{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Demo for the DoWhy causal API\n",
"We show a simple example of adding a causal extension to any dataframe. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import os, sys\n",
"sys.path.append(os.path.abspath(\"../../../\"))"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import dowhy.datasets\n",
"import dowhy.api\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"from statsmodels.api import OLS"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>W0</th>\n",
" <th>v0</th>\n",
" <th>y</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>-1.289334</td>\n",
" <td>False</td>\n",
" <td>-3.324194</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>-1.100803</td>\n",
" <td>False</td>\n",
" <td>-2.035903</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>-3.564829</td>\n",
" <td>False</td>\n",
" <td>-5.986921</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>-2.036167</td>\n",
" <td>False</td>\n",
" <td>-2.869478</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>-2.781469</td>\n",
" <td>False</td>\n",
" <td>-6.127631</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>995</th>\n",
" <td>-1.178597</td>\n",
" <td>True</td>\n",
" <td>2.965997</td>\n",
" </tr>\n",
" <tr>\n",
" <th>996</th>\n",
" <td>0.223498</td>\n",
" <td>True</td>\n",
" <td>4.161892</td>\n",
" </tr>\n",
" <tr>\n",
" <th>997</th>\n",
" <td>-2.582064</td>\n",
" <td>False</td>\n",
" <td>-3.472824</td>\n",
" </tr>\n",
" <tr>\n",
" <th>998</th>\n",
" <td>-1.998788</td>\n",
" <td>False</td>\n",
" <td>-0.725005</td>\n",
" </tr>\n",
" <tr>\n",
" <th>999</th>\n",
" <td>-0.789288</td>\n",
" <td>False</td>\n",
" <td>-2.080137</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>1000 rows × 3 columns</p>\n",
"</div>"
],
"text/plain": [
" W0 v0 y\n",
"0 -1.289334 False -3.324194\n",
"1 -1.100803 False -2.035903\n",
"2 -3.564829 False -5.986921\n",
"3 -2.036167 False -2.869478\n",
"4 -2.781469 False -6.127631\n",
".. ... ... ...\n",
"995 -1.178597 True 2.965997\n",
"996 0.223498 True 4.161892\n",
"997 -2.582064 False -3.472824\n",
"998 -1.998788 False -0.725005\n",
"999 -0.789288 False -2.080137\n",
"\n",
"[1000 rows x 3 columns]"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data = dowhy.datasets.linear_dataset(beta=5,\n",
" num_common_causes=1,\n",
" num_instruments = 0,\n",
" num_samples=1000,\n",
" treatment_is_binary=True)\n",
"df = data['df']\n",
"df['y'] = df['y'] + np.random.normal(size=len(df)) # Adding noise to data. Without noise, the variance in Y|X, Z is zero, and mcmc fails.\n",
"#data['dot_graph'] = 'digraph { v ->y;X0-> v;X0-> y;}'\n",
"\n",
"treatment= data[\"treatment_name\"][0]\n",
"outcome = data[\"outcome_name\"][0]\n",
"common_cause = data[\"common_causes_names\"][0]\n",
"df"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING:dowhy.causal_model:Causal Graph not provided. DoWhy will construct a graph based on data inputs.\n",
"INFO:dowhy.causal_graph:If this is observed data (not from a randomized experiment), there might always be missing confounders. Adding a node named \"Unobserved Confounders\" to reflect this.\n",
"INFO:dowhy.causal_model:Model to find the causal effect of treatment ['v0'] on outcome ['y']\n",
"WARNING:dowhy.causal_identifier:If this is observed data (not from a randomized experiment), there might always be missing confounders. Causal effect cannot be identified perfectly.\n",
"INFO:dowhy.causal_identifier:Continuing by ignoring these unobserved confounders because proceed_when_unidentifiable flag is True.\n",
"INFO:dowhy.causal_identifier:Instrumental variables for treatment and outcome:[]\n",
"INFO:dowhy.causal_identifier:Frontdoor variables for treatment and outcome:[]\n",
"INFO:dowhy.do_sampler:Using WeightingSampler for do sampling.\n",
"INFO:dowhy.do_sampler:Caution: do samplers assume iid data.\n"
]
},
{
"data": {
"text/plain": [
"<AxesSubplot:xlabel='v0'>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# data['df'] is just a regular pandas.DataFrame\n",
"df.causal.do(x=treatment,\n",
" variable_types={treatment: 'b', outcome: 'c', common_cause: 'c'},\n",
" outcome=outcome,\n",
" common_causes=[common_cause],\n",
" proceed_when_unidentifiable=True).groupby(treatment).mean().plot(y=outcome, kind='bar')"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING:dowhy.causal_model:Causal Graph not provided. DoWhy will construct a graph based on data inputs.\n",
"INFO:dowhy.causal_graph:If this is observed data (not from a randomized experiment), there might always be missing confounders. Adding a node named \"Unobserved Confounders\" to reflect this.\n",
"INFO:dowhy.causal_model:Model to find the causal effect of treatment ['v0'] on outcome ['y']\n",
"WARNING:dowhy.causal_identifier:If this is observed data (not from a randomized experiment), there might always be missing confounders. Causal effect cannot be identified perfectly.\n",
"INFO:dowhy.causal_identifier:Continuing by ignoring these unobserved confounders because proceed_when_unidentifiable flag is True.\n",
"INFO:dowhy.causal_identifier:Instrumental variables for treatment and outcome:[]\n",
"INFO:dowhy.causal_identifier:Frontdoor variables for treatment and outcome:[]\n",
"INFO:dowhy.do_sampler:Using WeightingSampler for do sampling.\n",
"INFO:dowhy.do_sampler:Caution: do samplers assume iid data.\n"
]
},
{
"data": {
"text/plain": [
"<AxesSubplot:xlabel='v0'>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"text/plain": [
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]
},
"metadata": {
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},
"output_type": "display_data"
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],
"source": [
"df.causal.do(x={treatment: 1}, \n",
" variable_types={treatment:'b', outcome: 'c', common_cause: 'c'}, \n",
" outcome=outcome,\n",
" method='weighting', \n",
" common_causes=[common_cause],\n",
" proceed_when_unidentifiable=True).groupby(treatment).mean().plot(y=outcome, kind='bar')"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:dowhy.causal_model:Model to find the causal effect of treatment ['v0'] on outcome ['y']\n",
"WARNING:dowhy.causal_identifier:If this is observed data (not from a randomized experiment), there might always be missing confounders. Causal effect cannot be identified perfectly.\n",
"INFO:dowhy.causal_identifier:Continuing by ignoring these unobserved confounders because proceed_when_unidentifiable flag is True.\n",
"INFO:dowhy.causal_identifier:Instrumental variables for treatment and outcome:[]\n",
"INFO:dowhy.causal_identifier:Frontdoor variables for treatment and outcome:[]\n",
"INFO:dowhy.do_sampler:Using WeightingSampler for do sampling.\n",
"INFO:dowhy.do_sampler:Caution: do samplers assume iid data.\n",
"INFO:dowhy.causal_model:Model to find the causal effect of treatment ['v0'] on outcome ['y']\n",
"WARNING:dowhy.causal_identifier:If this is observed data (not from a randomized experiment), there might always be missing confounders. Causal effect cannot be identified perfectly.\n",
"INFO:dowhy.causal_identifier:Continuing by ignoring these unobserved confounders because proceed_when_unidentifiable flag is True.\n",
"INFO:dowhy.causal_identifier:Instrumental variables for treatment and outcome:[]\n",
"INFO:dowhy.causal_identifier:Frontdoor variables for treatment and outcome:[]\n",
"INFO:dowhy.do_sampler:Using WeightingSampler for do sampling.\n",
"INFO:dowhy.do_sampler:Caution: do samplers assume iid data.\n"
]
}
],
"source": [
"cdf_1 = df.causal.do(x={treatment: 1}, \n",
" variable_types={treatment: 'b', outcome: 'c', common_cause: 'c'}, \n",
" outcome=outcome, \n",
" dot_graph=data['dot_graph'],\n",
" proceed_when_unidentifiable=True)\n",
"\n",
"cdf_0 = df.causal.do(x={treatment: 0}, \n",
" variable_types={treatment: 'b', outcome: 'c', common_cause: 'c'}, \n",
" outcome=outcome, \n",
" dot_graph=data['dot_graph'],\n",
" proceed_when_unidentifiable=True)\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"scrolled": true
},
"outputs": [
{
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"text/plain": [
" W0 v0 y propensity_score weight\n",
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"999 -1.636781 False -4.698411 0.966051 1.035142\n",
"\n",
"[1000 rows x 5 columns]"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cdf_0"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"scrolled": false
},
"outputs": [
{
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"text/plain": [
" W0 v0 y propensity_score weight\n",
"0 -2.094548 True 1.099802 0.013245 75.499593\n",
"1 -1.584775 True 1.996253 0.037724 26.508238\n",
"2 -2.287651 True -0.454571 0.008865 112.808679\n",
"3 -2.287651 True -0.454571 0.008865 112.808679\n",
"4 -0.427584 True 2.698249 0.308738 3.238989\n",
".. ... ... ... ... ...\n",
"995 1.803262 True 8.249998 0.979852 1.020562\n",
"996 -0.335329 True 4.826016 0.351590 2.844225\n",
"997 0.656759 True 8.514054 0.813633 1.229055\n",
"998 0.946281 True 5.565004 0.889192 1.124617\n",
"999 0.192547 True 3.447829 0.621941 1.607870\n",
"\n",
"[1000 rows x 5 columns]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cdf_1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Comparing the estimate to Linear Regression\n",
"First, estimating the effect using the causal data frame, and the 95% confidence interval."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAASCAYAAAAucYD2AAAHjUlEQVR4nO3be/BVVRUH8A9EoWlmYwXTTA9+pEVqmRZJCtFDGqUMLHuNpk1CTTqU5aOY0J81jVhJZM0UvcxHo1OkjSZZiIzI2MiU/DKyEgJBMCkhCBNM0f5Y+8w9nN8593Hu5b/7nbmz791nr/1Yj73XWvvcEYODg/roo4/uMLLF8zPwbPqc02Hf0/FbbMZurMfPMakF3TtxMx7Fk3gEv8EpJW1HYBbuxeP4L36PTxm+trNza6n67C0Z4wosw8NpHduxGpfisIo1dErzAXwbd+M/aS7XV/RdRCf8KqKOfJvRHJbqbsY6sfadWIlPqNa3h1TL5NEKmjpy6WQtZzeZ0zB9GdVkkJfjO0JBD25zYhmuwEXYhl/iMbwa78P78THlivI1XCiM75ZE9xIch6lYUmh/PT6Kf+IGPIGT8F28NY2TYQiXVcx3Mt6BX5c8Ox/3YWka5yAcj0HMTt8f7pLmS3iD4PVmvLZinkV0yq886si3Fc3pgvf/wHJswhichh/i5NTm2RLanVhYUv94xVzqyKWTtQzpQF+qDGkErhaGcBMuaDKhIsam9lvxerHIDG/Hnfiy4YY0SyjFNYIR/ys8f27h90xhRBswUSgRPA+/wJnCiG9K9UPpU4bfpfL7Jc8OwZ6S+q9iLr6IT3dJc74whnV4m1DCVuiUX3nUkW87NA/iVNyGZ3L1c7FKbKKnCfkUsUMYQbuoI5cM7axlSAf6UnXUzhEW93HhLnWCV6Z+77WvEREKskvsmnmMFgzYpFwp4KnC75mpvFLDiCTaeen7eW3M92ixe20RClBEmbDgZ6k8vAc0y7FW+U5dhjr8yqOOfNuhuRO32teICPfse+n71DbHa4U6csnQjX6X6kvZiTQB8/EtrEgDdoK1QrAT8WL7KvkUvECcFHmcJIxroRDCdBwlmLVKYwfIY2wq15c8y+omixOqTNEyzE7lj5THSFV4byrv3880ZajDrwx15NutTtAw7Kcrno8WMcsrhHLfn8bqRCa05nG3aynVl6IhjcJ1Yqeb2+EAGbbjYizAA8JotmG8OPaX4pMFmjenco8IGI8qPF8hAvJ/5eoyAx1XMoeBVI5K3/9aMdcDhfD2Ch++GS4QvvQL8SacKIQ1v8c07aAOv6gn317oxCiNePX2ijZj0zh5bBCnxl1N+u6Ex92upVJfioZ0Cd6YJrO7xkAZFopMzI+FL59hHX5iuMv30lReKIxvsvBPx+EbmCYyflNzNLfhI/gcbhQGTMQG+SDxRU3m+UEcmvpqFpgSAhuT+327yOwUlbVbmnZQh1/Uk28vdGK+MPYlIqNYxNUiY/ln4foPCLd8tgjoJ+GPFX13wuNu11KpL/kY6S3CSq/U3DVoBxdhsTCa8SKjcpxwuX4qsk1l83hanForRTblTyIW2iyC8Hzq/EYhlPFCmRaJ43pIKNam1K7or+eRHdOL2ljTWBGkjhUB84A4DY7tMU07qMOvOvLthU7MweeFV3BmRZvLRHy1VWRe14grjAXiFBhs0n+7PO7FWir1JRPIKFwrsi7zio06xFSR/r5FnBbrBXPuE0LeIhg7kKPZkcrV4iTL4wmNXWxirn6v8Ie/IHafs9JnrUh970rtiqdfhiNTu82ap4mL2CruSaaJ+4pr9xNNM+xIZbv8qiPfXujEeWJze0BkbLc3bz4MWYJiShttm/G4F2tpqi+ZIR2MI0Qgtse+l06XpjY/SL8XthjwPaksS+E+IYLhkeKIzfC3VO6o6PPfqTywUP+UMNqjcYA4dmcI5TpcxFEbKvqsm2TIsFEoyJEiqbK/aMrQKb/qyLdbnfisuGReI4yo6mK1GTL37KAOaMp43Av9bqovWYz0ZGpQhmOF0q8UAmx1LI5OZTHFrVCfz6QtE4t4nTCyojuWBdNVRlHEh0W27oaK5wcIN2Ov6nW3g5elshNDrENTRKf8qiPfbnTiYhEXDYkM42Pq4fhUlmVmm6HI4271u6W+ZIa0W/UrIoNpoGsMz2yNF8H93zXSm3drBIqLhCuX4WScIHaFe3L1G8X9w6n4DL6ZezYN7xa7bzHjc4h4pSaPY/B1sStXZcdOF0mIX2meZDhCuAw7C/Uj8RUR9N+jcQLUpekUnfKrjnzr6sQ8ceH+hzSXVu7cBBHPFu9zXiXePGD45X2nPK67lgwt9aXZK0LtYJm4gB2n4asvxh14F/6i8R7YBOH2jRBxzbZCX+eKBS0Q9yKrU78zxE5wjuGMWyqYtEbERBMS7W4RPz1SMe/smC57kyGPU3C52K02pDmPEYH8QFrXrB7QzEgfGvdjk0SyhtjRi7fvdfi1v3GWMKK9YkOdU9LmIY11wYdEzLxCbBC7xAY9XZwES0QmMo86PO4GLfWlW0MqwzNioecKF2smni92piW4SrzMWsRmkdm7ROy0U8Rpc6tg2qoSmsVpjDNEPLBFLPby1F8ZJoj0ZztJhjvEO4InCqU9VOycD4r7iKsM33Hr0BwjlDCPAY2EzEbDDakOv/Y3sju954gYqQx32deQluM1glcniHhohzCS69Kn+MZHHR7XRVv6MqL/N4o++ugerf5G0UcffbSBviH10UcP8H/9I7v0iWMPrQAAAABJRU5ErkJggg==\n",
"text/latex": [
"$\\displaystyle 4.869733164425347$"
],
"text/plain": [
"4.869733164425347"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(cdf_1['y'] - cdf_0['y']).mean()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
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"text/latex": [
"$\\displaystyle 0.18841744756332976$"
],
"text/plain": [
"0.18841744756332976"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1.96*(cdf_1['y'] - cdf_0['y']).std() / np.sqrt(len(df))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Comparing to the estimate from OLS."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"text/html": [
"<table class=\"simpletable\">\n",
"<caption>OLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>y</td> <th> R-squared (uncentered):</th> <td> 0.926</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>OLS</td> <th> Adj. R-squared (uncentered):</th> <td> 0.926</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 6276.</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Sat, 05 Dec 2020</td> <th> Prob (F-statistic):</th> <td> 0.00</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>18:02:18</td> <th> Log-Likelihood: </th> <td> -1436.6</td>\n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 1000</td> <th> AIC: </th> <td> 2877.</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 998</td> <th> BIC: </th> <td> 2887.</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 2</td> <th> </th> <td> </td> \n",
"</tr>\n",
"<tr>\n",
" <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[0.025</th> <th>0.975]</th> \n",
"</tr>\n",
"<tr>\n",
" <th>x1</th> <td> 1.8467</td> <td> 0.022</td> <td> 82.505</td> <td> 0.000</td> <td> 1.803</td> <td> 1.891</td>\n",
"</tr>\n",
"<tr>\n",
" <th>x2</th> <td> 5.0277</td> <td> 0.067</td> <td> 74.507</td> <td> 0.000</td> <td> 4.895</td> <td> 5.160</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <th>Omnibus:</th> <td> 0.268</td> <th> Durbin-Watson: </th> <td> 1.984</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Prob(Omnibus):</th> <td> 0.874</td> <th> Jarque-Bera (JB): </th> <td> 0.291</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Skew:</th> <td> 0.040</td> <th> Prob(JB): </th> <td> 0.864</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Kurtosis:</th> <td> 2.973</td> <th> Cond. No. </th> <td> 3.02</td>\n",
"</tr>\n",
"</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
],
"text/plain": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" OLS Regression Results \n",
"=======================================================================================\n",
"Dep. Variable: y R-squared (uncentered): 0.926\n",
"Model: OLS Adj. R-squared (uncentered): 0.926\n",
"Method: Least Squares F-statistic: 6276.\n",
"Date: Sat, 05 Dec 2020 Prob (F-statistic): 0.00\n",
"Time: 18:02:18 Log-Likelihood: -1436.6\n",
"No. Observations: 1000 AIC: 2877.\n",
"Df Residuals: 998 BIC: 2887.\n",
"Df Model: 2 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"x1 1.8467 0.022 82.505 0.000 1.803 1.891\n",
"x2 5.0277 0.067 74.507 0.000 4.895 5.160\n",
"==============================================================================\n",
"Omnibus: 0.268 Durbin-Watson: 1.984\n",
"Prob(Omnibus): 0.874 Jarque-Bera (JB): 0.291\n",
"Skew: 0.040 Prob(JB): 0.864\n",
"Kurtosis: 2.973 Cond. No. 3.02\n",
"==============================================================================\n",
"\n",
"Notes:\n",
"[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
"[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"\"\"\""
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model = OLS(np.asarray(df[outcome]), np.asarray(df[[common_cause, treatment]], dtype=np.float64))\n",
"result = model.fit()\n",
"result.summary()"
]
}
],
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