{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Python: PLM and IRM for Multiple Treatments\n", "\n", "In this example, we show the behavior of the PLM and IRM estimators when the treatment effect is heterogeneous across different treatments. We show that since the PLM estimates a convex-weighted average of treatment effects, it is not able to recover the true treatment effects when they are heterogeneous. On the other hand, the IRM estimator is able to recover the true treatment effects when they are heterogeneous. This is shown to matter substantially when ranking treatments by their estimated treatment effects.\n", "\n", "\n", "We assume basic knowledge of the potential outcomes framework and the assumptions of the PLM and IRM estimators. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-08-31T09:54:37.659988Z", "iopub.status.busy": "2024-08-31T09:54:37.659536Z", "iopub.status.idle": "2024-08-31T09:54:38.962570Z", "shell.execute_reply": "2024-08-31T09:54:38.961963Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "\n", "from doubleml import DoubleMLData, DoubleMLPLR, DoubleMLIRM\n", "from xgboost import XGBRegressor, XGBClassifier\n", "\n", "%matplotlib inline\n", "%config InlineBackend.figure_format = 'retina'\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ranking Treatment Effects under Treatment Propensity and Treatment Effect Heterogeneity\n", "\n", "We consider a setting with two treatments $D_1$ and $D_2$, a single binary covariate $X$ (with $p=0.5$), and a continuous outcome $Y$. The propensity scores for the two treatments are given by:\n", "\n", "| X \\ D | $D_1$ = 1 | $D_2$ = 1 |\n", "|-------|--------|--------|\n", "| X = 0 | 0.01 | 0.5 |\n", "| X = 1 | 0.5 | 0.01 |\n", "\n", "And the underlying heterogeneous treatment effects are given by:\n", "\n", "| X \\ $\\tau$ | $\\tau_1$ | $\\tau_2$ |\n", "|-------|----|----|\n", "| X = 0 | -3 | -2 |\n", "| X = 1 | 3 | 3 |\n", "| ATE | 0 | 0.5|\n", "\n", "The researcher seeks to rank the two treatments based on their average treatment effects. We compare the behavior of the PLM and IRM estimators in this setting.\n", "\n", "We implement the DGP below." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-08-31T09:54:38.965315Z", "iopub.status.busy": "2024-08-31T09:54:38.964746Z", "iopub.status.idle": "2024-08-31T09:54:39.006638Z", "shell.execute_reply": "2024-08-31T09:54:39.006061Z" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " x d1 d2 y\n", "0 0 0 0 1.415545\n", "1 1 0 0 -1.710202\n", "2 1 1 0 0.908788\n", "3 1 1 0 2.309962\n", "4 0 0 0 1.821121" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\n", "def dgp(\n", " n = 100_000,\n", " treat1_params = {\n", " \"p_x0\": 0.01, \"p_x1\": 0.50, \"τ_x0\": -3, \"τ_x1\": 3,\n", " },\n", " treat2_params = {\n", " \"p_x0\": 0.5, \"p_x1\": 0.01, \"τ_x0\": -2, \"τ_x1\": 3,\n", " },\n", " ):\n", " # utility functions to transform between the probability scale and the logit scale\n", " sigmoid = lambda x: 1 / (1 + np.exp(-x))\n", " inv_sigmoid = lambda p: np.log(p / (1 - p))\n", "\n", " df = pd.DataFrame()\n", " # noise terms\n", " eta1 = np.random.normal(0, 0.1, size=n)\n", " eta2 = np.random.normal(0, 0.1, size=n)\n", " eps = np.random.normal(0, 1, size=n)\n", " # binary covariate\n", " df[\"x\"] = np.random.randint(2, size=n) # half and half\n", " df[[\"x0\", \"x1\"]] = pd.get_dummies(df.x)\n", " # treatment 1 propensity score\n", " pscore1 = df.x0 * (inv_sigmoid(treat1_params[\"p_x0\"]) + eta1) + df.x1 * (\n", " inv_sigmoid(treat1_params[\"p_x1\"]) + eta2\n", " )\n", " # treatment 2 propensity score\n", " pscore2= df.x0 * (inv_sigmoid(treat2_params[\"p_x0\"]) + eta2) + df.x1 * (\n", " inv_sigmoid(treat2_params[\"p_x1\"]) + eta2\n", " )\n", " df['d1'] = np.random.binomial(1, sigmoid(pscore1))\n", " df['d2'] = np.random.binomial(1, sigmoid(pscore2))\n", " # outcome 1\n", " df[\"y\"] = (\n", " 0\n", " + 1 * df.x0 # arbitrary covariate coefs\n", " - 2 * df.x1\n", " + df.x0 * df.d1 * (treat1_params[\"τ_x0\"])\n", " + df.x1 * df.d1 * (treat1_params[\"τ_x1\"])\n", " + df.x0 * df.d2 * (treat2_params[\"τ_x0\"])\n", " + df.x1 * df.d2 * (treat2_params[\"τ_x1\"])\n", " + eps\n", " )\n", " return df.drop([\"x0\", \"x1\"], axis=1)\n", "df = dgp()\n", "df.head()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-08-31T09:54:39.008845Z", "iopub.status.busy": "2024-08-31T09:54:39.008650Z", "iopub.status.idle": "2024-08-31T09:54:39.028311Z", "shell.execute_reply": "2024-08-31T09:54:39.027730Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "d1 0 1\n", "x \n", "0 0.990585 0.009415\n", "1 0.500531 0.499469\n", "d2 0 1\n", "x \n", "0 0.503261 0.496739\n", "1 0.988831 0.011169\n" ] } ], "source": [ "print(pd.crosstab(df.x, df.d1, normalize='index'))\n", "print(pd.crosstab(df.x, df.d2, normalize='index'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Partially Linear Model performs overlap weighting\n", "\n", "The partially linear model inherits the properties of linear regression under treatment effect heterogeneity (Angrist (1998), Angrist and Krueger(1999), Aronow and Samii (2016)). The probability limit of the treatment coefficient in the partially linear model $Y_i = \\tau D_i + g(X_i) + \\epsilon_i$ is given by:\n", "\n", "$$\n", "p\\!\\!-\\!\\!\\lim \\hat{\\tau} = \\mathbb{E} [\\gamma(X) \\tau(X)]\n", "$$\n", "\n", "where \n", "\n", "$$\n", "\\gamma(X) = \\frac{\\mathbb{V}(D \\mid X)}{\\mathbb{E} [\\mathbb{V}(D \\mid X)]}\n", "$$\n", "\n", "This simplifies to \n", "\n", "$$\n", "\\gamma(X) = \\frac{p(X)(1-p(X))}{\\mathbb{E}[p(X)(1-p(X))]}\n", "$$\n", "\n", "when $D$ is binary.\n", "\n", "We have deliberately generated a dataset with varying propensity scores across treatments and covariates. Since we have a single binary covariate, we can analytically estimate the plim of the above estimator. The regression coefficients are equal to:\n", "\n", "$$\n", "\\begin{align*}\n", "\\tilde{\\tau}_1 & = \\frac{-3 \\cdot 0.01 \\cdot 0.99 + 3 \\cdot 0.5 \\cdot 0.5}{\n", " 0.01 \\cdot 0.99 + 0.5 \\cdot 0.5\n", "} = 2.7714 \\\\\n", "\\tilde{\\tau}_2 & = \\frac{-2 \\cdot 0.5 \\cdot 0.5 + 3 \\cdot 0.01 \\cdot 0.99}{0.01 \\cdot 0.99 + 0.5 \\cdot 0.5} = -1.8095\n", "\\end{align*}\n", "$$\n", "\n", "So, we see that the PLM gets the ranking wrong; even though the treatment effect of $D_1$ (0) is lower than that of $D_2$ (0.5), the PLM estimates the treatment effect of $D_1$ to be higher than that of $D_2$ because it upweights the stratum with large positive effects when estimating the effect for $D_1$ and vice versa for $D_2$.\n", "\n", "We verify this numerically with the `DoubleML`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2024-08-31T09:54:39.030393Z", "iopub.status.busy": "2024-08-31T09:54:39.030223Z", "iopub.status.idle": "2024-08-31T09:54:40.590556Z", "shell.execute_reply": "2024-08-31T09:54:40.589929Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " coef std err t P>|t| 2.5 % 97.5 %\n", "d1 2.770751 0.013033 212.600484 0.0 2.745207 2.796294\n", "d2 -1.798697 0.011962 -150.365934 0.0 -1.822143 -1.775252\n" ] } ], "source": [ "df = dgp()\n", "dml_data = DoubleMLData(df, 'y', ['d1', 'd2'], 'x')\n", "plr_obj = DoubleMLPLR(dml_data,\n", " ml_l = XGBRegressor(),\n", " ml_m = XGBClassifier(),\n", " n_folds=5)\n", "plr_obj.fit()\n", "plr_est = plr_obj.summary\n", "print(plr_est)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Augmented Inverse Propensity Weighting Model estimates the ATE under arbitrary effect and propensity score heterogeneity\n", "\n", "The AIPW estimator is given by:\n", "\n", "$$\n", "\\tau_{\\text{AIPW}} = \\frac{1}{n} \\sum_i \\left( \\left[ \\hat{g}(1, X_i) - \\hat{g}(0, X_i) \\right] + \n", "\\frac{D_i(Y_i - \\hat{g}(1, X_i))}{\\hat{m}(X_i)} - \\frac{(1-D_i)(Y_i - \\hat{g}(0, X_i))}{1 - \\hat{m}(X_i)}\n", "\\right)\n", "$$\n", "\n", "and estimates the ATE consistently under arbitrary treatment effect and propensity score heterogeneity, and therefore ranks the two treatments correctly (i.e. $D_2$ has a higher treatment effect than $D_1$).\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2024-08-31T09:54:40.592957Z", "iopub.status.busy": "2024-08-31T09:54:40.592571Z", "iopub.status.idle": "2024-08-31T09:54:42.193451Z", "shell.execute_reply": "2024-08-31T09:54:42.192838Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " coef std err t P>|t| 2.5 % 97.5 %\n", "d1 -0.0523 0.032638 -1.602417 0.109063 -0.11627 0.01167\n", " coef std err t P>|t| 2.5 % 97.5 %\n", "d2 0.483694 0.039102 12.370186 3.789422e-35 0.407056 0.560332\n" ] } ], "source": [ "df = dgp()\n", "aipw_obj_1 = DoubleMLIRM(DoubleMLData(df, 'y', ['d1'], 'x'),\n", " ml_g = XGBRegressor(),\n", " ml_m = XGBClassifier(),\n", " n_folds=5)\n", "aipw_obj_1.fit()\n", "aipw_obj_2 = DoubleMLIRM(DoubleMLData(df, 'y', ['d2'], 'x'),\n", " ml_g = XGBRegressor(),\n", " ml_m = XGBClassifier(),\n", " n_folds=5)\n", "aipw_obj_2.fit()\n", "aipw_est_1, aipw_est_2 = aipw_obj_1.summary, aipw_obj_2.summary\n", "print(aipw_est_1)\n", "print(aipw_est_2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary Figure\n", "\n", "We summarize the true treatment effects, the PLM estimates, and the IRM estimates in a figure." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2024-08-31T09:54:42.196011Z", "iopub.status.busy": "2024-08-31T09:54:42.195532Z", "iopub.status.idle": "2024-08-31T09:54:42.428906Z", "shell.execute_reply": "2024-08-31T09:54:42.428287Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 392, "width": 534 } }, "output_type": "display_data" } ], "source": [ "\n", "colors = ['#da1440', '#e45228', '#ec973f', '#a4a147', '#008e80', '#008dbd',\n", " '#f6ebce', '#838235', '#3f5d93', '#50768b', '#133f5a', '#afd9e4']\n", "\n", "# Plot the data\n", "x = np.array([1, 2])\n", "y = [(-3+3)/2, (-2+3)/2]\n", "fig, ax = plt.subplots(dpi = 100, figsize = (6, 4))\n", "# plm\n", "plt.errorbar(x,\n", " plr_est.coef,\n", " yerr=1.96 * plr_est['std err'], markersize = 1,\n", " fmt='o', color=colors[0], ecolor=colors[0], capsize=5, label = 'PLM Estimate')\n", "plt.errorbar(x+.05,\n", " np.array([aipw_est_1.coef, aipw_est_2.coef]).flatten(),\n", " yerr = 1.96 * np.array([aipw_est_1.iloc[:,1].values[0],\n", " aipw_est_2.iloc[:,1].values[0]]),\n", " markersize = 3,\n", " fmt='o', color=colors[8], ecolor=colors[8], capsize=5, label = 'AIPW Estimate'\n", " )\n", "# true values\n", "plt.scatter(x-.05, y, color = colors[2], label = 'ATE')\n", "plt.scatter(x-.1, [-3, -2], color = colors[5], label=r\"CATE: $x=0$\")\n", "plt.scatter(x-.12, [3, 3], color = colors[4], label=r\"CATE: $x=1$\")\n", "plt.legend(loc = 0)\n", "plt.title(\"PLMs do not estimate ATEs \\n This is bad for ranking treatments\")\n", "plt.axis((.5, 3, -3.5, 4))\n", "ax.set_xticks([])\n", "string_labels = ['Treatment 1', 'Treatment 2']\n", "ax.set_xticks(x)\n", "ax.set_xticklabels(string_labels)\n", "ax.grid(True)\n", "ax.set_ylabel(\"Treatment Effect\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Additional Results: CATE estimates\n", "\n", "As an additional comparison, we can add the CATE estimates based on the previous PLR and IRM examples." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2024-08-31T09:54:42.431284Z", "iopub.status.busy": "2024-08-31T09:54:42.430837Z", "iopub.status.idle": "2024-08-31T09:54:42.435670Z", "shell.execute_reply": "2024-08-31T09:54:42.435101Z" } }, "outputs": [], "source": [ "# pandas data frame with one-hot encoded values for x\n", "groups = pd.get_dummies(df.x)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2024-08-31T09:54:42.437852Z", "iopub.status.busy": "2024-08-31T09:54:42.437541Z", "iopub.status.idle": "2024-08-31T09:54:43.231298Z", "shell.execute_reply": "2024-08-31T09:54:43.230755Z" } }, "outputs": [ { "data": { "text/html": [ "
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coefstd errtP>|t|[0.0250.975]
0-3.0320.045-66.7610.0-3.121-2.943
13.0070.009336.5770.02.9903.025
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" ], "text/plain": [ " coef std err t P>|t| [0.025 0.975]\n", "0 -3.032 0.045 -66.761 0.0 -3.121 -2.943\n", "1 3.007 0.009 336.577 0.0 2.990 3.025" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Repeat estimation for each treatment var separately\n", "# d1\n", "dml_data = DoubleMLData(df, 'y', 'd1', ['d2', 'x'])\n", "plr_obj_1 = DoubleMLPLR(dml_data,\n", " ml_l = XGBRegressor(),\n", " ml_m = XGBClassifier(),\n", " n_folds=5)\n", "plr_obj_1.fit()\n", "plr_est1 = plr_obj_1.summary\n", "plr_obj_1.gate(groups=groups).summary.round(3)\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2024-08-31T09:54:43.233815Z", "iopub.status.busy": "2024-08-31T09:54:43.233409Z", "iopub.status.idle": "2024-08-31T09:54:44.088595Z", "shell.execute_reply": "2024-08-31T09:54:44.088052Z" } }, "outputs": [ { "data": { "text/html": [ "
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coefstd errtP>|t|[0.0250.975]
0-1.9970.009-224.1350.0-2.014-1.979
12.9350.04466.6870.02.8493.022
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" ], "text/plain": [ " coef std err t P>|t| [0.025 0.975]\n", "0 -1.997 0.009 -224.135 0.0 -2.014 -1.979\n", "1 2.935 0.044 66.687 0.0 2.849 3.022" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# d2\n", "dml_data = DoubleMLData(df, 'y', 'd2', ['d1', 'x'])\n", "plr_obj_2 = DoubleMLPLR(dml_data,\n", " ml_l = XGBRegressor(),\n", " ml_m = XGBClassifier(),\n", " n_folds=5)\n", "plr_obj_2.fit()\n", "plr_est2 = plr_obj_2.summary\n", "plr_obj_2.gate(groups=groups).summary.round(3)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2024-08-31T09:54:44.091217Z", "iopub.status.busy": "2024-08-31T09:54:44.091008Z", "iopub.status.idle": "2024-08-31T09:54:44.115811Z", "shell.execute_reply": "2024-08-31T09:54:44.115216Z" } }, "outputs": [ { "data": { "text/html": [ "
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coefstd errtP>|t|[0.0250.975]
0-3.0950.044-70.2980.0-3.181-3.009
13.0090.04468.1430.02.9233.096
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" ], "text/plain": [ " coef std err t P>|t| [0.025 0.975]\n", "0 -3.095 0.044 -70.298 0.0 -3.181 -3.009\n", "1 3.009 0.044 68.143 0.0 2.923 3.096" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# IRM models\n", "# d1\n", "aipw_obj_1.gate(groups=groups).summary.round(3)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2024-08-31T09:54:44.118484Z", "iopub.status.busy": "2024-08-31T09:54:44.118278Z", "iopub.status.idle": "2024-08-31T09:54:44.142263Z", "shell.execute_reply": "2024-08-31T09:54:44.141582Z" } }, "outputs": [ { "data": { "text/html": [ "
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coefstd errtP>|t|[0.0250.975]
0-2.0000.054-36.9850.0-2.106-1.894
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" ], "text/plain": [ " coef std err t P>|t| [0.025 0.975]\n", "0 -2.000 0.054 -36.985 0.0 -2.106 -1.894\n", "1 2.983 0.054 54.990 0.0 2.877 3.090" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# IRM models\n", "# d2\n", "aipw_obj_2.gate(groups=groups).summary.round(3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "- Lal, A., Chou, W., & Schaefer, J. (2024). Using Double Machine Learning to Rank Treatments, Working Paper. Poster available at [https://apoorvalal.github.io/files/slides/acic_2024_poster.pdf](https://apoorvalal.github.io/files/slides/acic_2024_poster.pdf). Thread available at [https://x.com/Apoorva__Lal/status/1798913180930109556](https://x.com/Apoorva__Lal/status/1798913180930109556).\n", "- Angrist, J. D. (1998). Estimating the labor market impact of voluntary military service using social security data on military applicants. Econometrica, 66(2), 249-288.\n", "- Angrist, J. D., & Krueger, A. B. (1999). Empirical strategies in labor economics. Handbook of labor economics, 3, 1277-1366.\n", "- Aronow, P. M., & Samii, C. (2016). Does regression produce representative estimates of causal effects?. American Journal of Political Science, 60(1), 250-267.\n" ] } ], "metadata": { "kernelspec": { "display_name": "metrics", "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": "3.12.5" } }, "nbformat": 4, "nbformat_minor": 2 }