHQYPHozBgwdj1apV2LJli7hjJISQH57IY+3y8vKQnp6OQYMGCSxr1KgR3N3dcfPmTXHGRggh5H9ETtYNGzZEkyZNIC1d9sW4hIQE9zICQggh4lVuN8i///6L58+fo2PHjujUqRPc3Nywb98+uLryTxX6+vVr7Nq1C4aGhtUaLCGE/KiEJmsXFxc8efIE69evR3FxMd+DMBs3bsT48eMBAPPnz8eJEydQWFiI5cuXV3/EhBDyAxKarFetWgUAKC4uxtOnT/Ho0SM8evQIjx8/hpqaGlfvzp070NTUxNy5c6Gvr1/9ERNCyA+owtEg0tLS6Ny5Mzp37lzm8v3790NGRkbsgRFCCPl/Ig3dy8nJwYMHD5Ceno6CggJIS0ujSZMmUFdX515sSwghpPqUm6xfvHiBoKAgREVFoaSkhG9Z6dOLzZo1g6enJ0aOHMm9/ZwQQoh4CU3WL168gIeHB4qKiuDl5YW2bdviw4cPiIyMRFpaGmbNmgXGGK5evYp169YhIiIC27Zto7eME0JINRCarP/55x8oKChg7969UFZW5sonTZqEuXPn4tChQ9izZw/c3d0xatQojBkzBiEhIfj9999rJHBCCPmRCH0oJj4+Hj///DNfoi41ZswY3LhxA8+fPwcA6OrqYuTIkYiMjKy+SAkh5AcmNFnn5+cjKyurzGWfPn0CAGRkZHBlSkpKQusTQgj5NkKTtampKXbs2CEw30dBQQFWrFgBWVlZ7vVeeXl5CA8PF/q6L0IIId9GaJ/17NmzMXToUAwbNgzW1tbo3LkzcnNzERcXh1evXsHHxweKioqIiYmBn58fsrOzsWnTpioHcu/ePQwePBhRUVFQVVUVWu/IkSOYPXu2QLmnpyfmz59f5f0TQkhdJjRZd+7cGWFhYQgKCkJ8fDzOnz8PAGjfvj0CAgIwYMAArq6FhQXGjBlT5bmsk5OTMWHCBBQXF1dY9/79+9DQ0EBQUBBfuYqKSpX2TQgh9UG546w7dOiA9evXo6ioCJmZmWjYsCEaNWrEV8fe3h729vZV2nlxcTH27duH5cuXi/wU5IMHD6CrqwsjI6Mq7ZMQQuojkaZIlZGRQcuWLQUS9bdKSEjAsmXLMGbMGPj4+Ii0zv3796GlpSXWOAghpK4TeT7r6tCxY0dERkZiypQpkJKSqrD+27dvkZGRgaSkJPTq1Qu6urpwcXHB4cOHqz9YQgipRVV6u7m4VLaf+f79+wDAPUEpJyeHw4cPw9fXFyUlJWW+xaYsiYmJ3PBDUWRnZwP4/E2AiBe1qXhRe4pfZdrUxMSk2uKo1WRdWXp6eli/fj3MzMygqKgIAOjevTsyMjKwatUqkZO1rq5upfZ74MoFZGdnV+sH8SNKSEigNhUjak/xq0ttWqvdIJWlrKwMBwcHLlGXsrOzw5s3b5CZmVlLkRFCSPWqV8n6xo0bCAsLEygvnbZV3DdACSGkrhDaDeLk5FTpjUlISFTr/CA3b95EQEAA9PX1oa2tDQDg8Xg4c+YMunbtSi9BIIR8t4Qm69atWwuUJSUlITc3F1paWujQoQN4PB5SU1ORlJQEZWVldO/eXazBZWZmIiUlBZ06dYKioiIGDhyI0NBQTJkyBb/99hsUFBSwZ88ePHz4ELt37xbrvgkhpC4RmqxDQ0P5fj558iR+//137Ny5E+bm5nzLbty4gfHjx0NPT0+swZU+yr5z505YWFigSZMmCA0NxfLly7F06VLk5ORAT08P27dvpzerE0K+axKMMSZKxZ49e8LV1RXTp08vc3lISAgOHjyI6OhosQZYF/it/TwaJMTXtbZD+a7UpTvt3wNqT/GrS20q8g3Gd+/elTm3damGDRvSFKmEEFJNRE7WWlpaOHDgAPLy8gSWZWZmYvfu3dQVQQgh1UTkh2J+/fVXjB8/Hm5ubnBzc4O6ujoKCgrw7NkzHD16FEVFRVi1alV1xkoIIT8skZO1lZUVNm7ciGXLlmHjxo1cuYSEBExNTTFnzpxKPxlICCFENJV63NzKygqHDh1CZmYmXrx4AQkJCbRp0wZKSkrVFR8hhBBUcW4QZWXlcm82EkIIEa9KJeu9e/fi2LFjSE9PR0lJicDy6n6CkRBCflQiJ+uQkBCEhISgSZMmaN++PT3aTQghNUjkZH3w4EGYm5tj8+bNkJWVrc6YCCGEfEXkcdYZGRno27cvJWpCCKkFIifrzp074+nTp9UZCyGEECFETta//fYb9u/fj9jY2OqMhxBCSBlE7rPesWMHGjZsiIkTJ6JBgwZQUlKChIQEXx0aDUIIIdVD5GRdUFAADQ0NaGhoVGc8hBBCyiBysv56fmtCCCE1R6zvYExKShLn5gghhPyPyFfWRUVF2LhxI86ePYu8vDzweDxuWUlJCXJzc5GTk4N79+5VS6CEEPIjE/nK+p9//kFwcDCysrIgLy+PFy9eoFWrVpCWlsbr169RVFSE33//vTpjJYSQH5bIyfr06dMwNzfHuXPnsGnTJgDA/PnzcebMGWzYsAHFxcX0CDohhFQTkZP1mzdv0LNnT0hKSqJly5Zo1qwZbty4AQCws7PDTz/9hP3791dboIQQ8iMTOVk3aNCA78q5bdu2ePjwIfezgYEBUlNTxRsdIYQQAJVI1jo6OoiLi+N+7tChA3dlDXy+8v76IRlCCCHiIXKy9vT0RFRUFIYNG4acnBz06dMHSUlJ8PPzw6ZNm7B9+3bo6+tXZ6y1IiYhFQ+ev8fzt4UY438WMQn07YEQUvNEHrrXq1cvLFq0CNu2bYO8vDysrKwwbtw47mZj69at4efnV22B1oaYhFSEhN1CUfHnYYrv3ucjJOwWAMDeRL02QyOE/GAkGGPsWzbw8uVLZGVloWPHjt/d9Klj/M/i3ft8gfLmSvLYOq9nLUT0fUlISICJiUlth/HdoPYUv7rUpt/8BGPr1q2ho6PzzYn63r170NXVxevXr8utl5ubi4ULF8La2hrGxsYYN24cnj179k37Fia9jERdXjkhhFQXsT5uXlXJycmYMGECiouLK6w7ffp0nD59Gj4+PggMDMSbN28wYsQIZGdniz0uFSX5SpUTUlv81l7Atsi3tR0GqUa1mqyLi4uxe/duDB48GAUFBRXWv3btGmJjYxEYGIiffvoJPXv2xPbt25GdnY29e/eKPb4RrjqQk5HiK5OTkcIIVx2x74sQQspTq8k6ISEBy5Ytw5gxY+Dj41Nh/fj4eCgoKMDa2porU1ZWhpmZGd+wQnGxN1HHFHdDyEh/bqbmSvKY4m5INxcJITWuVpN1x44dERkZiSlTpkBKSqrC+snJydDQ0BCo27Zt22p75Zi9iTq0NJSg0UIWW+f1pERNCKkVIg/dK0tRURHi4+MhKSkJKysrSEtXbnMqKiqVqp+TkwNFRUWBcgUFBeTk5Ii8ncTERHz69Enk+qX94QkJCSKvQ8r3//2r1KbiQOeo+FXlHK3OkSMiZ9fCwkL4+/sjLS0NW7duRWFhITw8PHD//n0An6+Sd+zYgWbNmlVbsOWNMpSUFP1Lgq6ubqX2e+DKBWRnZ9eZITzfA2pT8aL2FL+61qYiZ7iQkBDs378frVq1AgAcPnwY9+7dg5eXF5YsWYJ3795h1apV1RYoACgqKiI3N1egPDc3t8wrbkII+V6IfGV96tQpDB48GP7+/gCAM2fOoFGjRpg9ezakpaWRmpqKsLCwagsUANq3b49Lly6BMcY3D8nz58/Rvn37at03IYTUJpGvrF+/fg0jIyMAQH5+Pv777z9YWlpy/dStWrXCx48fqyXIUt27d8fHjx9x8eJFriwzMxPXrl2DlZVVte6bEEJqk8jJWkVFBenp6QCA8+fPo7CwEPb29tzyBw8eoEWLFmINLjMzEzdv3uRuHpqZmcHc3BwzZsxAWFgYIiIiMGrUKDRq1Ag///yzWPdNSH1Bk439GERO1hYWFtixYwe2bduGoKAgyMvLw9nZGR8/fsS2bduwf/9+ODg4iDW4mJgYeHh4IDExkSsLCQmBo6MjgoKCMGfOHKiqqmL79u1o0qSJWPdNSH0gbLIxStjfH5H7rOfOnYs3b94gMDAQDRs2hL+/Pxo3boyEhAQEBgbC1NQUU6ZMqXIgAwcOxMCBAyssa9KkCZYuXYqlS5dWeV+EfC92nrqHgqISvrKCohLsPHWPngn4zoicrBs3boxt27YhMzMTioqK3MRNOjo62LdvHwwNDastSPJ9Kf3aXlTMwxj/sxjhqkOJpYposrEfh8jdIH5+frh16xaUlZX5Zthr2LAhDA0NcfnyZYwbN65agiTfD/raLl402diPQ+RkHR4eXu47Fq9cuYIrV66IJSjy/SrvazupPJps7MchtBskNTUVbm5uKCws5MpmzZqFWbNmCd3Y9/haLyJe9LVdvEq7j1bvv4miYh6aK8lTt9J3SmiyVldXx/z583Ht2jUwxnD48GGYmJhAXV3wJJCUlISysjINnyMVUlGSL/PtO/S1versTdRx5spzZGdnI8SX3mAkDnXxvkq5NxgHDRqEQYMGAQBevHiByZMnw9LSskYCI9+nEa46CAm7xdcVQl/bSV1SV9+9KvJokNDQ0OqMo0bd+X2+QJmKtRVa9e6FkoICJP21mG+Z5YssPGrWAYArij5+xP3AZQLrq/ZyQXMbaxS8S8fDf1YLLG/Tvy+Uzc2Ql/YCT9ZtEFiu7j4ITY0MkZP8FE+3bBNYrjF8GBrraOPjvft4vmuPwPL2Y0dDsUN7fLh5C6lhBwWWd5w0AQ3V2iDz6n94ceSYwHLN336FXHMVvDsfj9enzwgs1/b1gUzjxngTdQ5vz8UILO8y/3dIycnh1cnTSI+/KLBcf/FfAIDOKdfRjyXjVEkr5Eg2QFOJQrhIvYG9iRsAIHVfGD7cvsO3rkwjRWjPmQ0AeLZzF7IfPORbLtesGTRnTAMAJG/eitynz/iWy7duhU7ekwAAj9esQ/7LV3zLFdq3Q4dfxgAAHq5YhYKMDL7ljbQ00W7EcADA/YAgFGXzz/DY1EAf6h7uAIDEhf7gfdF1CADKpiZo81N/AJU/9wCghaM9Wjo5lnvuAUDDgpwyt0/n3udz70X4EWRe459BT1JWFroL5gH4/3Nvyyc9FECOr15BUQm2hl1Ds0Ob+Mq/PvdKz6PqUKk5TR8/fozjx48jPT0dJSUlAsslJCSwZMkSsQVHvk/G0u/R9M0zFJcUo3PbZpD8zl60TOq3Dyj7fHxfJAFUPO1+tRH57eanT5/GjBkzwOPxhG9MQgL37n1/d/X91l74X3+ga22H8t2gNhUvak/xGeN/tsz7Ks2V5LF1Xu3dExD5ynrNmjVo3bo1VqxYAW1t7W9+mzkhhNRFdfW+isjjrJ89e4ZRo0bBwMCAEjUh5LtVV9+9KvKVtaqqaqVehUUIqTlLJ3enV3qJUV0cDinylbWnpyd2796NzMzM6oyHEEJIGUS+si4qKoKEhAScnZ1hamoKZWVlvre1ADQahIiOrgQJqRyRk/Xy5cu5/8fFxZVZh5I1IYRUD5GTdelbzAkhhNQ8kfusv8Tj8ZCens43yRMhhJDqU6lk/fz5c0ydOhUmJiawsbFBQkICLl26BHd3d1y7dq26YiSEkB9epcZZu7u74+rVq7CxseHKpaSkkJycjDFjxuDmzZvVESMhhPzwRE7WK1asQIMGDXDy5En8+eefKH1K3dzcHCdPnoSKigpCQkKqLVBCCPmRiZysL1++jJ9//hnNmjUTGLLXsmVLDBs2DHfv3hV7gIQQQiqRrAsLC9G4cWOhy2VkZFBQUCCWoAghhPATOVlra2vj3LlzZS4rLi7G0aNHoaWlJbbACCGE/D+Rk/WECRNw8eJF+Pj44PLlywA+vz0mKioKI0aMQFJSEkaPHl1tgRJCSE1aOrk7Rju3qO0wOCI/FOPg4IDFixdjyZIlOHHiBADgjz/+AGMMcnJy8PX1hYuLS6UDOH78ONatW4fU1FS0adMGEyZMwIABA4TWP3LkCGbPni1Q7unpifnzBd+SQQgh34NKvSlm4MCB6NmzJ+Lj45Gamgoej4c2bdrAysoKSkpKld75qVOn4OPjgxEjRsDGxgaRkZHw9fVFgwYN0KtXrzLXuX//PjQ0NBAUFMRXrqKiUun9E0JIfVGpZA0AioqKVbqCLsuKFSvg6uqKuXPnAgBsbGyQlZWFVatWCU3WDx48gK6uLoyMjMQSAyGE1AdCk7Wfnx+GDh0KQ0ND7ueKVGYip9TUVKSkpGDGjBl85S4uLjh16hRSU1Ohri442ff9+/cxYsQIkfZBCCHfC6HJOjw8HFZWVlyyDg8Pr3BjlUnWycnJAID27dvzlWtoaAAAnj59KpCs3759i4yMDCQlJaFXr15ITU2FmpoaJk2aVG4/NyGE1HdCk/XXs+yJe9a97OxsAJ+7Vb6koKAAAMjJyREaU1paGmbNmgU5OTkcPnwYvr6+KCkpwaBBg8QaIyGE1BWV6rPm8Xi4cOECLCwsICcnBwCIioqCpKQk7O3tBZ5sLE/p4+pfr1NaLikpOKpQT08P69evh5mZGZfku3fvjoyMDKxatUrkZJ2YmFipV5SV/mGhyfLFj9pUvKg9xa8ybWpiYlJtcYicrN+/f48JEybgzp07OHToEHR0Pr/p99ixYzh9+jQsLS2xZs0aNGzYUKTtNWrUCIDgFXRubi7f8i8pKyvDwcFBoNzOzg4XL15EZmYmlJWVK9y3rq6uSDGWOnDlArKzs6v1g/gRJSQkUJuKEbWn+NWlNhX5oZiVK1fi0aNH+Ouvv9CxY0euPCgoCEFBQbh58yaCg4NF3nFpX3VKSgpf+fPnz/mWf+nGjRsICwsTKC8oKIC0tHSZCZ4QQr4HIifr2NhYjBo1Cu7u7pCVleXKZWVl0a9fPwwfPhxnz54VeccaGhpQU1PD6dOn+crPnj2Ldu3aoXXr1gLr3Lx5E/PmzePrP+fxeDhz5gy6du0KGRkZkfdPCCH1icjdIB8/fkSzZs2ELldVVUV6enqldu7t7Q0/Pz80adIE9vb2OHfuHE6dOoWVK1cCADIzM5GSkoJOnTpBUVERAwcORGhoKKZMmYLffvsNCgoK2LNnDx4+fIjdu3dXat+EEFKfiHxl3bFjR5w5c4a7Afi1qKioMrsuyjNw4EAsXLgQFy5cgLe3N65evYrAwED07t0bABATEwMPDw8kJiYCAJo0aYLQ0FAYGBhg6dKl+O2335CXl4ft27dzQwwJIeR7JPKVtZeXF3x9fTFx4kQMGzYMGhoakJSUxPPnz7F//35cunQJixcvrnQAQ4cOxdChQ8tcNnDgQAwcOJCvrE2bNlixYkWl90MIIfWZyMm6f//+ePv2LUJCQhAXF8e/EWlpTJs2TSCxEkIIEY9KjbMeN24cPDw8EB8fj5cvX6KkpAStW7eGlZWVSEPmCCGEVE2lJ3Jq3LgxXF1dqyMWQgghQghN1iEhIejZsyc0NTW5nysiISEBb29v8UVHCCEEQAXJWkNDg5I1IYTUAUKT9YEDB9CpUyfu56ioqBoJiBBCiCCh46zHjRuHY8eOcT+Hh4cjNzcXbdq0KfcfIYQQ8ROarPPy8pCRkcH9HBISgocPH9ZIUIQQQvgJ7QYxMDBAcHAwIiIiuDmm161bh/379wvdmISEBHbs2CH+KAkh5AcnNFkHBgYiICAADx48wPv37yEhIYHMzEzk5+fXZHyEEEJQTrKOjY3FjBkz0K5dOwCAtrY25s6di759+9ZUbIQQQv5HaJ91UFAQ3xsSWrduDWnpSj9DQwghRAyEZl9ZWVlERETA0NAQ8vLyePnyJdLT0/Hy5ctyN1jWPNSEEEK+jdBkPXjwYGzZsgWxsbFc2ZIlSyp8e/m9e/fEFx0hhBAA5STrWbNmwczMDA8ePEBhYSHWrFkDZ2dnaGlp1WR8hBBCUMFETvb29rC3twfw+aGYAQMGwMnJqSbiIoQQ8gWR7xieO3eO+/+bN2/w+vVrdOjQAXJycpCWloakpMgvnSGEEFJJlcqwCQkJGDhwIOzt7TF06FDcvXsXV69ehb29PU6ePFldMRJCyA9P5GR9+/ZtjB49Grm5uRg5ciRX3qRJE0hLS8PHx4fvZiQhhBDxETlZr1q1Cmpqajhy5AjGjx/PvThXX18fR48eRceOHbFhw4ZqC5QQQn5kIifrGzduYODAgWjQoAEkJCT4likqKmLIkCF49OiR2AMkhBBSyT5rWVlZocsKCgrA4/G+OSBCCCGCRE7WhoaGOH78eJnL8vLyEBYWBn19fbEFRggh5P+JnKx//fVXJCUlYfjw4Th8+DAkJCRw+/Zt7Ny5E/3790daWhomTpxYnbESQsgPS+Rx1sbGxtiwYQMWLFiAwMBAAMDKlSsBAM2bN8fKlSvRrVu36omSEEJ+cJWaRs/a2hoRERFISkpCSkoKeDwe2rRpAz09vSrPyHf8+HGsW7cOqampaNOmDSZMmIABAwYIrZ+bm4tly5bh7NmzyMvLg6mpKX7//XduKldCCPkeVfqxQx6Ph+LiYjDGuKcXq5qoT506BR8fH1hbW2PNmjUwNzeHr68vTp8+LXSd6dOn4/Tp0/Dx8UFgYCDevHmDESNGIDs7u0oxEEJIfVCpLBsdHY2FCxfizZs3fOUtWrTAggUL4OjoWKmdr1ixAq6urpg7dy4AwMbGBllZWVi1ahV69eolUP/atWuIjY3Fpk2bYGtrCwAwNTWFk5MT9u7di/Hjx1dq/4QQUl+IfGV97do1TJ06FYwxTJ8+HSEhIQgODsb06dMhISGBX3/9FdevXxd5x6mpqUhJSUHPnj35yl1cXJCcnIzU1FSBdeLj46GgoABra2uuTFlZGWZmZoiLixN534QQUt+IfGUdHByMNm3a4MCBA2jUqBHfsmHDhmHQoEFYt24dNm3aJNL2kpOTAQDt27fnK9fQ0AAAPH36FOrq6gLraGhoQEpKiq+8bdu2OHXqlKiHQggh9Y7Iyfr27dvw9vYWSNTA5ycYBw8eLHKiBsD1MSsqKvKVl75JPScnR2CdnJwcgfql65RVX5jExER8+vSp0rF++ZozIh7UpuJF7Sl+lWlTExOTaotDbC9VlJCQQFFRkcj1S+cW+frR9dLysqZcLV1WlspM0aqrqytyXQA4cOUCsrOzq/WD+BElJCRQm4oRtaf41aU2rdQTjAcOHEBeXp7AspycnEo/wVh6hf71FXFubi7f8i8pKipyy79ep6wrbkII+V6IfGU9ZcoUjBgxAm5ubhg+fDg3rjk5ORl79uzBmzdvsHDhQpF3XNpXnZKSwveqsOfPn/Mt/3qdS5cugTHGd0X+/PnzMusTQsj3QuQra1NTUwQHB6OkpARBQUHw9vaGt7c3li1bhqKioko/waihoQE1NTWBMdVnz55Fu3btynxLevfu3fHx40dcvHiRK8vMzMS1a9dgZWUl8r4JIaS+qVSftZOTE+zt7ZGYmIi0tDQAQJs2baCrq1ulB2O8vb3h5+eHJk2awN7eHufOncOpU6e4x9gzMzORkpKCTp06QVFREWZmZjA3N8eMGTPg4+ODpk2bIjg4GI0aNcLPP/9c6f0TQkh9UekMKyUlBQMDAxgYGCAjIwNNmzYVGEonqoEDB6KwsBBbt25FWFgY1NXVERgYiN69ewMAYmJi4Ofnh507d8LCwgIAEBISgoCAAAQFBYHH48HExAT//PMPmjRpUqUYCCGkPpBg5Q2xALBr1y7s27cP4eHhAlfPM2fOxKVLlzB+/HiMGjWqOuOsVX5rP48GCfF1re1Qvit16U7794DaU/zqUpsK7bNmjGH27Nnw9/fH27dv8fLlS4E6ampqkJSURGBgIGbMmFGtgRJCyI9MaLIOCwvD0aNHMWzYMMTFxaFt27YCdaZPn46oqCj0798fp06dwuHDh6szVkII+WGVm6zNzMwwf/58yMnJCd2AnJwclixZAm1tbfz777/VEiQhhPzohCbrx48fw8nJSbSNSErCxcUFDx48EFtghBBC/p/QZC0lJVXuC3K/pqSkVKlHvgkhhIhO6NA9DQ0N3L17V+QN3blzp8wHWb4HSyd3pwlyCCG1SuilcJ8+fXDs2DE8evSowo08evQIx44d414IQAghRLyEJmsPDw+0bt0aXl5eOHr0KEpKSgTq8Hg8HD9+HKNHj4aCggJGjhxZrcESQsiPSmg3iIKCAtatW4fJkyfD19cXCxcuhK6uLpo3bw4ej4eMjAwkJiYiLy8PrVq1wpo1a9CiRYuajJ0QQn4Y5T5u3qFDBxw9ehS7d+/GiRMncP36dRQXFwMAZGRkYGRkhJ49e8LDw6NSNyMJIYRUToVzg8jKymL06NEYPXo0gM+TK0lJSdFcHIQQUoMqPZGTsrJydcRBCCGkHDQwmhBC6gFK1oQQUg9UOEUqIYSQ2kdX1oQQUg9QsiaEkHqAkjUhhNQDlKwJIaQeoGRNCCH1ACVrQgipByhZE0JIPUDJmhBC6gFK1oQQUg9QsiaE8KGHmmuWqO1NyboGBQcHo0uXLrUdxjfR0tLC2rVrazuM78abN2/g5eUFfX19WFlZoaCgoFbjOXjwIAIDA2s1hupU134Ho6Oj4evrK1LdSk+RSqrO3d2d3lNJ+ISGhuL69ev4+++/oaqqCjk5uVqNZ/369TAxManVGH4kO3bsKPOViWWhZF2DVFVVoaqqWtthkDrkw4cPaNGiBXr37l3boZA6rk52gzg6OiIgIABeXl7o2rUrli5divfv32PevHmwtLSEgYEBfv75ZyQkJPCtl52dDT8/P1hYWMDExAR//PEHVqxYAUdHx3K3DUCk7cfHx2PIkCEwNjaGmZkZJk+ejCdPnnDLU1JSMHHiRFhYWMDQ0BAeHh6IjY3llpf1Fezw4cP46aefYGRkBFtbWwQGBuLTp0/c8jlz5mDs2LEICwtDz549oaenh/79++P8+fPf3tBicO/ePXh7e6Nbt27Q1dWFra0tFi9ezPd1/lvbDQBu3ryJ0aNHw8zMDGZmZpg2bRrS0tJq7Dirg6OjI8LCwvDy5UtoaWkhODgYr1+/xuzZs2FjYwNDQ0N4enri6tWr3DppaWnQ0tLC9u3b4eLiAgsLC5w8eRIA8ODBA4wbNw7GxsYwMTHBtGnT8Pr1a7597tixA7169YK+vj5sbGzw559/Iicnh4snJSUF4eHh0NLSqnPtGxkZCS0tLaxbt44ru3fvHvT09Ljf47CwMLi4uMDAwABDhgxBVFQUtLS0cOXKFb5tnT59Gj169ICBgQGGDx+O27dv8y1/8uQJJk+eDEtLSxgbG+OXX37B/fv3+epU9FkBwPHjx9GvXz8YGBjA0tISPj4+ePPmDQDAy8sLly5dwtWrV8uMUQCrgxwcHFiXLl1YQEAAi4uLY1evXmX9+vVj1tbWbP/+/Sw6OppNmDCB6enpsVu3bnHrDR8+nJmbm7P9+/ezqKgoNnToUKanp8ccHByEbvvWrVvs06dPFW4/JSWFGRgYsIULF7JLly6x06dPMxcXF+bk5MR4PB4rKSlhvXr1YiNGjGAxMTHswoULbPz48UxHR4c9f/6cMcbY6tWrmY6ODhfLqlWrmJaWFlu8eDE7f/4827p1KzMyMmIjR45kPB6PMcaYr68vMzExYa6uruz48eMsJiaG/fTTT8zIyIh9/PixJj4OPpqammzNmjWMMcZev37NjI2N2dixY1lMTAyLj49nS5cuZZqammzjxo2MMfG0W3x8PNPR0WG//PILi4qKYkePHmU9evRg1tbW7N27dzXeBuKSmJjIJk6cyKytrdmNGzfYy5cvmbW1NevZsyc7evQoi4qKYmPGjGFdunRhFy9eZIwxlpqayjQ1NZmBgQE7ePAgO3nyJHv37h1LTk5mxsbGzN3dnUVERLATJ06wXr16MUdHR+48OXbsGNPV1WU7d+5kV65cYXv37mVGRkZszpw5XDy2trZs3Lhx7MaNG6ygoKDW2kaYmTNnMn19ffb8+XNWUFDA+vbty9zc3FhBQQE7cOAA09TUZAsXLmRxcXEsKCiIGRgYME1NTXb58mXG2OffQU1NTWZubs727t3LIiMj2eDBg5mRkRF7+/YtY4yx+/fvMyMjIzZ48GB25swZdubMGTZw4EBmZGTEHj16xBhj7M2bNxV+VteuXWM6OjosODiYXblyhR0+fJhZW1uz4cOHM8YYe/ToERs0aBAbMGAAu3HjBsvOzi732OtssnZ0dOQS1r59+5iWlha7ffs2V6ekpIT99NNPbNSoUYwxxi5evMg0NTVZdHQ0Vyc3N5d169ZNIFl/uW1Rt3/8+HGmqanJXr9+zdW5desWW7FiBcvOzmZv375lmpqa7OjRo9zyjx8/siVLlrCHDx8yxviT9fv375menh5buHAh37GfOHGC7zh8fX2ZpqYmS0lJ4epcvXqVaWpqsoiIiEq0qnh8maxjY2OZp6cny8nJ4avj5ubGxo0bxxgTT7sNHDiQubm5sZKSEq7OixcvmJ6eHgsICKi2Y60Jc+fO5c7PgIAApq+vz16+fMktLykpYW5ubmzgwIGMsf9P1r6+vnzbmTFjBrO2tub7LN6+fcsMDAzY2rVrGWOM/fHHH8zFxYXv3D9y5AjbuXMn97Ozs7PAtuuS9+/fM2tra/bLL7+wlStXMl1dXXbv3j3GGGP29vZs6tSpfPUXLFhQZrI+e/YsVyczM5MZGRmxoKAgxhhjU6dOZZaWliw3N5erk5OTwywtLbnti/JZbdiwgRkbG/P90YuJiWHBwcHcZzBy5EgueVekTnaDAEDnzp0hISEBALh06RJatmwJHR0dFBcXo7i4GDweDw4ODvjvv/9QWFiIy5cvQ05ODnZ2dtw2GjZsCHt7+3K3Ler2DQ0NIScnh8GDB2Px4sU4f/48tLW1MX36dCgqKkJFRQWdOnXCH3/8AV9fXxw7dgw8Hg9+fn7o3LmzQAy3bt1CYWEh+vTpw1feq1cvyMjI8H0lat68OdTV1bmfS/u98/Pzq9a4YmJra4tdu3ZBVlYWjx8/RlRUFNatW4fMzEwUFRUBwDe3W15eHhITE9G7d29ISv7/6dq6dWuYmpoKfO2sz65duwYTExO0atWKK5OUlETv3r2RmJjIdVcAgKamJt+6ly9fRrdu3SAnJ8edw0pKSjAwMMDFixcBAN26dcPTp0/x008/ISQkBHfu3EHfvn3h5eVVMwcoBk2bNsXChQsRFxeHDRs2YNq0adDW1sbz58/x8uVLuLi48NUv616AjIwMnJycuJ+VlJTQtWtXrivk2rVrcHR0RMOGDbk6CgoKcHR05M43UT4rMzMz5Ofno2/fvli+fDmuXbuG7t27Y8qUKXz5R1R19gZjs2bNuP9/+PABr1+/hq6ubpl1379/j/fv30NJSUmgEVRUVMrdtqjbV1NTw65du7Bx40YcOHAAO3fuROPGjTFs2DD89ttvkJCQwNatW7Fu3TpERETg8OHDkJGRgbOzMxYuXCjwNvisrCwAnxPxlyQlJaGsrMz3iykvL89Xp/QYeTxemfHWFB6PhxUrVmD37t3Iy8tDq1atYGBgADk5OW7s6Le226dPn8AYE/o5vnz5sqYPu9pkZWWhXbt2AuUqKipgjCE3N5crK+scPnbsGI4dOyawfuk2e/fuDR6Phz179mDt2rUIDg5GmzZt4OPjU69ucNrY2EBFRQXp6encxVhmZiYAwRd6l3XeKCkp8f3hL12vNFlnZWUJPd9Kfy9F+ayMjY2xceNGbN++Hdu2bcPGjRuhoqKCiRMnVukPZJ1N1l9q1KgROnbsKHT8p5KSElq0aIHMzEwwxvgSdkZGhli2DwAGBgYICQlBYWEhEhISsG/fPqxfvx5dunSBi4sLWrZsiT///BMLFizA/fv3cfr0aWzatAnNmjXDH3/8wbfN0uT97t07tG3blivn8XjIzMzk9lmXlZ6If/31F3r06IFGjRoBAAYPHsxX71vabcaMGZCQkEB6errA/t+9e1cv2klUjRs3LvM43759C+DzeVj6/68pKirC1tYWI0aMEFgmKyvL/d/NzQ1ubm7Izs7GhQsXsGnTJsyaNQvm5uZlJqi6aNWqVcjJyUG7du3w+++/Y+/evWjZsiUAwd/30iT+pezsbIE8kZ6ezp1Lwj6Hd+/eoWnTpuXW+fKzAj7/YbGxsUF+fj4uX76MnTt3wt/fH8bGxtDT06vUcdfZbpAvmZmZ4eXLl2jRogX09fW5f1FRUQgNDYWMjAzMzMxQWFjIN0ri65+/ZfuhoaFwdHREYWEhZGVlYWlpiUWLFgEAXr16hdu3b8PKygq3b9+GhIQEdHR0MH36dGhqauLVq1cC+zQ0NISsrCxOnDjBV3769GkUFRXVi7GuCQkJ0NLSwsCBA7lE/ebNGzx8+JC76v/WdlNQUICuri5OnjzJ903i1atXuH79Orp27VrzB15NzMzMkJCQwDeCg8fj4fTp09DX1+dLul8zNzfHkydPoKury52/Xbp0wcaNGxEXFwcAmDlzJqZMmQLg8wWKq6srJk+ejOLiYrx79w4ABK4465pbt25h27ZtmDp1KpYuXYrbt29j27ZtaNWqFdTU1BAVFcVXPzIyUmAb+fn5uHbtGvfzu3fvkJCQAAsLCwCfP4fo6Gjk5eVxdfLy8hAdHc39XoryWf39998YPHgwGGOQl5eHg4MD9wBM6XpSUlIiH3vd/mT+Z+DAgWjZsiVGjx6NI0eO4PLlywgICMC6deugrq4OCQkJWFhYwMLCAnPmzEFYWBhiYmIwYcIEpKenV9g/JMr2u3Xrhnfv3sHb2xuxsbG4cOEC/Pz8ICcnBwcHB2hra6Nhw4aYPXs2Tpw4gStXrmDlypW4d++eQD8a8LnvbezYsdizZw+WLFmC+Ph4bN++HX/88QfMzc1hY2NTXc0pNgYGBkhKSsKmTZtw9epVhIWFwdPTE4WFhVx/ujjabfr06Xj8+DEmTpyI6OhoHD9+HKNGjYKioiJGjRpViy0gXqNHj4aioiJGjhyJ48ePIzo6GhMmTMCTJ08wffr0ctf19vbG48ePMWnSJERFRSE2NhYTJ07EuXPnuO69bt26ISIiAoGBgbh06RLOnDmDVatWoX379tx9lcaNGyMpKQlXr17lG0JaFxQUFMDPzw+ampoYNWoUunbtiiFDhmD16tVITk7G1KlTcfLkSfj7+yM+Ph7BwcHYtWsXAP4/QjIyMvD19cXJkycRGRmJsWPHolGjRty3Em9vb+Tk5GDUqFGIiIjA2bNnMWrUKOTl5cHb2xuAaJ+VlZUV7t69izlz5iA+Ph4xMTHw9/eHkpISzM3NAXz+o/n06VNcunSJ6xoVSqTbkDXMwcGBzZ07l6/s3bt3bM6cOaxbt25MX1+f9e7dm4WGhvLVyczMZD4+Pqxr167MxMSE/fnnn2zq1KnMzc2t3G2Luv34+Hg2dOhQ1rVrV2ZoaMg8PT3Zf//9xy1/9uwZdydZV1eX9enTh+3bt49b/vXQPcYYCw0NZS4uLkxXV5fZ2dmxwMBAlpeXxy339fVlzs7OfOuUjgg4fPhwRU0pdl+OBikoKGALFy5k1tbWzMDAgLm4uLDVq1ez4OBgpq+vzw1F+tZ2K92Gh4cH09fXZ+bm5uy3335jaWlpNXfg1eTL0SCMfW6LKVOmsK5duzIjIyM2fPhwbiQDY+V/9rdv32ZjxoxhRkZGzNjYmP3888/swoULfHV27drFevfuzQwMDJi5uTmbNm0ae/HiBbc8MjKSWVpaMj09PZaQkFANR1x1gYGBTEdHh2/UVlZWFrO2tmZDhgxhxcXFbNeuXczR0ZHp6uqyoUOHsm3btjFNTU129+5dxtjn30EbGxt2+PBhZm9vz/T19dmYMWNYcnIy377u3LnDRo8ezYyMjFjXrl3Z+PHjuVEnpSr6rBj7PLqrdKitsbEx++WXX9iDBw+45Tdv3mT29vZMV1eXnThxotzjl2Ds+5i15cWLF7h16xacnZ35vi4OHjwYqqqqCAkJqcXoCCHV7fjx49DX14eGhgZXtnv3bvj7++PKlSto3LhxLUb37erFDUZR+fr6wtXVFQMGDABjDKdOncLdu3cxc+bM2g6NEFLNwsPDERwcjGnTpqF58+Z49OgRVq1ahf79+9f7RA0A382VNfD5seY1a9bgwYMH4PF40NbWxuTJk+tF/y8h5NtkZGRg2bJlOH/+PD58+ABVVVX0798fEydOhIyMTG2H982+q2RNCCHfq3oxGoQQQn50lKwJIaQeoGRNCCH1ACVrUuPmzJkDLS0t6OjolPk4cKl+/fpBS0sLc+bMEVi3rs21XIrH4/HFdujQIdHmKv5GNbUfUnsoWZNaw+PxEB0dXeay1NRUPHjwoIYj+jY5OTkYMmQIwsPDazsU8h2iZE1qTVlzOZSKjIwUmEGtrvvw4QPu3LlT22GQ7xQla1JrnJyccPHixTLnoIiIiOB7HRshPzpK1qTWODs7Iz8/n5scv1RGRgZu3LiBnj17im1fpX269+/fx6+//gpjY2N069YNgYGBKCkpQXh4OFxcXGBkZIShQ4cKvG8vKysLixYtgo2NDfT09ODq6oodO3Zw83ZfuXKFm9A+JCREoF89IyMDPj4+MDU1RdeuXeHt7S0wF3d+fj6WL18OR0dH6OnpwdHREcuWLRN4yURGRgb8/PzQrVs3mJiYYP78+SgsLBRbW5G66bt63JzULyYmJlBSUkJUVBTfVXRUVBTk5eVhaWkp9n2OHz8eJiYmmDNnDs6ePYutW7fi4cOHePDgAUaOHAnGGNatW4dff/0VJ0+ehLS0NPLy8jB8+HC8evUKw4YNg6qqKi5fvowlS5bg2bNnWLBgATp27Ag/Pz8sXboUPXr0QI8ePfi6cebOnQtTU1P4+Pjg8ePH2LNnD9LS0nDkyBEAn6fzHT16NG7evImBAwdCT08Pt2/fxqZNm5CQkICdO3dCRkYGBQUFGD58ONLS0jBixAg0b94c4eHh3EtzyfeLkjWpNVJSUnBwcEB0dDR4PB43jWVERATs7e3Lnb+5qoyMjLBy5UoAn9+cYmlpiYsXL+Lo0aPcNKG5ublYv3490tLS0K5dO2zZsgVPnz7FwYMHoaWlBQAYNmwYVqxYgQ0bNsDDwwPa2tpwdnbG0qVLoaWlhf79+/Pt18rKCmvXruV+zs3NxaFDh5Camgp1dXUcPHgQN27cgJ+fHzft67Bhw9CpUyf8/fffCAsLw7BhwxAWFobk5GSsWbMGzs7OAIAhQ4bA3d0d2dnZYm8vUndQNwipVU5OTsjIyMDNmzcBfB5RcenSJS4RiduX223UqBGUlZXRrl07vvdkqqmpAQA3If/Zs2ehqamJ5s2bIzMzk/tXui1hI1q+9PW7NvX19fn2ce7cOSgqKsLT05Ov3ogRI6CoqMjdiI2Li4OKigrfcTRs2BDu7u6iNQCpt+jKmtSq7t27Q15eHufOnUPXrl0RGxsLSUlJvhcfi9PXr66SlpYWeJ9h6ds7St9Mk5KSgk+fPgntlinrTUBf+3pkS4MGDQCAe7FwWloa1NXVBSYckpWVhbq6Ol68eAHg81TAX748uVT79u0rjIHUb5SsSa1q0KABrKysEBUVBR8fH0RERMDKygoKCgrVsr+yXqNU0ZuESkpKYGJiwr0S62stWrSocL8VvS6rvPnUeDwel8QlJCRQUFBQqfXJ94G6QUitc3Z2RnJyMh4+fIi4uDj06NGjtkPi06ZNG+Tm5sLKyorvn66uLj5+/Cjw9vmq7iM1NZW70i5VWFiItLQ0tGrVCsDnLprU1FQUFxfz1UtNTf3mGEjdRsma1DoHBwdISUkhMDAQnz59qnPjqx0dHXH//n3ExMTwla9btw7Tpk3Do0ePAAh2n1R2Hzk5Odi9ezdf+Z49e5Cbmwt7e3sAQM+ePZGdnY2wsDCuTlFREfbv31/pfZL6hbpBSK1TUlKCiYkJLly4AAsLCygpKVW4zsqVK8vsKnF1dRX7kL8JEybg7NmzmDJlCoYOHYrOnTsjISEBR44cga2tLWxtbQF8fgmypKQkzp07h9atW1dqnLi7uzvCw8MREBCAhw8fQk9PD3fv3sWhQ4dgaGjI3UDs378/9u/fj0WLFuHJkydo164djh49yt2oJN8vStakTnBycsLVq1dFTnDHjx8vs7xDhw5iT9ZNmzbFvn37sHr1apw+fRr79u1D69atMXnyZIwfP57rj5aXl8f06dOxZcsW+Pv7o23btiLvQ1ZWFtu3b8eaNWtw6tQpHD16FKqqqpgwYQImTZrE9VlLSUlh8+bNWLlyJU6dOoW8vDzY2tpi1KhRFb4BndRv9KYYQgipB6jPmhBC6gFK1oQQUg9QsiaEkHqAkjUhhNQDlKwJIaQeoGRNCCH1ACVrQgipByhZE0JIPUDJmhBC6oH/AydTQt5rSEBKAAAAAElFTkSuQmCC\n", + "image/png": 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", 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\n", 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", 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\n", 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", 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" ] @@ -2277,7 +2275,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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gQYO0ceNGjRw5UvXq1dOmTZs0Y8YM+fv7q3379pIkLy+vK57r7V3yhSVhYWFlEm9JlaaQZQaZmZkuG3tpMF735Uljlew3XopSAAAAANxSVlaW1q1bp3Hjxqlr166SpCZNmujGG2/USy+9pMcee0xS0RlRha8DAgIcGzAAeBj2lAIAAADglg4ePChJuvfee63aIyIiJEnbt2+Xj4+PsrOzrY4Xvr58rykAQNmiKAUAAADALRUWlX788Uer9p9++kmSFBwcrIiICK1atUqGYViOr1y5UgEBAapfv77DYgUAT8TyPQAAAABuKSwsTNHR0XrjjTd0+vRp3X333dqyZYumT5+uqKgoNWzYUIMGDVKfPn2UnJysLl26aOPGjUpPT9fQoUNVqVIlZw/hivLyz8u3vI/d+gOAo1CUAgAAAOC2pkyZomnTpmnevHk6duyYatSoofj4eA0YMECSFBkZqbS0NKWmpioxMVFVq1bV8OHDFR8f7+TIr863vI86Dv20xP2XTupkx2gAoPQoSgEAAABwW76+vhoyZIiGDBly1T4xMTGKiYlxYFQAAIk9pQAAAAAAAOAEFKUAAAAAAADgcBSlAAAAAAAA4HAUpQAAMJm8/PN27Q8AAACYgUtsdP7hhx/qn//8pw4dOqRatWqpf//+euSRRyzH161bpylTpmjnzp2qUqWKevbsaeqnZQAAUByeqgQAAABPYPqZUgsWLNArr7yiBx54QDNmzFCzZs30/PPPKyMjQ5KUlZWlgQMHKjg4WGlpaerYsaNSUlKUnp7u5MgBAAAAAABwNaafKbVo0SLdf//9euGFFyRJzZo105YtWzR//ny1a9dOqampqlevniZMmCBJioqKUkFBgWbNmqW4uDj5+vo6M3wAgAMwoxYAAABwPaafKZWbmys/Pz+rtptuukknTpxQbm6uNmzYoLZt21odj42N1cmTJ5WVleXIUAEATsCMWgAAAMA12VSUOnXqlL3iuKqnnnpKa9euVUZGhnJycvTZZ5/pq6++UqdOnbRv3z7l5+crKCjI6pw6depIkvbs2ePweAHAkzkjT1w6o7ZZs2YaOXKkIiIiNH/+fEmymlEbFRWl5ORk9e3bV7NmzVJeXp7D4wUAT+aMPAEAMC+blu81a9ZMrVq10sMPP6zWrVurQoUK9orLokOHDvruu++UlJRkaevSpYv69eunjRs3SpL8/f2tzimcWZWTk1Piz9m6davOnTtXqhgbN25s8zmZmZml+iyzcPX4beFJY5UYrzsr7VhtucY5I0/k5ubq5ptvtmq76aablJ2dbZlRe2kOkS7OqJ09e7aysrLUtGlTu8cIALjIGXkCAGBeNhWlnnrqKX322WdavXq1/Pz8FB0drQ4dOqh58+by8fGxS4CDBg3Sxo0bNXLkSNWrV0+bNm3SjBkz5O/vr/bt20uSvLy8rniut3fJJ4KFhYWVSbwlVZpClllkZma6dPy28KSxSozXnTlqrM7IE0899ZRefPFFZWRkqGXLllq3bp2++uorJScnl2hGLUUpAHAcZ+QJAIB52VSUev755/X8889r48aNWr58uVauXKlPP/1UN998s2JjY/Xwww8rIiKizILLysrSunXrNG7cOHXt2lWS1KRJE91444166aWX9Nhjj0kqOiOq8HVAQECZxQIAuDZH5wnJfWfU2spss/7MFo89edJYJcbrzhwxo9YZeQIAYF6levpeeHi4wsPDNXr0aP3www/68ssv9fXXX2vBggWqVq2aOnbsqM6dOys4OPi6gjt48KAk6d5777VqL0xU27dvl4+Pj7Kzs62OF76+/M44AMAxHJUnJPedUWsrM836Yxai+2K87svRY3VkngAAmNd1PX3Py8tLlSpVsvwxDEOnTp3Shx9+qA4dOigxMVHHjx8v9fsXFpV+/PFHq/affvpJkhQcHKyIiAitWrVKhmFYjq9cuVIBAQGqX79+qT8bAHD97J0nCmfUjhkzRr1791aTJk3Uv39/jRgxQu+//75uuOEGScyoBQCzsneeAACYW6lmSm3evFkZGRlauXKlDh48qPLly6tVq1YaOHCgWrduLUlavny5XnnlFQ0ZMkTz5s0rVXBhYWGKjo7WG2+8odOnT+vuu+/Wli1bNH36dEVFRalhw4YaNGiQ+vTpo+TkZHXp0kUbN25Uenq6hg4dqkqVKpXqcwEA18dReYIZtQDgmhyVJwAA5mZTUWrixIn67LPPdODAAXl5eem+++7ToEGDFBsbW+Ruc5cuXfTFF19o/fr11xXglClTNG3aNM2bN0/Hjh1TjRo1FB8frwEDBkiSIiMjlZaWptTUVCUmJqpq1aoaPny44uPjr+tzAcDM8vLPy7d8yTeErXu3Y5aeOTpPXDqj9o477rC0X2lGba9evSzL+JhRCwDO4YzvEwAA87KpKDV79mzVq1dPPXv2VPv27XXbbbcV279x48Zq1KjR9cQnX19fDRkyREOGDLlqn5iYGMXExFzX5wCAK/Et76OOQz8tcf+lkzrZMZq/ODpPMKMWAFyLM75PAACKMstNbpuKUhkZGcUudbhw4YIOHDigWrVqSZL69OlzfdEBAFyKM/IEM2oBwHXwfQIAzMEsN7lt2ui8ffv2WrZs2VWPL1y4UJ07d77emAAALsoZeaJwRu1XX32lzZs367PPPtPgwYPl6+tr6RMTE6OlS5dqy5Yt+uKLLyhIAYCT8H0CAHCpYmdKHTlyRP/5z38srw3D0I8//qiCgoIifS9cuKClS5de9bHbAAD3Q54AABSHPAEAKE6xRanAwEDNmjVLv/32m6SLj2xdsGCBFixYcNVz4uLiyjRAAIB5kScAAMUhTwAAilNsUap8+fKaM2eO9u/fL8Mw1KtXLyUkJKh58+ZF+np7eyswMFDBwcF2CxYAYC7kCQBAccgTAIDiXHOj8+rVq6t69eqSpHHjxikiIsKy8SAAAOQJAEBxyBMAgKux6el7Xbp0sVccAAA3QJ4AABSHPAEAuFSxRam7775bKSkp6tixoySpbt2619x40MvLS9u2bSu7CAEApkWeAAAUhzwBAChOsUWpzp07q3bt2laveRoGAKAQeQIAUBzyBACgOMUWpcaNG2f1evz48XYNxlPk5Z+Xb3kfu/UHAEchTwAAikOeAAAUx6Y9pa4kPz9f69evl7e3t5o1a6Zy5a77Ld2eb3kfdRz6aYn7L53UyY7RAIB9kScAwPFsvalZ9+4wO0ZTPPIEAHgum674eXl5Gjt2rPbv3685c+YoLy9P3bt313//+19JUkhIiN577z1VqVLFLsECAMyNPAEA5mDWm6DkCQDApbxt6Txt2jR99NFHuv322yVJixcv1vbt2xUXF6c33nhDv//+u9566y27BAoAMD/yBACgOOQJAMClbJoplZGRoccee0xjx46VJK1cuVIBAQEaPny4ypUrp3379unjjz+2S6AAAPMjTwAAiuOsPPHjjz9q8uTJ2rZtmwICAhQbG6shQ4bIz89PkrRu3TpNmTJFO3fuVJUqVdSzZ0/Fx8eXeRwAAGs2zZQ6fPiwGjVqJEk6e/asfvzxR0VGRlrWfd9+++06efJkmQcJAHAN5AkAQHGckSd++ukn9enTR7feeqtmzpypxMRELVmyRGPGjJEkZWVlaeDAgQoODlZaWpo6duyolJQUpaenl2kcAICibJopdcstt+jo0aOSpLVr1yovL08PPPCA5fiOHTt02223lWmAAADXQZ4AABTHGXli4sSJatSokd566y15eXmpWbNmunDhgubOnauzZ88qNTVV9erV04QJEyRJUVFRKigo0KxZsxQXFydfX98yjQcA8BebilL333+/3nvvPVWoUEEffPCBKlWqpOjoaJ08eVKffPKJPvroIz3++OP2ihUAYHLkCQBAcRydJ44fP64NGzZo0qRJ8vLysrT36NFDPXr0UG5urjZs2KCkpCSr82JjYzV79mxlZWWpadOmZRYPAMCaTcv3Ro0apbp16+rNN9/U8ePHNXbsWN1444369ddf9eabb6phw4YaPHiwvWIFAJgceQIAUBxH54lffvlFhmGocuXKSkpKUqNGjdS4cWO9/PLLOnfunPbt26f8/HwFBQVZnVenTh1J0p49e8osFgBAUTbNlLrxxhs1d+5cHT9+XP7+/paprHfffbcWLFighg0b2iVIAIBrIE8AAIrj6Dxx/PhxSdKIESMUExOjmTNnaseOHZo6dapyc3PVvXt3SZK/v7/VeYUboOfk5JRpPAAAazYVpQoFBgZavb7hhhv4ogEAsCBPAACK46g8kZ+fL0m699579fLLL0uSIiMjZRiG3nzzTXXr1k2SrJb2Xcrbu+QLS7Zu3apz586VKs7GjRuX6jxbZGZm2v0zSspMsTgC43VfrjzW0lx3Sjve4j7L5qLUN998o6VLl+ro0aM6f/58keNeXl567733bH1bAICbIE8AAIrjyDxROOMpKirKqr1FixYaP368Nm/eLKnojKjC1wEBASX+rLCwsOsJ1e4cUfgqiczMTNPE4giM13150lgL2WO8NhWlPvjgA40dO1aSVKVKFZ5EAQCwQp4AABTH0XnijjvukCTl5eVZtRfOoKpZs6Z8fHyUnZ1tdbzw9eV7TQEAypZNRal//vOfqlu3rt59913dcsst9ooJAOCiyBMAgOI4Ok+EhISoRo0aWrFihZ588klL+5o1a1SuXDmFh4crIiJCq1atUq9evSzL+FauXKmAgADVr1/f7jECgCez6el7hw4dUvfu3fmiAQC4IvIEAKA4js4TXl5eGjZsmDZs2KBhw4bp22+/1TvvvKOZM2cqLi5OgYGBGjRokLKyspScnKyvv/5aU6dOVXp6uhISElSpUiWHxAkAnsqmmVK1a9fW0aNH7RULAMDFkScAAMVxRp5o3769fH19NX36dCUkJKhKlSpKTExUQkKCpIsbn6elpSk1NVWJiYmqWrWqhg8frvj4eIfGCQCeyKai1IABA/T6668rNjZWf/vb3+wVEwDARZEnAADFcVaeiI6OVnR09FWPx8TEKCYmxmHxOFpe/nn5lvexW38AKC2bilKZmZny8/NTp06dFBQUpMDAwCKPT7XHU5V+/PFHTZ48Wdu2bVNAQIBiY2M1ZMgQy9M01q1bpylTpmjnzp2qUqWKevbsyZ0NAHACZ+UJAIBrIE84h295H3Uc+mmJ+y+d1MmO0QDAX2wqSq1du1aSVK1aNZ09e1YHDhywS1CX+umnn9SnTx+1adNGM2fO1N69ezV58mQdP35cU6ZMUVZWlgYOHKh27drpueeeU2ZmplJSUmQYhvr27Wv3+AAAf3FGngAAuA7yBADgUjYVpb788kt7xXFVEydOVKNGjfTWW2/Jy8tLzZo104ULFzR37lydPXtWqampqlevniZMmCBJioqKUkFBgWbNmqW4uDgeRw4ADuSMPCExoxYAXIWz8gQAwJxsevrepY4cOaJNmzbp1KlTysvL04ULF8oyLknS8ePHtWHDBj3xxBNW03p79Oih1atXy9vbWxs2bFDbtm2tzouNjdXJkyeVlZVV5jE5Q17+ebv2BwB7cESekP6aUXvrrbdq5syZSkxM1JIlSzRmzBhJssyoDQ4OVlpamjp27KiUlBSlp6fbJR4AQMk4Kk8AAMzLpplS0sV14K+//rq2b98uSZozZ47Onz+vUaNGacSIEWrfvn2ZBffLL7/IMAxVrlxZSUlJ+uqrr+Tj46OHH35YI0eO1P79+5Wfn6+goCCr8+rUqSNJ2rNnj5o2bVpm8TgLa8ABuBJH5gmJGbUA4GocnScAAOZlU1Hq559/Vp8+fXT77berV69elg0IK1eurHLlymnYsGHy8/NTq1atyiS448ePS5JGjBihmJgYzZw5Uzt27NDUqVOVm5ur7t27S5L8/f2tzitcrpGTk1Piz9q6davOnTtXqjgbN25cqvPsKTMz06Xf30w8aawS43UVpbnulHastnyWM/LEhg0bNGnSpCIzanv06KHc3Fxt2LBBSUlJVufFxsZq9uzZysrKcoubFwDgKhydJwAA5mZTUeqtt95SzZo1tXDhQp05c0bz5s2TJDVo0EBLlizRE088obfffrvMkkh+fr4k6d5779XLL78sSYqMjJRhGHrzzTfVrVs3SSryxI5C3t4lX50YFhZ2ndGaiz0LZZmZmaYsxNmDJ41VYrzuzhFjdXSeYEYtALgWR+cJlE5e/nn5lvexW38AKGRTUWrjxo16+umnVbFiRZ09e9bqmL+/v7p166bU1NQyC65wxlNUVJRVe4sWLTR+/Hht3rxZUtEZUYWvAwICyiwWAMC1OTpPMKP2L2ab9We2eOzJk8YqMV5XYdYZtY7OEygdtg8B4Cg27ylV3N4bubm5ZbpB4R133CFJysvLs2ovnEFVs2ZN+fj4KDs72+p44evL74wDAOzPkXmCGbV/MdOsP0+ahehJY5UYr7tz1FgdmScAAOZm09P3GjZsqGXLll3x2JkzZ/Txxx+rQYMGZRKYJIWEhKhGjRpasWKFVfuaNWtUrlw5hYeHKyIiQqtWrZJhGJbjK1euVEBAgOrXr19msQAArs3ReaK4GbWGYTCjFgBMxtF5AgBgbjYVpZ599llt27ZNPXv21OLFi+Xl5aWff/5Z//znP9WpUyft379fAwcOLLPgvLy8NGzYMG3YsEHDhg3Tt99+q3feeUczZ85UXFycAgMDNWjQIGVlZSk5OVlff/21pk6dqvT0dCUkJKhSpUplFgsA4NocnSeYUQsArsXReQIAYG42FaXCw8P19ttv6/Dhw3rzzTdlGIamTJmiN954Q+fOndOUKVPKfMPY9u3ba9q0adq1a5cSEhI0f/58JSYmavjw4ZIuLtNIS0vTrl27lJiYqKVLl2r48OHq379/mcYBALg2R+cJZtQCgGtxxvcJAIB52bynVPPmzfX5559r27Ztys7O1oULF1SjRg3Vr19f5crZ/HYlEh0drejo6Ksej4mJUUxMjF0+GwBgG0fmicIZtUOGDNGwYcPUtWtXbdmypciM2j59+ig5OVldunTRxo0blZ6erqFDhzKjFgCcwBnfJ2Bftjx9r+7d5t6jEYBjFXvVf+qpp2x+Qy8vL7333nulDggA4DrMkCfat28vX19fTZ8+XQkJCapSpYoSExOVkJAg6a8ZtampqUpMTFTVqlU1fPhwxcfHl1kMAIArM0OegP3Z8rQ+ntQH4FLFFqX2799fpO3YsWPKzc1V5cqVVadOHV24cEEHDhzQH3/8oZtuukkhISF2CxYAYC5myRPMqAUAczJLngAAmFOxRakvv/zS6vX333+vgQMHavz48XrkkUesHqW9bNkyjRkzRj169LBPpAAA0yFPAACKQ54AABTHpo3Ox44dq8cee0ydO3e2SiCS9PDDD+vJJ5/UW2+9VaYBAgBcB3kCAOwjL/+8s0MoE+QJAMClbNpJMDs7W48//vhVj1erVk3/+9//rjsoAIBrIk8AgH3YsmePZN59e8gTAIBL2TRTKigoSMuXL9f580Xv1OTm5uqTTz7RXXfdVWbBAQBcC3kCAFAc8gQA4FI2zZQaMGCAhgwZoieffFJdu3ZVrVq1lJubq99++00ffvihDh48qLfffttesQIATI48AQAoDnkCAHApm4pS7du317lz5zRp0iS9/PLL8vLykiQZhqEaNWpo2rRpat68uV0CBQCYH3kCAFAc8gQA4FI2FaUkqWvXrurcubO2bt2qAwcOyMvLS7Vq1VK9evXsER8AwMWQJwAAxSFPAAAK2VyUkiRvb281aNBADRo0KOt4AABugDwBACgOeQIAINm40TkAAAAAAABQFihKAQAAAAAAwOEoSgEAAAAAAMDhKEoBAAAAAADA4ShKAQAAAAAAuLC8/PPODqFUSvX0PQAAAAAAAJiDb3kfdRz6aYn7L53UyY7RlBwzpQAAAAAAAOBwFKUAwCRcdcotnM/Wfzv27l/37jCb+gMAAMAzsXwPAEzClim3ZpluC3Ow93RtV50ODgCXGzx4sHbs2KHPP//c0rZu3TpNmTJFO3fuVJUqVdSzZ0/Fx8c7MUoA8BzMlAIAAADg9j799FOrYpQkZWVlaeDAgQoODlZaWpo6duyolJQUpaenOylKAPAszJQCAAAA4NaOHDmi119/XdWqVbNqT01NVb169TRhwgRJUlRUlAoKCjRr1izFxcXJ19fXGeECgMdgppQbsvdeIQAAAIArGTNmjJo3b67IyEhLW25urjZs2KC2bdta9Y2NjdXJkyeVlZXl6DABwMJTvqczU8oNsfcHAAAAcNHHH3+srVu3atmyZUpJSbG079u3T/n5+QoKCrLqX6dOHUnSnj171LRpU4fGCgCFPOV7PUUpAAA8TF7+efmW93F2GABgdwcOHNC4ceM0btw4BQYGWh07deqUJMnf39+q3c/PT5KUk5Nj02dt3bpV586dK1WcjRs3LtV5rsjWHHT6zDn9d/tWO0Zkf5mZmSXuW/fuMPndULHE/c3487FlvK7OnmM143WhtOMtbiwUpQAA8DCecucNgGczDEOjRo1Sq1atFBsbe8XjkuTl5XXF8729bdvpJCwszPYgPVBpcpAZv5yXVGZmps3xu/LPpzTjdVWeNNZC9hgvRSkAAAAAbueDDz7Qjh07tHTpUhUUFEj6qxBVUFCggIAASUVnRBW+LjwOALAflytKDR48WDt27LB6nOu6des0ZcoU7dy5U1WqVFHPnj0VHx/vxCgBAAAAONPKlSv1xx9/qEWLFkWOhYWF6ZVXXpGPj4+ys7OtjhW+vnyvKQBA2XOpotSnn36qzz//XLVr17a0ZWVlaeDAgWrXrp2ee+45ZWZmKiUlRYZhqG/fvk6MFgDgaNy4AAAUevXVV3X69GmrtunTp2v79u2aNm2aatasqYyMDK1atUq9evWyLONbuXKlAgICVL9+fWeEDXgUW/cYc+V9MV05dntymaLUkSNH9Prrr6tatWpW7ampqapXr54mTJggSYqKilJBQYFmzZqluLg4+fr6OiNcAICDceMCAHCp4ODgIm033XSTfH191aBBA0nSoEGD1KdPHyUnJ6tLly7auHGj0tPTNXToUFWqVMnRIQMex5P2ufSksdrCtt37nGjMmDFq3ry5IiMjLW25ubnasGGD2rZta9U3NjZWJ0+eVFZWlqPDBAA4QUluXERFRSk5OVl9+/bVrFmzlJeX56RoAQBmERkZqbS0NO3atUuJiYlaunSphg8frv79+zs7NADwCC5RlPr444+1detWvfjii1bt+/btU35+fpH13nXq1JEk7dmzx2ExAgCchxsXAICSGD9+vNUSb0mKiYnR0qVLtWXLFn3xxRcs8QYABzL98r0DBw5o3LhxGjdunAIDA62OnTp1SpLk7+9v1e7n5yep6JM0irN161adO3euVDG6w2MgMzMz7drflXnSWCXG60z2vpaUdqxmv8YV3rhYtmyZUlJSLO0luXHRtGlTh8YKAAAA4C+mLkoZhqFRo0apVatWio2NveJxSZZNCS/n7V3yiWBhYWGlC9JN2PKlMzMz0/RfUsuKJ41VYrzuzh3H6qgbFxI3L2xlpoKvvXnSWCXG6yyOuI64680LAIB5mboo9cEHH2jHjh1aunSpCgoKJP1ViCooKFBAQICkol8sCl8XHodrseWpBDzBAPBcjrxxIXHzwlae8iXV04rbjNe9edJYAQDmYOqi1MqVK/XHH3+oRYsWRY6FhYXplVdekY+Pj7Kzs62OFb6+fMkGXIMtTyXwlCcSACiKGxcAAACAazN1UerVV1/V6dOnrdqmT5+u7du3a9q0aapZs6YyMjK0atUq9erVy3I3fOXKlQoICFD9+vWdETYAJ7F15lzdu5n54sq4cQEAAAC4NlMXpYKDg4u03XTTTfL19VWDBg0kSYMGDVKfPn2UnJysLl26aOPGjUpPT9fQoUNVqVIlR4cMwIlsmWUnMdPO1XHjwjPZWnxmmTcAAIB5mbooVRKRkZFKS0tTamqqEhMTVbVqVQ0fPpx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", 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" ] @@ -2306,7 +2304,7 @@ "outputs": [ { "data": { - "image/png": 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" ] @@ -3210,7 +3208,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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", 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\n", 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", 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\n", 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", 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" ] @@ -3575,7 +3573,7 @@ "outputs": [ { "data": { - "image/png": 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x4sQJ/PLLL0hKSkLt2rXh7OwMIyOj8o+YqArjvbqIqDpKTEyCqak5dHX1KjuUd55IJIKurh5MTc2RmJj0ZokbAJiamqJXr17lHiCRpuG9uoiousnPz4dEwikfVYlEoqv0tLXKxO3ixYsICgrCo0ePIAiCQtmdO3fKJ0IiIiKqNDw9WrWU9PdQmbgtXrwYLVq0QEBAAMRiPmiBiIiI1C8t7QV0dCSoUaNGZYdSqVRmYo8ePcKuXbugq8thVCIiIqocffv2wubN36NGjYaVHYqC0NAQPH0ai6CgBWppT+V93N5//30kJSW9VSM3btxAr1690LJlS/Tr1w8PHjwosk1+fj7mzJmDdu3awd7eHtOnT0dubu5btUtERETVQ3p6WmWHUCWoTNzc3NwwYsQIhIaGIiwsTOFfaeTl5WHs2LHw8fFBVFQUOnbsiKlTpxbZ7scff8STJ09w8uRJnDhxArGxsdi0aVOZD4iIiIiql5EjhwIAfHz64/LlaMydG4hZs6ajRw9XjB/vh9DQEAQGzpRvHxV1EV5e7vLlEyeOoV8/b7i4dMI330zCs2fJRdo4d+539O7tqbBu1KjhOHr0MAoKCrBu3Sr06dMTnTq1R79+3rh8+VKROsaMGYnw8J/lyyEhGzB37ssnTclk+QgOXg9PTze4u7tg9erlb3TfPJWnSnft2gUA2Llzp8J6kUgELy8vlQ1cuHABBgYG8Pb2BgCMGTMG33//Pe7evYumTZvKt3vw4AFkMpn8AgiRSASJRFLqAyEiIqqKIm8l4H5cGmQFAqZsPKcxtxF6tGhhkXXGbduilnMXFObl4cnKFUXKTTt0hGnHjpBlZODp+nVFyms6OcHEzh75KSn4+7tv8f70GaWKJTR0G+ztW+OHH3bByqohjhw5hJs3r+OHH3ZBLBZj584fle5748Z1LF++GKtXb0CTJh9i8+bvEBAwDSEhivejtbNrh+zsLNy5cxvNm3+EpKRE/PXXXTg6dkZExBFcuhSFzZu3w8DAAMHB67B+/Rps3bqjVPEDwI4d23Hp0kVs2bIdEokuAgKmYevWTRg1akyp6wBKkbidOXOmTBW+7uHDh7C2/vcGpdra2rCyssL9+/cVErd+/fphxIgRaNOmDQDA1tZW4WkNpRH/7UZIn7+QLxu1aQvTzs4ozMvD32tWFtne+PMOMPm8IwoyMhAXvF6+vkNSJrREImS8lwujtnbIT01Bwqbviuxf06UbDFu2gjQhHonbtxUpr+XhCYOPPkbuk8dI3vVTkXJz7z7Q/6AJcu79hWcH9hUpt+g/EHoN30PW7VtIPXywSHntwUMhqVMXmdeu4vmJY0XK64wYBZ1aZsiIuogXvxb9O9YbMx7aRkZIO/c70s/9r0h5/YlfQ0tXFy9+OY2MS1FFyq2mTgcApB6PQNb1awplIokEDSZNBgCkHApH9p3bCuXahoaoN3YCACB5/17k3r+nUC6uWQt1R44GACTt+hF5T54olEvq1EHtwS/7R+L2rZAmKD7oXbdhQ1j2/wIAEB/6LWTPUxXK9aw/gEXvvgCAuI3rUJCZqVBeo/lHMOvREwDwdPUKCFKpvKxDUiaSLRsDeHk7kNili4q8N2/a914x7eTEvqeBfa9DUiYyjC3xqm+Ud98DAIMWLVHL1Q0A+54m9L3rhWY4hEaQQfvl+vQ8fB/xB9KjLuKjZMW+Wda+h7xcmM0oegbrXdGmjR1MTWuq3O7o0UPw9OyFjz76GAAwYsRodOnigCdPHqNhw/fk24nFYjg7d8WpUyfQvPlHOHXqJD7/vCMMDAzQubMT2rX7HMbGxkhIiIeBgRFSUlLKFO/Ro4cxadI3MDe3AACMHDka06dPKf/EDQBiY2ORmJgoHw3Lz8/Hn3/+iaFDh6rcNzs7G/r6+grr9PX1i8xfk0ql6Nq1KyZOnIiCggJMnDgRK1euhL+/fykPBRDriCFI/j0kQ0M9WFgYoSBPgiRJ0UM1MnpZnq8rIPk/5Vr/XIZrZKwPCwsj5CEPKcXsb2Kij1oWRsjOS0dqMeWmJvowtTBCZoYBXhRXbloDxhZGSH9WA2nFlNesaQBDCyPomOgjQ0l5DQsjaJvoI7OYcrNahtC1MAKM9ZFVXLm5IXSMjVBopIecYsrNLYygrasLmaEecospt7B4eRNmqYEupK+Va0nE8vJcA13kv1auo/tveVYNCQpeK9fV05GXZ+hLUPhaud5/ytP0dBT+7gCgry+Rlz/X00Hea+U1avxbnqIrRr5UsdzAQFdeniQRoxD/Pi3hVf94VZ5QzHvzpn1PXs6+p5F97/W+Ud59DwAM/1POvlf1+96ZXCvk/5O0vSKVFeJEqgFavGXfkxXKisRXnkoaDdPS1S2xXGxkVGK5jplZqUfblKlVy6xU2yUmJiIi4ijCwvbL1wmCgPj4eIXEDQC6deuOWbNmYMKESTh16gSGDfMFAEil+Vi6dCGuXr2C+vXrw8LCssgt0koTR0DANGhpif6J4eXp07y8vDJdACoSVLQcGhqKlSv//dUmCAJEIhGaNWuGn3/+uYQ9X9q6dSuio6OxYcMG+Tpvb2+MGjUK3bp1k69zc3PD/PnzYWNjAwC4dOkSxo0bh6ioor94lElJyURhYdneyOIs+fEKb7BKSrF/kDLsG/S64YuVn7XaMs3prerW0hLBzMzwreoAgFu3bqNevfdUb1jJ7O1bY+/eMFhZNcTcuYGwtLSEn984AMDmzd/hwYP7WLBgCQDg5Mnj2LBhLcLCjmDBgiDUr98AQ4f6yut69Ogh6tdvAB0dnSLt9OnjiXHjJmLx4gU4cuQ4xGIdLFo0D7m5uZg1aw7EYh2cPfsLli9fgkOHjilcVTpu3Ch07twFffr8HwBgyZKFyMvLw+zZQejd2xOBgfPw2WcvPx9yc3Pw7NkzNGhgVezxxsU9xscff1RkvcqLE3788UesXbsWISEh6NOnDy5cuIDu3bvj888/V7UrAKBx48Z49OiRfLmgoABPnjxB48aNFbZLTExEQUGBfFksFhf7hhIREWkKM+PiR1KUrSfldHR0kJWVVWxZgwZWuHIlGvHxcUhLS8PPP/87uubq6oYDB/bh3r2/IAgCwsL2Y/hwH+Tk5BRbl6urG1atWg4npy4Qi1/mIZmZmdDV1YOWljYSExPw/fdbIZMVHfFs0MAKv/56BtnZ2Xj48AF+++1XhXpDQ0Pw/Plz5ObmYvnyJfILF8pCZeKWlpaGrl27omnTprh16xZMTU0xc+ZMHD16tFQN2NnZ4cWLF9i/fz+kUimCg4NRr149NGnSRGE7BwcHrFmzBmlpaXjx4gXWrVunMCJHRESkabwdrSERK37VSsRa8Ha0VrIHKePu3gN+fr44e/aXImWdOzujQwdHDBkyEL6+PnB07CQvs7Vti1GjxmDmTH84O3fEzz/vx4oVa2BsbFxsO66u3ZGUlAhX139zkBEjRuPu3Tvo0sUB48aNgpOTMzIzM/D8+XOFfYcNGwFAgIeHKxYsCEL37h7ysqFDffHhhx9iyJCB8PBwQWpqKubPLzpPVRWVp0pdXV1x4MAB1KhRA3Z2drh48SJEIhFsbGxw+fLlUjUSExODwMBAPHjwAM2aNcOiRYvw/vvvw93dHaNHj4anpyfS0tKwaNEi/Pbbb9DS0kLXrl0xderUIvPjSsJTpaQO7B+kDPsGFSfyVgK2Hr0DWYEAM2Pdcruq9F07VfquUXaqVOXFCW3atJFfKPDpp59i5cqV0NXVRe3atUvd+CeffIL9+/cXWX/kyBH5axMTEyxevLjUdRIREWmCdh/XwW/X4pjUU7lQeap02rRpsLKygkwmw7Rp03D69Gns2bMHM2fOVLUrEREREZUjlSNuhoaGCAx8OXmuVq1apZ7bRkRERETlS+WIGxERERFVDUzciIiI3mEiESAIhao3JLURhEL8cz/vIpi4ERERvcMMDAyQmvoMMll+mZ8GQOVLEATIZPlITX0GAwODYrcp1SOviIiIqHqysrLCs2fPkJqaCJmsQPUOVKHEYm3UrFkT5ubmxZe/acWHDx+Gh4eH6g2JiN4R/l+0hoWFEZKTMyo7FKJS09LSgqWlJSwtLSs7FCqFNz5VOmvWrPKMg4iIiIhUUJq43b9/v8Qdr169Wu7BEBEREZFyShO3gQMHAgB8fX3VFgwRERERKad0jpsgCNi0aROio6MRFhZW7DZeXl4VFBYRERERvU5p4jZ27Fjs3LkTUqkUa9euLVIuEomYuNE7iRPQiYiosihN3NLT03H8+HF07NgRZ86cUWdMRERERFQMpXPctm3bBgDIzMxUVyxEREREVAKlI26Wlpbo0aMHpFIpBg8eXOw227dvr7DAiIiIiEiR0sRt/fr1OHnyJDZs2IC2bduqMyYiIiIiKobSxO2DDz7ABx98gKysLIwfP16dMRERERFRMVQ+OeGbb77B06dPsXbtWkyfPh3p6ekIDw9XR2xERERE9B8qE7dLly7B09MTt2/fxvHjx5GRkYH58+dzfhsRERGRmqlM3JYtW4alS5ciJCQE2traqF+/PkJCQrBjxw51xEdERERE/1CZuD148ADOzs4AXt50FwBsbGyQkpJSsZERERERkQKViVvdunVx/fp1hXW3bt1C3bp1KywoIiIiIipK6VWlr4wYMQKjR49G//79kZ+fj02bNmHHjh2YMGGCOuIjIiIion+oTNx69uwJIyMj7Nq1C/Xq1cP58+cxdepUdO/eXR3xEREREdE/VCZuAODk5AQnJyekpKTAxMQEYnGpdiMiIiKicqRyjptUKsXChQvRqlUrdOjQATY2Npg9ezakUqk64iMiIiKif6hM3IKDg3Hx4kWsXr0ahw8fxurVq3Ht2jWsXbtWHfERERER0T9UnvM8dOgQtm7dCisrKwCAtbU1GjduDB8fH3zzzTcVHiARERERvaRyxC0tLa3IrT/q1auHnJycCguKiIiIiIpSmbg1bdoUe/bsUVi3Z88efPjhhxUWFBEREREVpfJU6aRJkzB8+HCEhYXBysoKsbGx+Ouvv7B582Z1xEdERERE/1A54mZra4vw8HB06NABBgYG6NKlCw4fPozWrVuXupEbN26gV69eaNmyJfr164cHDx4Uu92ePXvg6uoKW1tb+Pn5ITU1tfRHQkRERFTNqUzccnJy0KhRI3z55ZeYO3cuOnXqhPr165e6gby8PIwdOxY+Pj6IiopCx44dMXXq1CLbRUREIDg4GMHBwTh37hz09fWxbNmysh0NERERUTWmNHErLCzE9OnTMXPmTPm6Z8+ewdPTEzNmzIAgCKVq4MKFCzAwMIC3tzckEgnGjBmDx48f4+7duwrb7dmzB+PGjUPjxo2hq6uLOXPmwM/P7w0Pi4iIiKj6UZq4bdmyBVeuXMHQoUPl68zNzbFnzx5ERUVh+/btpWrg4cOHsLa2li9ra2vDysoK9+/fV9ju9u3byM3NhZeXF9q3b4+FCxfCzMysjIdDREREVH0pvTghLCwMK1aswCeffKKw/rPPPsOCBQswf/58DBkyRGUD2dnZ0NfXV1inr6+P3NxchXUZGRnYt28f1q9fDxMTE0yZMgULFizAokWLSn0wZmaGpd62JDoSbQCAhYVRudRH1RP7BynDvkGv4/cKlReliVtCQkKRpO2VNm3aIC4urlQNFJek5eTkoEaNGgrrJBIJBg0ahAYNGgAAxowZg1GjRpWqjVdSUjJRWFi6U7glyZcWQEeijeTkjLeui6onCwsj9g8qFvsGFacivle0tETlNmBBmkPpqVJdXV1kZWUVW5abmwsdHZ1SNdC4cWM8evRIvlxQUIAnT56gcePGCtu9//77yMzMVNiOiIioOvD/ojUWje1Q2WFQNaA0cbOxsUFYWFixZYcOHULz5s1L1YCdnR1evHiB/fv3QyqVIjg4GPXq1UOTJk0UtvPy8sL333+PJ0+eIDMzExs2bEC3bt1KfyRERERE1ZzSxM3X1xfLly/Hli1bkJiYiIKCAiQkJGDr1q1YvHgxfH19S9WAnp4evv32W/z000+ws7PDuXPnsHbtWohEIri7u+PgwYMAgMGDB2PAgAEYOnQoHB0dUatWLUyZMqV8jpKIiIioGhAJJdzXIyIiAnPmzEF6erp8nampKWbMmIEePXqoJcCyKK85bkt+vAIdiTa+7tuiHKKi6ojzmEgZ9g1Sprz7Bue4vZtKfOSVm5sbnJ2dcfnyZaSmpsLS0hItW7Ys9fw2IiIiIio/Kp9VKpFI0K5dO3XEQkREREQlUPnIKyIiIiKqGpi4EREREWkIJm5EREREGoKJGxEREZGGYOJGREREpCGYuBERERFpCCZuRERERBqCiRsRERGRhmDiRkRERKQhmLgRERERaQgmbkREREQaQuWzSjWJlpaoXOqpaawLsY52udVH1RP7BynDvkHKlGffYD97N4kEQRAqOwgiIiIiUo2nSomIiIg0BBM3IiIiIg3BxI2IiIhIQzBxIyIiItIQTNyIiIiINAQTNyIiIiINwcSNiIiISEMwcSMiIiLSEEzciIiIiDQEEzciokokCALi4uIqOwzSME+fPq3sEKiSMHErZ7Nnz8aGDRsqOwwqpYsXL8LBwaGyw6AqJjQ0FK1bt4aLi0uFt7VkyRLs3r27wtuhiuXj44O9e/eqpa3bt29j8ODBammLqp5q9ZD5qmDu3LmVHQIRvaXdu3dj7ty58PDwqPC2Xrx4gdq1a1d4O1R9ZGRkQCaTVXYYVEk0ZsTt6dOnaNeuHb766iu0adMGR48exaRJk2BnZ4euXbsq/NKJj4/HkCFD0Lp1awwaNAgzZ87EunXrALz8VTRt2jS0a9cOM2bMAABs27YNXbp0gb29Pfz9/ZGZmQkASE9Ph5+fH9q0aQMnJycsWbIEgiDI93FwcIC9vT18fX0RGxsLAJg2bRpWrVoFAEhMTMSXX34JOzs7ODk5YdOmTfL9fXx8sHbtWri7u8PGxgZjx45FWlqaet5MKqKgoABLliyBi4sLWrZsCTc3N1y4cAHAm/WDjIwMBAQEoF27dnBwcMDSpUshlUor7fio9Dw9PfH06VPMmDEDK1aswNKlS9GxY0e0b98eM2fOlH8+rFu3Dn5+fnBxcYGbmxsKCgpw/vx5eHl5wdbWFj4+Pnjw4IG83mXLlqF9+/bo0KEDJkyYgOfPn+PHH3/EoUOHsHnzZsycObOyDples3PnTnTo0AEZGRkAgICAAIwYMaLE7xYAuHnzJjw8PPD5559jyZIl8uSqpO+CksrOnz8Pd3d32NrawtvbG7///jsyMjIwcuRIJCUloVWrVigoKFDzu0OVTtAQsbGxwocffiiEhoYKOTk5wqBBg4SZM2cKOTk5wr179wRHR0fh/PnzgiAIwoABA4R58+YJeXl5QmRkpPDJJ58Ia9euFQRBEAYNGiT06dNHyMzMFNLT04WDBw8KTk5OwoMHD4Ts7Gxh6tSpwpQpUwRBEIRVq1YJ33zzjZCfny8kJCQInTp1Ei5cuCA8evRIaNu2rZCQkCDk5+cLs2bNEqZPny4IgiD4+/sLK1euFARBEPr06SOP8cGDB4Kzs7OwZ88eeRwuLi7C33//LaSkpAgeHh5CcHCwut/Wd96FCxeEjh07Cvv37xd69uwpPH/+XMjPzxcWL14seHt7C4LwZv1g4sSJwqhRo4S0tDQhMTFR6N27t7Bq1apKPFIqi86dOwvnzp0Tli5dKvTu3VtISEgQ0tPThVGjRgnffPONIAiCsHbtWqFVq1bC48ePhfT0dOHJkydCy5YthV9//VXIz88XfvrpJ6FLly5CXl6ecP78eaFbt25Cenq6kJubK4waNUpYv369IAiKnxlUNRQWFgqDBw8WgoKChN9++03+/1zVd4uTk5Pw5MkTISkpSfDw8BB27NghCELJ3wUllTk4OAi//fabIAiC8PPPPwvOzs6CIPz7uUXvJo07Veru7o709HRcvnwZwcHB0NPTg7W1NQYMGIB9+/bhvffew7Vr17B582ZIJBLY29sXmafSqVMnGBgYAADCwsLg6+uLRo0aAQAmT54MR0dHzJs3DwYGBrh58yaOHTuGDh064PTp09DS0kJiYiKys7Oxd+9edOvWDXPmzIGWluLg5ePHjxETE4OtW7dCT08PjRo1wogRI3Dw4EH07dsXANCrVy/Uq1cPAODg4IDHjx9X9NtHSri4uMDBwQEmJiaIi4uDkZERnj17BgBl7ge5ubk4efIkwsPDYWxsDGNjY0ycOBGBgYGYNGlS5R5oKTg5OSE5ORli8b8fD5aWlujXrx+GDx8OHx8ftG3bFhMmTCh2/6ZNm0JXVxfa2toAgMLCQujr68Pe3h6BgYGoWbOmWo6jPBw6dAjz5s2Tn8r09/dHjx49sHDhQgDAp59+ioYNGwIAfvrpJzg6OsLR0REAMGDAAGzbtg1RUVEwNjZGYmIi9u/fD2dnZwQHBxf5zKCqQyQSYf78+fDy8sKJEycwe/ZsFBQUqPxuGTx4MKysrOSvw8PD0aFDB6XfBW3bti3xe8LAwAAHDx6Evr4+PDw80LNnz8p4O6iK0bhPDnNzcyQkJKCwsBCdOnWCra0tbG1tERISgsTERCQmJsLY2Bj6+vryfV4lR69YWFjIX8fHx2PZsmXyerp37w6xWIy4uDgMGzYM7u7uWL9+Pdq3b4+xY8ciJSUFtWvXxsaNGxEdHY1evXqhW7duOHv2rEIbqampMDExgaGhoUIcCQkJ8mUzMzP5a7FYLB8eJ/WTSqUIDAyEvb09vvzyS8TExMj/HmXtB+np6ZDJZAr97vW/fVUXFBSEq1evyv8tWLAAq1evLvXk69DQUPm+169fx48//ohbt25h/vz5FRx5+UpNTVX4O9avXx8ymQwpKSkAXn4evRIfH4/Tp0/LP0tsbW2RkJCA+Ph4fPbZZwgKCsKxY8fg6uqKXr164caNG2o/Hio9KysrtG3bFrm5uejUqVOpvlv+u1ynTh0kJyeX+F2g6nti48aNkMlkGDt2LD7//HOEhoZW1OGSBtG4xE0kEsHCwgISiQQXL15EdHQ0oqOjcerUKaxatQp16tRBWloasrOz5fu8/oUpEonkry0sLDB37lx5PRcuXEB4eDgaNmyIe/fuoW/fvjh27BiOHz+OzMxMBAcHy/+zbdu2DRcvXkSfPn3w9ddfK7TxKo5X82EA4O+//1ZI1qjqWLVqFfT19fG///0P+/fvh7e3t7ysrP3A3NwcOjo6Crd4+Pvvv1GrVq3KOLRyYWtriyZNmuDOnTtvtL+1tTW6dOmCu3fvlnNkFatOnToKf8enT59CW1sbJiYmAIp+lnh5eck/S6Kjo3Hw4EF4eHggPj4eTZo0wa5duxAZGYk2bdogICBA7cdDpXf+/Hlcu3YNLVq0wLJly0r13ZKcnCx/HR8fj7p165b4XVBSmVQqRVxcHFatWoXIyEgsW7YM69evx+3btyvwqEkTaFziBgB169bFp59+ipUrV0IqlSIpKQm+vr7YsWMH6tatCxsbG6xatQpSqRRXrlzByZMnldbVo0cPbNq0CU+fPoVMJsP69esxYsQICIKAPXv2ICgoCFlZWTA3N4dEIoGpqSmePn0KX19f3L17FzVq1ICpqan8g/y/MdrY2GDx4sXIzc3F48ePsWXLFnTv3r2i3x56A+np6dDT04O2tjbi4+Px7bffyicWl7UfaGlpwd3dHcuWLUN6ejqSk5Oxfv16uLu7V/JRvhmpVIpTp07h7t27aN++fZn3FwQB165dw9GjR9GxY8cKiLDieHp6Yt26dUhMTERGRgaWL18OJycnhVGXV9zc3HDixAlER0dDEAT8+uuv8PDwQFxcHK5fv46xY8fKT8MbGhrKPzMkEgmysrLUfWhUgqysLAQEBMDf3x/z58/HwYMH8eTJE5XfLTt27EBCQgISEhKwdetWeHl5lfhdoOp7YtKkSQgPD4eWlhZq164NkUgEIyMjSCQS5OXl8crSd5TGzXF7ZeXKlViwYIH8Hlzdu3fHuHHjAACLFi2Cv78/7Ozs8Mknn6BNmzbQ0dEptp7evXsjNTUVQ4YMwYsXL9CsWTOEhIRALBZj0qRJCAgIQOfOnSEIAjp37gxfX1/o6+vjyy+/xOjRo/HixQs0btwYq1evLlL3ihUrMG/ePDg6OkJHRwf9+/fHoEGDKuw9oTc3YcIETJ06FTY2NjA3N0e/fv2wevVqpKamvlE/CAgIwKJFi9CtWzcUFBTA09OzyKhsVRYUFISFCxdCJBJBEAQ0aNAA06dPR5cuXfD999+r3N/Pzw/a2trIz8+HVCrFRx99hCFDhsDHx0cN0ZcfPz8/5OTkoE+fPsjJyYGTk5PSkbLGjRtjyZIlmDdvHmJjY1G7dm2sWLEC1tbWsLa2xp07d9C3b19kZ2fjk08+wbx58wC8nF/51VdfITk5GWvWrFHn4ZESK1asQP369eHl5QUAGD9+PAICAhAcHIzZs2cr/W5p3749Bg4ciLy8PAwYMEA+J62k7wJlZVpaWlizZg0WLVqEOXPmoGbNmpg9ezasrKxgZmaGBg0aoG3btjh16pRGj+ZT2YmEajaxShAEXLhwAXZ2dvLJv69uGzJgwIBKjo6o6nNycsL48eMVThf/V2kuTti+fTvs7OyQkZGBhQsXIjo6Gt9//32ROUFEmoLfLVRVaOSp0pKIRCLMmjUL4eHhAICYmBicO3cO9vb2lRwZ0bvHyMgICxYsgJWVFYYPH64wl4dIk/C7haqKape4AcDy5cvxww8/oFWrVpg8eTKCgoLkt/sgoreXmZkpn8vz6l9OTk6x22ppaWHp0qV48eIFnyxCGo3fLVQVaOwct5K0bNkSBw4cqOwwiKqtbdu2Ydu2bQrrli5dqvQ+U+bm5pg3bx7Gjx+Pzp07w83NTQ1REpUvfrdQVVDt5rgRERERVVdqPVUaERGBgQMHFluWnZ2NmTNnon379rCzs8PkyZP57E4iIiKi/1BL4lZQUIAtW7ZgypQpSp8OsGbNGsTHxyMiIgKnT59GdnY2Fi9erI7wiIiIiDSCWhK35cuX4/Tp0xg1apTSbQoKCjB27Fj54z/69u2La9euqSM8IiIiIo2glosThg0bBktLyxIndb5+U8tff/0VTZs2rejQiIiIiDSGWhI3S0vLMm2/Y8cOHD9+HHv27KmgiIiIiIg0T5W6HYggCFi+fDnCwsKwbds2vPfee2Xa//nzLBQWls9FsmZmhkhJ4c1CqXjsH6QM+wYpU959Q0tLhJo1DcqtPtIMVSZxk8lkmDJlCv7880/s3r0bDRo0KHMdhYVCuSVur+ojUob9g5Rh3yBl2DfobVWZxG3FihW4d+8edu7cCWNj48oOh4iIiKjKqdTEzd3dHaNHj0a3bt3www8/AAAcHR3l5ZaWljh+/HhlhUdERERUpVSrJyekpGSW2zC0hYURkpMzyqUuqn7YP0gZ9g1Sprz7hpaWCGZmhuVWH2mGavmQeSIiIqLqiIkbERERkYZg4kZERESkIZi4EREREWkIJm5EREREGoKJGxEREZGGYOJGREREpCGYuBERERFpCCZuRERERBqCiRsRERGRhmDiRkRERKQhmLgRERERaQixsoJmzZpBJBKVuPOdO3fKPSAiIiIiKp7SxG379u3qjIOIiIiIVFCauLVt21adcRARERGRCiXOcYuMjFQYecvLy0Pv3r0RGRlZ4YERERERkSKlidulS5fg5+eHrKws+br8/Hx8+umn8PPzw9WrV9USIBERERG9pDRxCwkJwdSpUzFmzBj5OkNDQ8yZMwfjx4/Hxo0b1RIgEREREb2kNHG7ffs2+vbtW2zZgAEDEBMTU2FBEREREVFRShO3/Px8iMXFX7tgYGAAmUxWYUERERERUVFKE7f3338f169fL7bsxo0bsLS0rLCgiIiIiKgopYlbr169EBgYiMTERIX1iYmJmDNnDtzd3Ss8OCIiIiL6l9L7uA0cOBDnz5+Hi4sLWrduDXNzcyQnJ+Pq1ato27YtRo0apc44iYiIiN55ShM3kUiEDRs2ICIiAr/88gtSUlJQt25dfPHFF+jatas6YyQiIiIilJC4veLm5gY3NzcAwOXLl2FjY1PhQRERERFRUSU+OeF1I0eOrKg4iIiIiEiFMiVugiBUVBxEREREpEKZEjciIiIiqjxlStz8/PwqKg4iIiIiUqFMiVv//v1x8+ZNpKamVlQ8RERERKREqRO3o0ePomfPnliwYAF69OiB3bt3V2RcRERERPQapYnb6xcibNmyBQcPHsSuXbsQHh6OdevWlbmxiIgIDBw4sNiywsJCLF68GHZ2drCzs8P69evLXD8RERFRdaY0cfP29sbly5flyxKJBPfv34dMJsO9e/egp6dX6kYKCgqwZcsWTJkyRemVqTt27EBUVBQiIiKwd+9eHDhwAGfPni3DoRARERFVb0pvwDt79mzMnz8fjRo1wtSpUzFr1iwEBATg3r17aNiwIRYtWlTqRpYvX44bN25g1KhRiIyMLHabQ4cOYfjw4ahVqxZq1aqFQYMGYd++fXB0dCz7URERERFVQ0oTt1atWmHfvn3YvXs3+vfvjwEDBmDXrl3Q0dEpcyPDhg2DpaUlDhw4oHSbBw8ewNraWr7cqFEj7Nu3r8xtEREREVVXJT7ySiQSoX///nBzc8Pq1avRs2dP+Pv7l3kUzNLSUuU2OTk5Cqdf9fT0kJubW6Z2zMwMy7S9KhYWRuVaH1Uv7B+kDPsGKcO+QW9LaeIWHR2NpUuXQiwWY/r06QgMDMSdO3cwb9487Ny5EzNnzoSVlVW5BaKnp4e8vDz5cm5uLmrUqFGmOlJSMlFYWD5Pd7CwMEJycka51EXVD/sHKcO+QcqUd9/Q0hKV+4AFVX1KL06YNWsWRowYgUGDBmHWrFkAgObNm+Onn35Ct27dMHTo0HINpHHjxnj48KF8+eHDh2jcuHG5tkFERESkyZQmbklJSejYsSMcHByQmJioUObl5YWDBw+WayAeHh4IDQ3Fs2fPEBsbix07dsDDw6Nc2yAiIiLSZEpPlTo7O2PYsGEQiUTo2rVrkXIDA4O3btzd3R2jR4+Gp6cnBg0ahMTERHh5eaGgoABDhgyBi4vLW7dBREREVF2IBCU3VissLMTvv/8OsViM9u3bQyQSqTu2MuMcN1IX9g9Shn2DlOEcNyoPSkfctLS0FK4ezczMxOXLl6Grq4s2bdpAW1tbLQESERER0Uslnio9ffo0AOD+/fsYNmwYsrKyIJPJYGVlhdDQUNStW1dtgRIREWmq7EOLEKcjhk63KZUdCmk4pRcnpKamyl8vWbIEbm5uiI6ORnR0NFq3bo358+erJUAiIiIieklp4vbfOW0xMTGYOHEiRCIRdHR04O/vj4sXL6olQCIiIiJ6SWni9l9mZmYKN8ctLCyEWFziQxeIiIiIqJwpTdyys7PRuXNnTJgwAfr6+vjuu+8AALGxsZg2bRrs7e3VFiQRERERlXBxwsWLF3Hz5k3ExMRAEAS8ePECALB7924kJydj3bp16oqRqErhJGNShn2DiCqa0sTNxMQEHTp0QIcOHRTWf/nll5BIJBUeGBEREREpKnGi2qNHj7B//348fPgQOTk5MDU1xaeffgovLy+YmpqqKUQiIiIiAkqY4xYdHY1evXrhjz/+QH5+Pi5dugRdXV1ERETA1dUVf/75pzrjJCIiInrnKR1xW758OZYuXSp/TumpU6dw+vRp7N69G9u2bcPChQuxbds2dcVJRERE9M5TOuL2119/oUuXLvLlzp074+zZswCAAQMGICYmpuKjqyTZhxYh7ofZlR0GERERkQKliZulpSV+//13+fKVK1dgZGQEAEhJSYG+vn7FR0dEREREckpPlY4cORLjx49Hjx49oK+vj/DwcEyaNAmPHz/G4MGD0a9fP3XGSURERPTOU5q4eXt7w8TEBEeOHEFmZiaCgoLQvXt3PHv2DP7+/ujevbs64yQiIiJ655V4OxBnZ2c4OzsrrDM3N2fSRkRERFQJSvWsUiIiIiKqfEzciIiIiDQEEzciIiIiDcHEjYiIiEhDKL04wcfHByKRqMSdt2/fXu4BEREREVHxlI642dnZoW3btqhXrx5u376N5s2bw9XVFS1atMDdu3fRqFEjdcZJRERE9M5TOuI2fvx4AMDAgQPx3XffoXXr1vKyrl27IjAwsOKjIyIiIiI5lXPc7ty5gxYtWiisa968OR49elRRMRERERFRMVQmbtbW1kXmsoWEhKBZs2YVFhQRERERFVXikxMAYMaMGfDz88P27dtRu3ZtxMXFobCwEJs3b1ZHfERERFSBCgsL8ezZM6SmPkdBQUFlh/PO09bWRq1aNWFubg4traLjayoTt9atW+PEiRP45ZdfkJSUhNq1a8PZ2RlGRkYVEjARERGpT2xsLGSyQpiZ1Ya2tljlHSWo4giCgIICGdLTnyMnJwfvvfdekW1UJm4AYGpqil69epV7gERERNWd9K/zKEi8j4JCGfJ+mgxJm96QNGlf2WHJZWVloU4dK4hEvLVrZROJRBCLdVCzpjkSEmKL3UZl4nbx4kUEBQXh0aNHEARBoezOnTvlEykREVE1JP3rPPJ+3wYUygAAQmbKy2WgyiRvggAmbVWMSKSF11IuOZWJ2+LFi9GiRQsEBARALC7VAB0REREBkF7aD8ikiitlUkgv7a8yiRtpFpWZ2KNHj7Br1y7o6uqqIx4iIqJqQ8hMKdN6Ui4t7QV0dCSoUaNGZYdSqVSOjb7//vtISkpSRyxEVd6ruSq5T24h86fJkP51vrJDIqIqTGRoVqb1pFzfvr2QkvKsssMoIjQ0BIGBM9XWnsoRNzc3N4wYMQJ9+vSBhYWFQpmXl1epGrlx4wYCAwPx8OFDNG3aFIsWLULjxo0VtsnPz8eCBQtw/PhxCIKAzp07IzAwEHp6eqU/GqIKpAlzVajyVPUJ6FQ5JG16v/yc+O/pUrEEkja9Ky0mTZWenlbZIVQJKkfcdu3ahfz8fOzcuRNr166V/1u3bl2pGsjLy8PYsWPh4+ODqKgodOzYEVOnTi2y3Y8//ognT57g5MmTOHHiBGJjY7Fp06ayHxFRBSlprgq925Ql9RyRJUmT9tDtOBTQejlOIjI0g27HoUzqy2jkyKEAAB+f/rh8ORpz5wZi1qzp6NHDFePH+xUZ9YqKuggvL3f58okTx9CvnzdcXDrhm28m4dmz5CJtnDv3O3r39lRYN2rUcBw9ehgFBQVYt24V+vTpiU6d2qNfP29cvnypSB1jxoxEePjP8uWQkA2YO/flI0JlsnwEB6+Hp6cb3N1dsHr1cuTn55f5vVA54nbmzJkyV/pfFy5cgIGBAby9vQEAY8aMwffff4+7d++iadOm8u0ePHgAmUwmv3JVJBJBIpGUqa34bzdC+vyFfNmoTVuYdnZGYV4e/l6zssj2xp93gMnnHVGQkYG44PXy9QUpT6AlEqFmrYswamuH/NQUJGz6rsj+NV26wbBlK0gT4pG4fVuR8loenjD46GPkPnmM5F0/FSk39+4D/Q+aIOfeX3h2YF+Rcov+A6HX8D1k3b6F1MMHi5TXHjwUkjp1kXntKp6fOFakvM6IUdCpZYaMqIt48WvRv2O9MeOhbWSEtHO/I/3c/4qU15/4NbR0dfHil9PIuBRVpNxq6nQAQOrxCGRdv6ZQJpJI0GDSZABAyqFwZN+5rVCubWiIemMnAACS9+9F7v17CuXimrVQd+RoAEDSrh+R9+SJQrmkTh3UHjwMAJC4fSukCQkK5boNG8Ky/xcAgPjQbyF7nqpQrmf9ASx69wUAxG1ch4LMTIXyGs0/glmPngCAp6tXQJBKYWKSguJub1SYkYLYpYsU1r1p33vFtJMT+54G9T0jo/vQ1pYpBimTIueXbUj8+azC6jfpe/9l0KIlarm6AUCRfgew71XVvleQogOxnj4aBK0AUD59D3m5MJtRdCCkvDxatLDIOuO2bVHLuQsK8/LwZOWKIuWmHTrCtGNHyDIy8HR90QGemk5OMLGzR35KCv7+7lu8P31GqWIJDd0Ge/vW+OGHXbCyaogjRw7h5s3r+OGHXRCLxdi580el+964cR3Lly/G6tUb0KTJh9i8+TsEBExDSIjigwTs7NohOzsLd+7cRvPmHyEpKRF//XUXjo6dERFxBJcuRWHz5u0wMDBAcPA6rF+/Blu37ihV/ACwY8d2XLp0EVu2bIdEoouAgGnYunUTRo0aU+o6gFLexy02NhaJiYnypCo/Px9//vknhg4dqnLfhw8fwtraWr6sra0NKysr3L9/XyFx69evH0aMGIE2bdoAAGxtbTFs2LCyHAvEOmIIkn8PydBQDxYWRijIkyBJUvRQjYxelufrCkj+p1xb+wV0GuZCSyxAdGcH9N6TwLj2R0gpZn8TE33UsjBCdl46UospNzXRh6mFETIzDPCiuHLTGjC2MEL6sxpIK6a8Zk0DGFoYQcdEHxlKymtYGEHbRB+ZxZSb1TKEroURYKyPrOLKzQ2hY2yEQiM95BRTbm5hBG1dXcgM9ZBbTLmFxcubMEsNdCF9rVxLIpaX5xroIv+1ch3df8uzakhQ8Fq5rp6OvDxDX4LC18r1/lOepqej8HcHAH19ibz8uZ4O8l4rr1Hj3/IUXTHypYrlBga68vIkiRiFKIQg6EAkKvrrSBB0oPNa/W/S9xTKjfVhYWGEPOSx72lA39PSei1p+4cI0iJ940363n8Z/qc8oZj3hn2vavY94Z9ffeXZ92SFxfe7d0WbNnYwNa2pcrujRw/B07MXPvroYwDAiBGj0aWLA548eYyGDf+9wa1YLIazc1ecOnUCzZt/hFOnTuLzzzvCwMAAnTs7oV27z2FsbIyEhHgYGBghJaVsF5gcPXoYkyZ9A3Pzl9PORo4cjenTp5Q5cRMJr9+c7TWhoaFYufLfX22CIEAkEqFZs2b4+eefS9jzpY0bN+L+/ftYseLfzPyLL75A79695aNwAHD16lX8/PPPmDhxIgoKCjBx4kS0bNkS/v7+pT6YlJRMFBaWeDglkp/ueG0uAoe1CWD/IOUyf5pc7FWCIkMzGA4sOipB757sQ4ugoyOGTrcp5VanlpYIZmaGb13PrVu3Ua9e0Tv0VzX29q2xd28YrKwaYu7cQFhYWGDMmPEAXl4g8PRpLIKCFgB4eap04cK5CAs7gq++moArVy5DR+ffRDg/Px9Ll66CnZ29QhsxMTcwa9YM/PzzYQwfPhjDhvmiY0dHPH/+HIsXz8fVq1dQv359WFhY4s6d2zh06JhC22PGjES3bt3Rs+fLhxaEhGxAUlISZs8OgqNje2hra0NL62USLwgvT5+eOPFrsXfuiIt7jI8//qjIepUjbj/++CPWrl0LiUSCU6dOYfLkyZg3bx7q1q1bqjdaX18fubm5CutycnKKXM47Y8YMzJ8/H2ZmL6+0+frrrzFu3LgyJW5vi/fboZK86gN5Z7cAhTKIDM04AZ0AcAI6UWX476O5tLS0IJP9OwKZlvZC/trc3BzDhvli6FBf+bpHjx6ifv0GRer85JPPoK2thV9+OY2//36Kdu1efr6HhKyHnp4ejh49AbFYB2fP/oI7r03DeBmHSGHeWlravxdUmJubIzBwHj77rAUAIDc3B8+ePSvz7dZUXpyQlpaGrl27omnTprh16xZMTU0xc+ZMHD16tFQNNG7cGI8ePZIvFxQU4MmTJ0WuKk1MTFR4uK1YLIaOjk4pD6N88H47pIqkSXto17aGXsOPYThwBZM2AsAJ6ETqoKOjg6ysrGLLGjSwwpUr0YiPj0NaWhp+/vnfi8ZcXd1w4MA+3Lv3FwRBQFjYfgwf7oOcnJxi63J1dcOqVcvh5NQFYvHLPCQzMxO6unrQ0tJGYmICvv9+q0Ki+N84fv31DLKzs/Hw4QP89tuvCvWGhobg+fPnyM3NxfLlS+QXLpSFysTN0tISWVlZqF27Np4+fQpBEFCrVi2FLLIkdnZ2ePHiBfbv3w+pVIrg4GDUq1cPTZo0UdjOwcEBa9asQVpaGl68eIF169ahW7duZT6gt8H77RDRm2JST1Sx3N17wM/PF2fP/lKkrHNnZ3To4IghQwbC19cHjo6d5GW2tm0xatQYzJzpD2fnjvj55/1YsWINjI2Ni23H1bU7kpIS4er6bw4yYsRo3L17B126OGDcuFFwcnJGZmYGnj9/rrDvsGEjAAjw8HDFggVB6N7dQ142dKgvPvzwQwwZMhAeHi5ITU3F/PlFLzBSReUct4CAACQkJGDlypX46quv8NFHH0FXVxdHjx4t9ahbTEwMAgMD8eDBAzRr1gyLFi3C+++/D3d3d4wePRqenp5IS0vDokWL8Ntvv0FLSwtdu3bF1KlToa+vX+qD4Rw3UoeKmKtC1QP7BinDOW5UVm88x23atGlYsWIFZDIZpk2bhokTJyIzMxOLFpU+S/zkk0+wf3/Re10dOXJE/trExASLFy8udZ0VgXOYiIiIqCpTmbgZGhoiMPDlOdhatWqVepRNU0matIfsj7P81UxERERVjso5bkRERERUNTBxIyIiItIQTNyIiIjeYSIRIAiFqjcktRGEwmIfsQgwcSMiInqnGRgYIDX1GWSyfKi40QRVMEEQIJPlIzX1GQwMDIrdplTPKi3O4cOH4eHhoXpDIiIiqrKsrKzw7NkzpKYmQiYrUL0DVSixWBs1a9aEubl58eVvWvGsWbOYuBEREWk4LS0tWFpawtLSsrJDoVJQeqr0/v37Je549erVcg+GiIiIiJRTmrgNHDgQAODr66tsEyIiIiJSI6WnSgVBwKZNmxAdHY2wsLBit/Hy8qqgsIiIiIjodUoTt7Fjx2Lnzp2QSqVYu3ZtkXKRSMTEjYiIiEiNlCZu6enpOH78ODp27IgzZ86oMyYiIiIiKobSOW7btm0DAGRmZqorFiIiIiIqgdIRN0tLS/To0QNSqRSDBw8udpvt27dXWGBEREREpEhp4rZ+/XqcPHkSGzZsQNu2bdUZExEREREVQ2ni9sEHH+CDDz5AVlYWxo8fr86YiIiIiKgYKp9V+s033+Dp06dYu3Ytpk+fjvT0dISHh6sjNiIiIiL6D5WJ26VLl+Dp6Ynbt2/j+PHjyMjIwPz58zm/jYiIqJRq9JiOej5zKzsMqgZUJm7Lli3D0qVLERISAm1tbdSvXx8hISHYsWOHOuIjIiIion+oTNwePHgAZ2dnAC9vugsANjY2SElJqdjIiIiIiEiBysStbt26uH79usK6W7duoW7duhUWFBEREREVpfSq0ldGjBiB0aNHo3///sjPz8emTZuwY8cOTJgwQR3xEVU5NXpMh4WFEZKTMyo7FCIieseoTNx69uwJIyMj7Nq1C/Xq1cP58+cxdepUdO/eXR3xEREREdE/RIIgCKXdOCUlBSYmJhCLVeZ7lSIlJROFhaU+nBJxRIVKwv5ByrBvkDLl3Te0tEQwMzMst/pIM6ic4yaVSrFw4UK0atUKHTp0gI2NDWbPng2pVKqO+IiIiIjoHyoTt+DgYFy8eBGrV6/G4cOHsXr1aly7dg1r165VR3xERERE9A+V5zwPHTqErVu3wsrKCgBgbW2Nxo0bw8fHB998802FB0hEREREL6kccUtLSyty64969eohJyenwoIiIiIioqJUJm5NmzbFnj17FNbt2bMHH374YYUFRURERERFqTxVOmnSJAwfPhxhYWGwsrJCbGws/vrrL2zevFkd8RERERHRP1SOuNna2iI8PBwdOnSAgYEBunTpgsOHD6N169bqiI+IiIiI/qEyccvJyUGjRo3w5ZdfYu7cuejUqRPq169fpkZu3LiBXr16oWXLlujXrx8ePHhQ7HZ79uyBq6srbG1t4efnh9TU1DK1Q0RERFSdKU3cCgsLMX36dMycOVO+7tmzZ/D09MSMGTNQ2vv25uXlYezYsfDx8UFUVBQ6duyIqVOnFtkuIiICwcHBCA4Oxrlz56Cvr49ly5a9wSERERERVU9KE7ctW7bgypUrGDp0qHydubk59uzZg6ioKGzfvr1UDVy4cAEGBgbw9vaGRCLBmDFj8PjxY9y9e1dhuz179mDcuHFo3LgxdHV1MWfOHPj5+b3ZURERERFVQ0ovTggLC8OKFSvwySefKKz/7LPPsGDBAsyfPx9DhgxR2cDDhw9hbW0tX9bW1oaVlRXu37+Ppk2bytffvn0bzs7O8PLyQlJSEjp27IhZs2aV6WDK+9EfFhZG5VofVS/sH6QM+wYpw75Bb0tp4paQkFAkaXulTZs2iIuLK1UD2dnZ0NfXV1inr6+P3NxchXUZGRnYt28f1q9fDxMTE0yZMgULFizAokWLStUOwGeVkvqwf5Ay7BukDJ9VSuVB6alSXV1dZGVlFVuWm5sLHR2dUjVQXJKWk5ODGjVqKKyTSCQYNGgQGjRoACMjI4wZMwZnzpwpVRtERERE7wKliZuNjQ3CwsKKLTt06BCaN29eqgYaN26MR48eyZcLCgrw5MkTNG7cWGG7999/H5mZmQrbEREREdG/lCZuvr6+WL58ObZs2YLExEQUFBQgISEBW7duxeLFi+Hr61uqBuzs7PDixQvs378fUqkUwcHBqFevHpo0aaKwnZeXF77//ns8efIEmZmZ2LBhA7p16/Z2R0dERERUjYiEEu7rERERgTlz5iA9PV2+ztTUFDNmzECPHj1K3UhMTAwCAwPx4MEDNGvWDIsWLcL7778Pd3d3jB49Gp6enigsLMSmTZuwa9cupKWlwcnJCYGBgTA0LP35e85xI3Vh/yBl2DdIGc5xo/JQYuIGAFKpFJcvX0ZqaiosLS3RsmXLUs9vUzcmbqQu7B+kDPsGKcPEjcqDymeVSiQStGvXTh2xEBEREVEJVD7yioiIiIiqBiZuRERERBqCiRsRERGRhmDiRkRERKQhmLgRERERaQgmbkREREQagokbERERkYZg4kZERESkIZi4EREREWkIJm5EREREGoKJGxEREZGGYOJGREREpCFUPmRek2hpiap0fVS9sH+QMuwbpEx59g32s3eTSBAEobKDICIiIiLVeKqUiIiISEMwcSMiIiLSEEzciIiIiDQEEzciIiIiDcHEjYiIiEhDMHEjIiIi0hBM3IiIiIg0BBM3IiIiIg3BxI2IqBIJgoC4uLjKDoOINAQTt3I2e/ZsbNiwobLDoFK6ePEiHBwcKjsMqmJCQ0PRunVruLi4VHhbS5Yswe7duyu8Hapenj59WtkhUCVh4lbO5s6di3HjxlV2GET0Fnbv3o25c+fixIkTFd7WixcvKrwNqng+Pj7Yu3evWtq6ffs2Bg8erJa2qOrRmMTt6dOnaNeuHb766iu0adMGR48exaRJk2BnZ4euXbsq/IeJj4/HkCFD0Lp1awwaNAgzZ87EunXrALz8zzVt2jS0a9cOM2bMAABs27YNXbp0gb29Pfz9/ZGZmQkASE9Ph5+fH9q0aQMnJycsWbIErx7tum3bNjg4OMDe3h6+vr6IjY0FAEybNg2rVq0CACQmJuLLL7+EnZ0dnJycsGnTJvn+Pj4+WLt2Ldzd3WFjY4OxY8ciLS1NPW8mFVFQUIAlS5bAxcUFLVu2hJubGy5cuADgzfpBRkYGAgIC0K5dOzg4OGDp0qWQSqWVdnxUep6ennj69ClmzJiBFStWYOnSpejYsSPat2+PmTNnyj8f1q1bBz8/P7i4uMDNzQ0FBQU4f/48vLy8YGtrCx8fHzx48EBe77Jly9C+fXt06NABEyZMwPPnz/Hjjz/i0KFD2Lx5M2bOnFlZh0waJiMjAzKZrLLDoEqiMYkbAKSmpuLjjz/G77//jp07d8LQ0BBnz55FSEgINmzYgMjISADA5MmT0aRJE1y4cAHjx4/HwYMHFeq5f/8+Tp06henTp+PQoUP44YcfEBoail9++QXAy1EzANiyZQuMjIwQGRmJnTt34tixY4iKisLjx48RHByMvXv34n//+x/q16+P4ODgIvGOHz8exsbGOHv2LDZv3oxdu3Zh37598vIjR44gNDQUJ0+eRGxsLHbu3FlRbx2pEB4ejsjISOzZswfR0dHo1KkTli1bBuDN+sGsWbOQnJyM48ePY9++fYiKisLGjRsr8xCplA4ePIh69eohJCQEhYWFiIqKwr59+3D8+HE8e/YMQUFB8m2joqKwadMm7NmzB3FxcRg3bhy++uorXLhwAd27d8fo0aMhlUoRGRmJM2fO4Pjx4zh9+jSkUil++uknfPHFF+jRowd8fX2xYMGCSjxq+q+dO3eiQ4cOyMjIAAAEBARgxIgRJQ4KAMDNmzfh4eGBzz//HEuWLJEnVyX9iC+p7Pz583B3d4etrS28vb3x+++/IyMjAyNHjkRSUhJatWqFgoICNb87VNk0KnEDAHd3d6Snp+Py5cuYNm0a9PT0YG1tjQEDBmDfvn2Ii4vDtWvXMHnyZEgkEtjb2xeZp9KpUycYGBjAyMgIYWFh8PX1RaNGjaCvr4/Jkyfj0KFDyMvLg4GBAW7evIljx45BV1cXp0+fhp2dHfT09JCdnY29e/fi0aNHmDNnDhYuXKjQxuPHjxETEyOPsVGjRhgxYoRCEtmrVy/Uq1cPtWrVgoODAx4/fqyW95CKcnFxwaZNm2BiYoLExEQYGRnh2bNnAFDmfpCbm4uTJ09iypQpMDY2hqWlJSZOnFjkBwRVfYcOHcKECRNQu3ZtGBkZwd/fH0ePHkV+fj4A4NNPP0XDhg1hZGSEo0ePwtHREY6OjhCLxRgwYAC0tLQQFRUFAwMDJCYmYv/+/UhKSkJwcDCnVFRh/fv3h7W1NVatWoXff/8dJ0+exIIFC1QOCpw7dw7BwcEICwvD//73P/ncxZJ+xJdUNn36dEybNg3R0dEYPHgwgoKCYGRkhNDQUFhaWuLq1avQ1tZW75tDlU7jEjdzc3MkJCSgsLAQnTp1gq2tLWxtbRESEoLExEQkJibC2NgY+vr68n3q1aunUIeFhYX8dXx8PJYtWyavp3v37hCLxYiLi8OwYcPg7u6O9evXo3379hg7dixSUlJQu3ZtbNy4EdHR0ejVqxe6deuGs2fPKrSRmpoKExMTGBoaKsSRkJAgXzYzM5O/FovF8l9ZpH5SqRSBgYGwt7fHl19+iZiYGPnfo6z9ID09HTKZTKHfvf63J82Qmpqq8HesX78+ZDIZUlJSALz8PHolPj4ep0+fln+W2NraIiEhAfHx8fjss88QFBSEY8eOwdXVFb169cKNGzfUfjxUOiKRCPPnz0d4eDimT5+O2bNno6CgQOWgwODBg2FlZQULCwsMHjwYERERJf6IV/UD38DAAAcPHkR0dDQ8PDxw8uTJyng7qIrRuMRNJBLBwsICEokEFy9eRHR0NKKjo3Hq1CmsWrUKderUQVpaGrKzs+X7vP6FKRKJ5K8tLCwwd+5ceT0XLlxAeHg4GjZsiHv37qFv3744duwYjh8/jszMTAQHB8uTsm3btuHixYvo06cPvv76a4U2XsXxaj4MAPz9998KyRpVHatWrYK+vj7+97//Yf/+/fD29paXlbUfmJubQ0dHR+EWD3///Tdq1apVGYdGb6FOnToKf8enT59CW1sbJiYmAIp+lnh5eck/S6Kjo3Hw4EF4eHggPj4eTZo0wa5duxAZGYk2bdogICBA7cdDpWdlZYW2bdsiNzcXnTp1KtWgwH+X69Spg+Tk5BJ/xKv6gb9x40bIZDKMHTsWn3/+OUJDQyvqcEmDaFziBgB169bFp59+ipUrV0IqlSIpKQm+vr7YsWMH6tatCxsbG6xatQpSqRRXrlwp8VdKjx49sGnTJjx9+hQymQzr16/HiBEjIAgC9uzZg6CgIGRlZcHc3BwSiQSmpqZ4+vQpfH19cffuXdSoUQOmpqbyD/L/xmhjY4PFixcjNzcXjx8/xpYtW9C9e/eKfnvoDaSnp0NPTw/a2tqIj4/Ht99+K5+fUtZ+oKWlBXd3dyxbtgzp6elITk7G+vXr4e7uXslHSWXl6emJdevWITExERkZGVi+fDmcnJwUvrxfcXNzw4kTJxAdHQ1BEPDrr7/Cw8MDcXFxuH79OsaOHYu4uDgYGRnB0NBQ/pkhkUiQlZWl7kMjFc6fP49r166hRYsWWLZsWakGBZKTk+Wv4+PjUbdu3RJ/xJdUJpVKERcXh1WrViEyMhLLli3D+vXrcfv27Qo8atIEGpm4AcDKlSsRGxsLBwcHeHp6onXr1vI5I4sWLcKtW7dgZ2eHVatWoU2bNtDR0Sm2nt69e8Pd3R1DhgyBnZ0dLl26hJCQEIjFYkyaNAk6Ojro3LkzHBwcYG5uDl9fX3z22Wf48ssvMXr0aLRs2RK7du3C6tWri9S9YsUKvHjxAo6Ojvjiiy/Qs2dPDBo0qCLfFnpDEyZMwO3bt2FjY4PBgwfD1dUV6enpSE1NfaN+EBAQADMzM3Tr1g0eHh5o0aJFkVFZqvpeXU3cp08fdO7cGUZGRkXms77SuHFjLFmyBPPmzYONjQ2WLFmCFStWwNraGt26dUOPHj3Qt29f2NjY4PLly5g3bx6Al/Mrw8PDMXHiRHUeGpUgKysLAQEB8Pf3x/z583Hw4EE8efJE5aDAjh07kJCQgISEBGzduhVeXl4l/ohX9QN/0qRJCA8Ph5aWFmrXrg2RSAQjIyNIJBLk5eXxytJ3lEioZhOrBEHAhQsXYGdnBy2tl3npq9uGDBgwoJKjIyKiqm7u3Ln466+/8MMPPwB4eWX5zp07ERwcjNmzZ+POnTv45JNPoKenBxsbG/j5+cHHxwdNmzbFmTNnkJeXhwEDBmDcuHEQiURITEzEvHnzcOnSJejo6KB///4YO3YstLS0SiyLjIzEokWLEBsbi5o1a2LcuHHo3bs3srOz4ePjg4cPH+LUqVOchvGOqXaJGwB06dIF48aNQ69evRATE4Nhw4Zhz549aNSoUWWHRkREGoiDAlRVaOyp0pIsX74cP/zwA1q1aoXJkycjKCiISRsREb0xkUiEWbNmITw8HAAQExODc+fOwd7evpIjo3dNtRxxIyIiKm/Xrl3D3Llz8fDhQ/n9GXnBGakbEzciIiIiDVEtT5USERERVUdM3IiIiIg0BBM3IqpwT548qewQiIiqBSZuRBqsadOmaNq0abGJ0eLFi9G0aVMcOHAAADBt2jRMmzZN3SHizJkzGDZsmHzZx8cH69atK7f6y7s+IqKqjIkbkYarWbOm/BYFr8hkMhw+fBg1atSopKj+9eLFC/AaKCKi8sHEjUjDeXh4FEncfvvtNzRp0gQ1a9Z8ozp9fHywfv169O/fHy1btkTPnj1x48YNfP3112jVqhWcnJzw66+/yre/ceMGvvjiC7Rp0waurq746aefAAAXL15EYGAg4uLi0KpVK6SkpAAAHj9+jGHDhsHW1hZdunTBiRMn5HXdvXsXI0eORNu2beHg4IA5c+YgIyNDXr537144OzujVatW8Pf3R05OzhsdIxGRJmLiRqThOnXqhIyMDFy+fFm+7sCBA/D29n6renfu3In58+cjKioKRkZGGDhwINzd3XHp0iW4urrKn7WZmJiIYcOGwcPDA5GRkVizZg2+++47HDp0CHZ2dggKCkK9evVw9epVmJmZAQAiIyMxdepUREVFoWfPnpg+fTry8/Px/PlzDB48GB9++CF+++037N+/Hw8fPsTUqVPl+82bNw8LFizApUuX0KJFC9y8efOtjpOISJMwcSPScDo6OnB3d5ePuqWmpuLy5ctwcXF5q3pdXFzwwQcfQCKRwNbWFtbW1nB2doZYLIaDgwP+/vtvAMDBgwfxwQcfYMCAARCLxWjWrBl8fHywc+dOpXW7ubmhefPm0NLSgoeHBzIzM5GamorTp09DR0cHkydPhp6eHiwsLDBr1iycOXMGycnJOHjwIFxcXGBvbw+xWIyBAwfio48+eqvjJCLSJOLKDoCI3p6Xlxd8fX0REBCAQ4cOwcXFBbq6um9V539Ps2pra8PY2Fi+rKWlJZ+39vfff+PWrVuwtbWVlxcWFsLU1FRp3SYmJvLXOjo6AID8/HykpKSgXr168mdBAkCDBg3k7SQmJuLjjz9WqMvKyuoNjo6ISDMxcSOqBj777DNYWFjgzJkzCAsLQ1BQ0FvXKRKJSrVd7dq1YW9vj02bNsnXpaamIi8vr8xt1q9fH3FxcSgoKIC2tjaAf28lYmFhgdq1ayM2NlZhn4SEBDRp0qTMbRERaSKeKiWqJry8vLBhwwZIpVJ89tlnxW6Tk5ODhIQEhX+ZmZlv1a6HhweuXLmCI0eOoKCgAPHx8Rg+fDjWrl0LAJBIJMjJyYFMJlNZl6OjIwBg5cqVyM3NRXJyMhYsWIB27dqhfv366NOnD06dOoVffvkFMpkMP//8M65fv/5W8RMRaRImbkTVRM+ePXHv3r0SL0o4duwYHB0dFf5t3779rdq1srJCaGgoduzYAXt7e/Tu3RufffYZZs+eDQBo27YtzMzM0KZNG9y/f7/EuoyMjLB161b88ccfcHR0hIeHB6ysrLBmzRoAgI2NDZYuXYrFixfD1tYWx48fx+eff/5W8RMRaRI+ZJ6IiIhIQ3DEjYiIiEhDMHEjIiIi0hBM3IiIiIg0BBM3IiIiIg3BxI2IiIhIQzBxIyIiItIQTNyIiIiINAQTNyIiIiIN8f/lOGtIzK9ZWQAAAABJRU5ErkJggg==\n", + "image/png": 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", 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" ] @@ -3647,7 +3645,7 @@ "outputs": [ { "data": { - "image/png": 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" ] @@ -3676,7 +3674,7 @@ "outputs": [ { "data": { - "image/png": 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" ] @@ -3705,7 +3703,7 @@ "outputs": [ { "data": { - "image/png": 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" ] @@ -3734,7 +3732,7 @@ "outputs": [ { "data": { - "image/png": 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" ] @@ -3765,7 +3763,7 @@ "outputs": [ { "data": { - "image/png": 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" ] @@ -3821,7 +3819,7 @@ "outputs": [ { "data": { - "image/png": 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" ] @@ -3850,7 +3848,7 @@ "outputs": [ { "data": { - "image/png": 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" ] @@ -3879,7 +3877,7 @@ "outputs": [ { "data": { - "image/png": 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" ] @@ -3908,7 +3906,7 @@ "outputs": [ { "data": { - "image/png": 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" ] @@ -3937,7 +3935,7 @@ "outputs": [ { "data": { - "image/png": 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