{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "

Table of Contents

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" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:28:39.160131Z", "start_time": "2020-11-07T21:28:38.957215Z" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# code for loading the format for the notebook\n", "import os\n", "\n", "# path : store the current path to convert back to it later\n", "path = os.getcwd()\n", "os.chdir(os.path.join('..', '..', 'notebook_format'))\n", "\n", "from formats import load_style\n", "load_style(plot_style=False)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:28:40.630483Z", "start_time": "2020-11-07T21:28:39.162179Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ethen 2020-11-07 13:28:40 \n", "\n", "CPython 3.6.4\n", "IPython 7.15.0\n", "\n", "numpy 1.18.5\n", "pandas 1.0.5\n", "sklearn 0.23.1\n", "matplotlib 3.1.0\n", "seaborn 0.9.0\n", "statsmodels 0.11.1\n" ] } ], "source": [ "os.chdir(path)\n", "\n", "# 1. magic for inline plot\n", "# 2. magic to print version\n", "# 3. magic so that the notebook will reload external python modules\n", "# 4. magic to enable retina (high resolution) plots\n", "# https://gist.github.com/minrk/3301035\n", "%matplotlib inline\n", "%load_ext watermark\n", "%load_ext autoreload\n", "%autoreload 2\n", "%config InlineBackend.figure_format='retina'\n", "\n", "import os\n", "import time\n", "import numpy as np\n", "import pandas as pd\n", "import seaborn as sns\n", "import matplotlib.pyplot as plt\n", "import statsmodels.formula.api as smf\n", "from sklearn.compose import ColumnTransformer\n", "from sklearn.preprocessing import OneHotEncoder\n", "from sklearn.linear_model import LogisticRegression, LinearRegression\n", "from sklearn.model_selection import train_test_split\n", "\n", "# prevent scientific notations\n", "pd.set_option('display.float_format', lambda x: '%.3f' % x)\n", "\n", "plt.style.use('fivethirtyeight')\n", "\n", "%watermark -a 'Ethen' -d -t -v -p numpy,pandas,sklearn,matplotlib,seaborn,statsmodels" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Inverse Propensity Weighting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The purpose of using propensity score is to balance the treatment/control groups on the observed covariates. The advantage with using weighting is that all individuals/records in our dataset can be leveraged. Unlike techniques such as matching, where we might be discarding large amount of data in the control group.\n", "\n", "In this document, we'll be:\n", "\n", "- Conducting the analysis on the outcome without the use of propensity score.\n", "- Performing the propensity score estimation.\n", "- Conducting the outcome analysis with the use of inverse propensity weighting." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data Preprocessing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll be working with data coming from the [ The National Study of Learning Mindsets](https://mindsetscholarsnetwork.org/about-the-network/current-initatives/national-mindset-study/). The background behind this data is an attempt to find out if instilling students with a growth mindset will improve their overall academic performance. In this dataset, the academic performance is recorded as a standardized `achievement_score`.\n", "\n", "Besides the treated and outcome variables, the study also recorded some other features:\n", "\n", "- schoolid: identifier of the student's school\n", "- success_expect: self-reported expectations for success in the future, a proxy for prior achievement, measured prior to random assignment\n", "- ethnicity: categorical variable for student race/ethnicity\n", "- gender: categorical variable for student identified gender\n", "- frst_in_family: categorical variable for student first-generation status, i.e. first in family to go to college\n", "- school_urbanicity: school-level categorical variable for urbanicity of the school, i.e. rural, suburban, etc\n", "- school_mindset: school-level mean of students' fixed mindsets, reported prior to random assignment, standardize\n", "- school_achievement: school achievement level, as measured by test scores and college preparation for the previous 4 cohorts of students, standardized\n", "- school_ethnic_minority: school racial/ethnic minority composition, i.e., percentage of student body that is Black, Latino, or Native American, standardized\n", "- school_poverty: school poverty concentration, i.e., percentage of students who are from families whose incomes fall below the federal poverty line, standardized\n", "- school_size: total number of students in all four grade levels in the school, standardized." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:28:40.692041Z", "start_time": "2020-11-07T21:28:40.632774Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(10391, 10)\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " achievement_score intervention school_mindset school_achievement \\\n", "0 0.277 1 0.335 0.649 \n", "1 -0.450 1 0.335 0.649 \n", "2 0.770 1 0.335 0.649 \n", "3 -0.122 1 0.335 0.649 \n", "4 1.526 1 0.335 0.649 \n", "\n", " school_ethnic_minority school_poverty school_size ethnicity gender \\\n", "0 -1.311 0.224 -0.427 4 2 \n", "1 -1.311 0.224 -0.427 12 2 \n", "2 -1.311 0.224 -0.427 4 2 \n", "3 -1.311 0.224 -0.427 4 2 \n", "4 -1.311 0.224 -0.427 4 1 \n", "\n", " school_urbanicity \n", "0 4 \n", "1 4 \n", "2 4 \n", "3 4 \n", "4 4 " ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# we'll only work with a subset of the columns, feel free to experiment with others\n", "cat_cols = ['ethnicity', 'gender', 'school_urbanicity']\n", "num_cols = ['school_mindset', 'school_achievement', 'school_ethnic_minority', 'school_poverty', 'school_size']\n", "treatment_col = 'intervention'\n", "label_col = 'achievement_score'\n", "\n", "use_cols = [label_col, treatment_col] + num_cols + cat_cols\n", "df = pd.read_csv('data/learning_mindset.csv', usecols=use_cols)[use_cols]\n", "print(df.shape)\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our data will be fed into a logistic regression in the next section, here we one hot encode the categorical variables. As the numeric features are already standardized, we leave them as is." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:28:40.738146Z", "start_time": "2020-11-07T21:28:40.697579Z" } }, "outputs": [ { "data": { "text/plain": [ "ColumnTransformer(remainder='passthrough', sparse_threshold=0,\n", " transformers=[('one_hot',\n", " OneHotEncoder(dtype=,\n", " handle_unknown='ignore',\n", " sparse=False),\n", " ['ethnicity', 'gender', 'school_urbanicity'])])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "one_hot_encoder = OneHotEncoder(handle_unknown='ignore', sparse=False, dtype=np.int32)\n", "column_transformer = ColumnTransformer(\n", " transformers = [\n", " ('one_hot', one_hot_encoder, cat_cols)\n", " ],\n", " sparse_threshold=0,\n", " remainder='passthrough'\n", ")\n", "column_transformer.fit(df)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:28:40.788880Z", "start_time": "2020-11-07T21:28:40.740131Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(10391, 29)\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " ethnicity_1 ethnicity_2 ethnicity_3 ethnicity_4 ethnicity_5 \\\n", "0 0.000 0.000 0.000 1.000 0.000 \n", "1 0.000 0.000 0.000 0.000 0.000 \n", "2 0.000 0.000 0.000 1.000 0.000 \n", "3 0.000 0.000 0.000 1.000 0.000 \n", "4 0.000 0.000 0.000 1.000 0.000 \n", "... ... ... ... ... ... \n", "10386 0.000 0.000 0.000 1.000 0.000 \n", "10387 0.000 0.000 0.000 1.000 0.000 \n", "10388 0.000 0.000 0.000 0.000 0.000 \n", "10389 0.000 0.000 0.000 1.000 0.000 \n", "10390 1.000 0.000 0.000 0.000 0.000 \n", "\n", " ethnicity_6 ethnicity_7 ethnicity_8 ethnicity_9 ethnicity_10 ... \\\n", "0 0.000 0.000 0.000 0.000 0.000 ... \n", "1 0.000 0.000 0.000 0.000 0.000 ... \n", "2 0.000 0.000 0.000 0.000 0.000 ... \n", "3 0.000 0.000 0.000 0.000 0.000 ... \n", "4 0.000 0.000 0.000 0.000 0.000 ... \n", "... ... ... ... ... ... ... \n", "10386 0.000 0.000 0.000 0.000 0.000 ... \n", "10387 0.000 0.000 0.000 0.000 0.000 ... \n", "10388 0.000 0.000 0.000 0.000 0.000 ... \n", "10389 0.000 0.000 0.000 0.000 0.000 ... \n", "10390 0.000 0.000 0.000 0.000 0.000 ... \n", "\n", " school_urbanicity_2 school_urbanicity_3 school_urbanicity_4 \\\n", "0 0.000 0.000 1.000 \n", "1 0.000 0.000 1.000 \n", "2 0.000 0.000 1.000 \n", "3 0.000 0.000 1.000 \n", "4 0.000 0.000 1.000 \n", "... ... ... ... \n", "10386 0.000 1.000 0.000 \n", "10387 0.000 1.000 0.000 \n", "10388 0.000 1.000 0.000 \n", "10389 0.000 1.000 0.000 \n", "10390 0.000 1.000 0.000 \n", "\n", " achievement_score intervention school_mindset school_achievement \\\n", "0 0.277 1.000 0.335 0.649 \n", "1 -0.450 1.000 0.335 0.649 \n", "2 0.770 1.000 0.335 0.649 \n", "3 -0.122 1.000 0.335 0.649 \n", "4 1.526 1.000 0.335 0.649 \n", "... ... ... ... ... \n", "10386 0.809 0.000 1.186 -1.130 \n", "10387 -0.156 0.000 1.186 -1.130 \n", "10388 0.371 0.000 1.186 -1.130 \n", "10389 -0.396 0.000 1.186 -1.130 \n", "10390 0.479 0.000 1.186 -1.130 \n", "\n", " school_ethnic_minority school_poverty school_size \n", "0 -1.311 0.224 -0.427 \n", "1 -1.311 0.224 -0.427 \n", "2 -1.311 0.224 -0.427 \n", "3 -1.311 0.224 -0.427 \n", "4 -1.311 0.224 -0.427 \n", "... ... ... ... \n", "10386 1.010 1.005 -1.175 \n", "10387 1.010 1.005 -1.175 \n", "10388 1.010 1.005 -1.175 \n", "10389 1.010 1.005 -1.175 \n", "10390 1.010 1.005 -1.175 \n", "\n", "[10391 rows x 29 columns]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "one_hot_encoder = column_transformer.named_transformers_['one_hot']\n", "one_hot_encoded_cols = one_hot_encoder.get_feature_names(cat_cols).tolist()\n", "columns = one_hot_encoded_cols + [label_col, treatment_col] + num_cols\n", "\n", "df = pd.DataFrame(column_transformer.transform(df), columns=columns)\n", "print(df.shape)\n", "df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Outcome Analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's often times useful to establish some baseline. Here, we would like to gauge what would the result look like if we don't use propensity score weighting to control for potential biases with assignment of individuals to the control and treatment group. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:28:41.340665Z", "start_time": "2020-11-07T21:28:40.791260Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 379, "width": 542 } }, "output_type": "display_data" } ], "source": [ "# change default style figure and font size\n", "plt.rcParams['figure.figsize'] = 8, 6\n", "plt.rcParams['font.size'] = 12\n", "\n", "# we can check the histogram of our label between the treatment and control\n", "plt.hist(df.loc[df[treatment_col] == 0.0, label_col], bins=20, alpha=0.3, label='control')\n", "plt.hist(df.loc[df[treatment_col] == 1.0, label_col], bins=20, alpha=0.3, label='treatment')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:28:41.372449Z", "start_time": "2020-11-07T21:28:41.342273Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-0.15380303423613792 [0.47227167]\n" ] } ], "source": [ "# fitting a linear regression to estimate the outcome\n", "linear = LinearRegression()\n", "linear.fit(df[[treatment_col]], df[label_col])\n", "print(linear.intercept_, linear.coef_)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:28:41.430110Z", "start_time": "2020-11-07T21:28:41.374713Z" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept -0.1538 0.012 -13.201 0.000 -0.177 -0.131
intervention 0.4723 0.020 23.133 0.000 0.432 0.512
" ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "smf.ols(f'{label_col} ~ {treatment_col}', data=df).fit().summary().tables[1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use Linear Regression from different packages to establish our baseline estimates. The one from `statsmodels` will give us some additional statistical information. By blindly comparing individuals with and without the intervention, we can see that, on average, those in the treatment group achieved a achievement score 0.4723 higher than the control. Be aware that in this dataset is score was standardized, i.e. it means the treated is 0.4723 standard deviation higher than the untreated.\n", "\n", "Upon establishing the baseline, our next task is to question these numbers." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Propensity Score Estimation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The idea behind propensity score is we don't need to directly control for our confounders $X$ to achieve conditional independence $(Y^1,Y^0) \\perp T \\text{ | } X$. Hence, $Y^1$ denotes the outcome if treatment, $T$, was applied, whereas $Y^0$ measures the outcome if individual was under the control group.\n", "\n", "Instead, it is sufficient to control for a single variable, propensity score, $P(x)$, which is the conditional probability of the treatment, $P(T|X)$. Or in notations form, with our propensity score, we now have $(Y^1,Y^0) \\perp T \\text{ | } P(X)$.\n", "\n", "Here, we'll use a logistic regression to estimate our propensity score. Feel free to use other classification techniques, but keep in mind that other classification techniques might not produce well [calibrated probabilities](http://ethen8181.github.io/machine-learning/model_selection/prob_calibration/prob_calibration.html) and the utmost goal of propensity score estimation is to make sure to include all the confounding variables instead of getting taken away of the different kinds of classification model that we can potentially use. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:28:41.579213Z", "start_time": "2020-11-07T21:28:41.433543Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(10391, 30)\n" ] }, { "data": { "text/html": [ "
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5 rows × 30 columns

\n", "
" ], "text/plain": [ " ethnicity_1 ethnicity_2 ethnicity_3 ethnicity_4 ethnicity_5 \\\n", "0 0.000 0.000 0.000 1.000 0.000 \n", "1 0.000 0.000 0.000 0.000 0.000 \n", "2 0.000 0.000 0.000 1.000 0.000 \n", "3 0.000 0.000 0.000 1.000 0.000 \n", "4 0.000 0.000 0.000 1.000 0.000 \n", "\n", " ethnicity_6 ethnicity_7 ethnicity_8 ethnicity_9 ethnicity_10 ... \\\n", "0 0.000 0.000 0.000 0.000 0.000 ... \n", "1 0.000 0.000 0.000 0.000 0.000 ... \n", "2 0.000 0.000 0.000 0.000 0.000 ... \n", "3 0.000 0.000 0.000 0.000 0.000 ... \n", "4 0.000 0.000 0.000 0.000 0.000 ... \n", "\n", " school_urbanicity_3 school_urbanicity_4 achievement_score intervention \\\n", "0 0.000 1.000 0.277 1.000 \n", "1 0.000 1.000 -0.450 1.000 \n", "2 0.000 1.000 0.770 1.000 \n", "3 0.000 1.000 -0.122 1.000 \n", "4 0.000 1.000 1.526 1.000 \n", "\n", " school_mindset school_achievement school_ethnic_minority school_poverty \\\n", "0 0.335 0.649 -1.311 0.224 \n", "1 0.335 0.649 -1.311 0.224 \n", "2 0.335 0.649 -1.311 0.224 \n", "3 0.335 0.649 -1.311 0.224 \n", "4 0.335 0.649 -1.311 0.224 \n", "\n", " school_size propensity_score \n", "0 -0.427 0.313 \n", "1 -0.427 0.295 \n", "2 -0.427 0.313 \n", "3 -0.427 0.313 \n", "4 -0.427 0.338 \n", "\n", "[5 rows x 30 columns]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "input_cols = one_hot_encoded_cols + num_cols\n", "\n", "logistic = LogisticRegression()\n", "logistic.fit(df[input_cols], df[treatment_col])\n", "\n", "propensity_score = 'propensity_score'\n", "df[propensity_score] = logistic.predict_proba(df[input_cols])[:, 1]\n", "print(df.shape)\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After training our propensity score, it's important to check for score overlap between the treated and untreated population. Looking at the distribution plot below, we can find both treated and untreated individuals in different regions. In this case, we have a balanced dataset and our positivity assumption holds true. Remember positivity refers to the scenario where all of the individuals have at least some chance of receiving either treatment and that appears to be the case here. In summary, this would be a situation where we would feel comfortable to proceed with our propensity score matching.\n", "\n", "Note that if we encounter a situation where the propensity score between the treatment and control does not overlap, then we should stop and better construct the prediction that controls for confounding, or in much simpler terms, see if we are missing any important features in our propensity score model. This requires domain knowledge of the data that we are working with. Failing to check for positivity and lack of balance can introduce bias in our estimation as we will be extrapolating the effect to unknown regions." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:28:42.435174Z", "start_time": "2020-11-07T21:28:41.582092Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 418, "width": 564 } }, "output_type": "display_data" } ], "source": [ "control_score = df.loc[df[treatment_col] == 0.0, propensity_score]\n", "treatment_score = df.loc[df[treatment_col] == 1.0, propensity_score]\n", "\n", "sns.distplot(control_score, label='control')\n", "sns.distplot(treatment_score, label='treatment')\n", "plt.title('Propensity Score Distribution of Control vs Treatment')\n", "plt.ylabel('Density')\n", "plt.xlabel('Scores')\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Outcome Analysis with Inverse Propensity Score Weighting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The final step in our analysis is to run our outcome model using the propensity score as weights, i.e. fit a weighted regression. In order to use our propensity score as weights, we will need to apply some transformation known as **Inverse Propensity Weighting (IPW)**. For individuals in the treatment group, $w = \\frac{1}{P(x)}$, whereas for individuals in the control group, $w = \\frac{1}{1 - P(x)}$.\n", "\n", "To understand why applying inverse propensity weighting helps us de-bias our potentially biased data. Say in the data we collected there are 200 records from group A and 2000 records from group B, to \"balance\" our dataset, we would like to \"up-weight\" the records from group A and \"down-weight\" the records from group B. If we were to weight each records in both groups by number of inverse records, $1 / 200$ for group A, and $1 / 2000$ for group B, we would end up with effectively 1 record on both group.\n", "\n", "Coming back to our example, we are taking all the individuals that are in the treatment group and scaling them with the inverse propensity of being treated $w = \\frac{1}{P(x)}$. What this effectively does is it makes those with a very low probability of treatment have a high weight, in other words, we have a individual in the treatment group that looks like he/she should belong to the control group, hence we will give a higher weight to this individual. What this does is create a population with the same size as the original, but where everyone is treated. We can apply the same reasoning for the control group." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:28:42.470247Z", "start_time": "2020-11-07T21:28:42.437599Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Original Sample Size 10391\n", "Treated Population Sample Size 10390.321766244168\n", "Untreated Population Sample Size 10390.61301069852\n" ] } ], "source": [ "treatment_weight = 1.0 / treatment_score\n", "control_weight = 1.0 / (1.0 - control_score)\n", "\n", "print('Original Sample Size', df.shape[0])\n", "print('Treated Population Sample Size', treatment_weight.sum())\n", "print('Untreated Population Sample Size', control_weight.sum())" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:28:42.508466Z", "start_time": "2020-11-07T21:28:42.472468Z" } }, "outputs": [], "source": [ "sample_weight = 'sample_weight'\n", "df[sample_weight] = np.where(\n", " df[treatment_col] == 1.0,\n", " 1.0 / df[propensity_score],\n", " 1.0 / (1.0 - df[propensity_score])\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once the sample weight are created, we can re-estimate the outcome with a weighted Linear Regression." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:28:42.572127Z", "start_time": "2020-11-07T21:28:42.510974Z" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept -0.1463 0.014 -10.771 0.000 -0.173 -0.120
intervention 0.4430 0.019 23.055 0.000 0.405 0.481
" ], "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "smf.wls(f'{label_col} ~ {treatment_col}', data=df, weights=df[sample_weight]).fit().summary().tables[1]" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:28:42.615998Z", "start_time": "2020-11-07T21:28:42.574811Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-0.14633238210898603 [0.44298379]\n" ] } ], "source": [ "linear = LinearRegression()\n", "linear.fit(df[[treatment_col]], df[label_col], sample_weight=df[sample_weight])\n", "print(linear.intercept_, linear.coef_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "FYI, even though scikit-learn's LinearRegression by default doesn't give us an estimated standard error, we can estimate this using bootstrapping. i.e. by sampling with replacement from the original data, and computing the average treatment effect like before. After repeating this step for lots of times, we will get a distribution of the outcome estimation. We will also use this time to organize the overall workflow into one single code cell." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:28:42.654750Z", "start_time": "2020-11-07T21:28:42.618472Z" } }, "outputs": [], "source": [ "def run_propensity_score_estimation(df, input_cols, treatment_col, label_col):\n", "\n", " # df is our pre-processed data\n", " df = df.sample(frac=1, replace=True)\n", "\n", " # estimate the propensity score\n", " logistic = LogisticRegression()\n", " logistic.fit(df[input_cols], df[treatment_col])\n", " propensity_score = logistic.predict_proba(df[input_cols])[:, 1]\n", "\n", " # calculate the inverse propensity weight\n", " sample_weight = np.where(\n", " df[treatment_col] == 1.0,\n", " 1.0 / propensity_score,\n", " 1.0 / (1.0 - propensity_score)\n", " )\n", "\n", " # estimate the outcome using weighted regression\n", " linear = LinearRegression()\n", " linear.fit(df[[treatment_col]], df[label_col], sample_weight=sample_weight)\n", " return linear.coef_[0]" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2020-11-07T21:29:41.423629Z", "start_time": "2020-11-07T21:28:42.657074Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ATE: 0.44207303186986624\n", "95% C.I.: (0.402353989536924, 0.4803417055971445)\n" ] } ], "source": [ "from joblib import Parallel, delayed\n", "\n", "np.random.seed(88)\n", "\n", "# the bootstrap approach of computing standard error can be computationally expensive on large datasets.\n", "bootstrap_sample = 1000\n", "parallel = Parallel(n_jobs=4)\n", "ates = parallel(delayed(run_propensity_score_estimation)(df,\n", " input_cols,\n", " treatment_col,\n", " label_col)\n", " for _ in range(bootstrap_sample))\n", "\n", "ates = np.array(ates)\n", "print(f\"ATE: {ates.mean()}\")\n", "print(f\"95% C.I.: {(np.percentile(ates, 2.5), np.percentile(ates, 97.5))}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ending Notes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this article, we look a stab at calculating average treatment effect, $E[Y|T=1] - E[Y|T=0]$, using propensity scores. We saw how using inverse propensity weighting helps us create an un-biased data from a biased data. With this method, it's important to call out identifying the features to use for the propensity score model should be treated with care. In general:\n", "\n", "- Aim to include confounding variables, variables that effects both the treatment and the outcome.\n", "- It's a good idea to add variables that predicts the outcome.\n", "- It's a bad idea to add variables that only predicts the treatment, this correlation with the treatment will make it harder for us to detect the true effect of the treatment." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Reference" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- [Github: Python Causality Handbook - Propensity Score](https://matheusfacure.github.io/python-causality-handbook/11-Propensity-Score.html)\n", "- [Github: Python Causality Handbook - Beyond Confounders](https://matheusfacure.github.io/python-causality-handbook/07-Beyond-Confounders.html)\n", "- [A Practical Guide for Using Propensity Score Weighting in R](http://www.math.umd.edu/~slud/s818M-MissingData/PropensityScoreWeightingR.pdf)" ] } ], "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": "3.7.11" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": { "height": "calc(100% - 180px)", "left": "10px", "top": "150px", "width": "229.594px" }, "toc_section_display": true, "toc_window_display": true }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }