3.7 - Mediation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "    <div style=\"width: 150px; float: left;\"> <img src=\"https://raw.githubusercontent.com/DataForScience/Networks/master/data/D4Sci_logo_ball.png\" alt=\"Data For Science, Inc\" align=\"left\" border=\"0\" width=150px> </div>\n",
    "    <div style=\"float: left; margin-left: 10px;\"> <h1>Causal Inference In Statistics - A Primer</h1>\n",
    "        <h1>3.7 Mediation</h1>\n",
    "        <p>Bruno Gonçalves<br/>\n",
    "        <a href=\"http://www.data4sci.com/\">www.data4sci.com</a><br/>\n",
    "            @bgoncalves, @data4sci</p></div>\n",
    "    <div style=\"float: right; margin-right:10px;\"> <p><a href=\"https://amzn.to/3gsFlkO\" target=_blank><img src='data/causality.jpeg' width='100px'>\n",
    "        <!--Amazon Affiliate Link--></a></p></div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "from pprint import pprint\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt \n",
    "\n",
    "from CausalModel import CausalModel\n",
    "\n",
    "import watermark\n",
    "\n",
    "%load_ext watermark\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by print out the versions of the libraries we're using for future reference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.8.5\n",
      "IPython version      : 7.19.0\n",
      "\n",
      "Compiler    : Clang 10.0.0 \n",
      "OS          : Darwin\n",
      "Release     : 20.3.0\n",
      "Machine     : x86_64\n",
      "Processor   : i386\n",
      "CPU cores   : 16\n",
      "Architecture: 64bit\n",
      "\n",
      "Git hash: c41ed8befecf49059999a81adcec3b026fe5d326\n",
      "\n",
      "json      : 2.0.9\n",
      "watermark : 2.1.0\n",
      "pandas    : 1.1.3\n",
      "numpy     : 1.19.2\n",
      "matplotlib: 3.3.2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%watermark -n -v -m -g -iv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load default figure style"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('./d4sci.mplstyle')\n",
    "colors = plt.rcParams['axes.prop_cycle'].by_key()['color']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We build the DAG from Fig 3.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = CausalModel()\n",
    "G.add_causation('X', 'Y')\n",
    "G.add_causation('X', 'Z')\n",
    "G.add_causation('Z', 'Y')\n",
    "\n",
    "G.pos = {'X': (0, 0), 'Z': (1, 1), 'Y': (2, 0)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 660x660 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, figsize=(2.2,2.2))\n",
    "G.plot(ax=ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "G.save_model('dags/Primer.Fig.3.11.dot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the DAG from Fig 3.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = CausalModel()\n",
    "G.add_causation('X', 'Y')\n",
    "G.add_causation('X', 'Z')\n",
    "G.add_causation('Z', 'Y')\n",
    "G.add_causation('I', 'Y')\n",
    "G.add_causation('I', 'Z')\n",
    "\n",
    "G.pos = {'X': (0, 0), 'Z': (1, 1), 'Y': (2, 0), 'I': (2, 1)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 660x660 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, figsize=(2.2,2.2))\n",
    "G.plot(ax=ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "G.save_model('dags/Primer.Fig.3.12.dot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can easily compute the modified graph resulting from intervening on X and Z:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 660x660 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G2 = G.intervention_graph(['X', 'Z'])\n",
    "fig, ax = plt.subplots(1, figsize=(2.2,2.2))\n",
    "G2.plot(ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "     <img src=\"data/D4Sci_logo_full.png\" alt=\"Data For Science, Inc\" align=\"center\" border=\"0\" width=300px> \n",
    "</div>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  },
  "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
}