02 - DoWhy + EconML - Process example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# !pip install dowhy==0.6\n",
    "# !pip install econml==0.12.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import combinations\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import dowhy\n",
    "from dowhy import CausalModel\n",
    "import dowhy.datasets\n",
    "\n",
    "from sklearn.linear_model import LassoCV\n",
    "from sklearn.ensemble import GradientBoostingRegressor\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('fivethirtyeight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Causal Inference in Python: An Introduction\n",
    "\n",
    "\n",
    "Causality was an *enfant terrible* of the big data and statistical learning revolution of the early 2010s. Many people believed (myself included) that having large enough datasets and efficient learning algorithms is sufficient and we do not need the concept of causality at all. Today, causal inference, modeling and discovery is being used more and more broadly across areas – from medical research and neuroscience to marketing and fraud detection. This talk briefly introduces main causal concepts and two Python libraries – DoWhy and EconML – for performing causal inference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Causal model with DoWhy & EconML"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate a dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create the dataset\n",
    "W = np.random.randn(1000)\n",
    "T = np.random.randn(1000) + .2*W + 3\n",
    "Y = 6*T + 2*W - 13\n",
    "\n",
    "df = pd.DataFrame(np.vstack([W, T, Y]).T, columns=['W', 'T', 'Y'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>W</th>\n",
       "      <th>T</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.942210</td>\n",
       "      <td>3.477641</td>\n",
       "      <td>11.750268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.883608</td>\n",
       "      <td>2.938262</td>\n",
       "      <td>2.862357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.053140</td>\n",
       "      <td>3.736973</td>\n",
       "      <td>9.528121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.107874</td>\n",
       "      <td>2.669720</td>\n",
       "      <td>2.802575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.568881</td>\n",
       "      <td>3.355904</td>\n",
       "      <td>3.997663</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "          W         T          Y\n",
       "0  1.942210  3.477641  11.750268\n",
       "1 -0.883608  2.938262   2.862357\n",
       "2  0.053140  3.736973   9.528121\n",
       "3 -0.107874  2.669720   2.802575\n",
       "4 -1.568881  3.355904   3.997663"
      ]
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     "execution_count": 5,
     "metadata": {},
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   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(3, 3))\n",
    "plt.scatter(df['T'], df['Y'], alpha=.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stage 1: Model the problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Stage 1.1 - Define the graph - `GML`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create the graph describing the causal structure\n",
    "\n",
    "graph = \"\"\"\n",
    "graph [\n",
    "    directed 1\n",
    "    \n",
    "    node [\n",
    "        id \"T\" \n",
    "        label \"T\"\n",
    "    ]    \n",
    "    node [\n",
    "        id \"W\"\n",
    "        label \"W\"\n",
    "    ]\n",
    "    node [\n",
    "        id \"Y\"\n",
    "        label \"Y\"\n",
    "    ]\n",
    "    \n",
    "    edge [\n",
    "        source \"W\"\n",
    "        target \"T\"\n",
    "    ]\n",
    "    \n",
    "    edge [\n",
    "        source \"W\"\n",
    "        target \"Y\"\n",
    "    ]\n",
    "    \n",
    "    edge [\n",
    "        source \"T\"\n",
    "        target \"Y\"\n",
    "    ]\n",
    "]\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Remove newlines\n",
    "graph = graph.replace('\\n', '')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Stage 1.2 - define the DoWhy model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# With graph\n",
    "model = CausalModel(\n",
    "    data=df,\n",
    "    treatment='T',\n",
    "    outcome='Y',\n",
    "    graph=graph\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(3, 3))\n",
    "model.view_model()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stage 2: Identify the estimand"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimand type: nonparametric-ate\n",
      "\n",
      "### Estimand : 1\n",
      "Estimand name: backdoor\n",
      "Estimand expression:\n",
      " d                    \n",
      "────(Expectation(Y|W))\n",
      "d[T]                  \n",
      "Estimand assumption 1, Unconfoundedness: If U→{T} and U→Y then P(Y|T,W,U) = P(Y|T,W)\n",
      "\n",
      "### Estimand : 2\n",
      "Estimand name: iv\n",
      "No such variable found!\n",
      "\n",
      "### Estimand : 3\n",
      "Estimand name: frontdoor\n",
      "No such variable found!\n",
      "\n"
     ]
    }
   ],
   "source": [
    "estimand = model.identify_effect(proceed_when_unidentifiable=True)\n",
    "print(estimand)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stage 3: Estimate the causal effect"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 1 - Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimate of causal effect (linear regression): 5.999999999999999\n"
     ]
    }
   ],
   "source": [
    "estimate = model.estimate_effect(\n",
    "    identified_estimand=estimand,\n",
    "    method_name='backdoor.linear_regression'\n",
    ")\n",
    "\n",
    "print(f'Estimate of causal effect (linear regression): {estimate.value}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 3 - Double Machne Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimate of causal effect (DML): 5.980371965222086\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n"
     ]
    }
   ],
   "source": [
    "estimate = model.estimate_effect(\n",
    "    identified_estimand=estimand,\n",
    "    method_name='backdoor.econml.dml.DML',\n",
    "    method_params={\n",
    "        'init_params': {\n",
    "            'model_y': GradientBoostingRegressor(),\n",
    "            'model_t': GradientBoostingRegressor(),\n",
    "            'model_final': LassoCV(fit_intercept=False),\n",
    "        },\n",
    "        'fit_params': {}}\n",
    ")\n",
    "\n",
    "print(f'Estimate of causal effect (DML): {estimate.value}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stage 4: Run refutation tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n"
     ]
    }
   ],
   "source": [
    "refute_results = model.refute_estimate(\n",
    "    estimand=estimand, \n",
    "    estimate=estimate,\n",
    "    method_name='placebo_treatment_refuter'\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Refute: Use a Placebo Treatment\n",
      "Estimated effect:5.980371965222086\n",
      "New effect:0.0\n",
      "p value:1.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(refute_results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n"
     ]
    }
   ],
   "source": [
    "refute_results = model.refute_estimate(\n",
    "    estimand=estimand, \n",
    "    estimate=estimate,\n",
    "    method_name='random_common_cause'\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Refute: Add a Random Common Cause\n",
      "Estimated effect:5.980371965222086\n",
      "New effect:5.952338153271622\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(refute_results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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