fonnesbeck/Dual Endpoints.ipynb

## Dual Endpoints.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "import pystan\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "np.random.seed(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x118957b00>"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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M/IEDB46YOySzkmWp0o+yJCYm0rVrVwBatmxJUlLSXff78MMPmTp1qslXPBM1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\nq9yYNn04FsvnxJzLwNfXiWnTh+Ph4c5fu7vj6bWe6t4qP66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0+qINxrEVWxZXz8ujHUJY\nHTYGT+8Y4i/58MhDIXaJoyAFxXTyRAJms8stz/WYTNfx9a2X81qbNrVZuewgFot1u/oNs2nZsjHO\nzs60b98iZ7ugwHUcOeQNQEKchdkfLOOzBW+W5McpcVr4f9a7byM+mh1LdpaRis7XCOzvb7O4Ll26\nhNlsxsfHp8D521q4NlpWHq6PdFmXsu+//55jx44RHBxMXFwcqampeHh45Ll9UlJaKUZXMHutuuLq\nWovuXb4nOfk6D/i7oSiKZlZ/uaEw18bLywW4DliLWPjUyMLBwSXXfn2f7sKpU5fYteM8zi46Ro95\nhtRUM6mpN7exWCxcupiZ81xRdJyPTdPcNbmVVlbseXXkc1T33sSxoxdo2ep+OnfuVOJxqarKpHc/\nYc2qi1gsCgFdXHl/2ghiY2OpXbv2batraeXaaJWWro8tvxjYapS11mgmIffr14+3336bgQMHotPp\nmD59unRXF5KiKLi5VbJ3GMXynxFBxMZ+QuSfl3AxOvD62J44Ozvn2kZRFMZPeBEm5H0cnU5Ho8bO\nxMdZB3spSjrNmuf9xU7k9vTTXWx6/F9++Y0V36VgNltX1dqwNoNtv47i+tV61K5rYsbMfjz8cEub\nxiDKHmkhlzJHR0f+97+ir3kpyjadTsf00LsoL5WPufNG8/7UxVxJzOT+Zh68PmZwiRxXFN/FC/Fk\nZztzs5e6AlevGNE7uBNzBj7+6EdJyOI2kpCFKKMqVarMrP+9bu8wxB107fYYixd9wOkT1kpgisMh\ndOrNOdRpqTKQTNxOErIQQpQwd/dqfPnVf/jyiw2oqkJqmg/hPziiWsDBIZV2HaVkpyi/JCELIUpV\nnTq1eH/aCMA6yMu/+WpOnEigcWM/nhtUssVOxL1BBnUJIYSNKYoiyzyKAqnl5E6GJGQhhBCaplqk\nhSyEEELYnQzqEkIIITSgvNxDlsobwi6uXk3i6tUke4chhBCaIS1kUapUVeWdt+ayITwOUOnV24ep\n014rsJ6xKJ60tDS2btlJ1WqVadv2AXuHI8RdkUFdQtjAunU/s2q5CYvFOt90xbJU2j7yC917PGnn\nyO5dSUlJPD94FtFR1XDQp9NvwO+Ezhht77CEKLTycg9ZuqxFqbp0MRGz+eYSitnZzly4kGDHiO59\nCz79nugoHxSlAhZzFb5fkciJEyfsHZYQhWZRlSI/yhJJyBqSkZHBD+vHE/HrM6xd/zLx8eftHVKJ\n69K1IzVqxeU89619ia7dOtkxontftplctwTM2XrS0tLtGJEQd0dVi/4oSyQha8jPEe/Rd8DPdOt9\ngsBBf7Lzj7ftHVKJq13bl/mfDeSZAfDMAJXPPh+Mr6+PvcO6p/Uf8Bg+vhcBUNVs2nUy07RpEztH\nJUThqapS5EdZIveQNaSCcwyOjjd/gIxusXaMxnaaNWvMzFmN7R1GueHnV59FS4fxw5ptuLg48tLQ\nETg4ONg7LCEKrax1PReVJGQNSU/1xmyOwsHB+sOXct3bzhGJe0X9+nUYN76OvcMQQuRDErKGBDwR\nwqrvMjG6niIt1Z2HHwi2d0iiHNm5Yzeh09eSdCWLps3cmPPRGJydne0dlhCoFhsdV1UJCQnh6NGj\nGAwGpk2bRs2aNXPe/+mnn/jiiy/Q6XT06NGDIUOG2CaQf0hC1hBnZ2f69vrI3mGIckhVVaaErObk\nMet0tIvnzcyYsYj33nvVzpEJYbtpTxEREZhMJsLCwoiKiiI0NJT58+cDYLFYmD17NqtXr6ZixYp0\n69aNXr16UblyZZvEApKQhRBAeno6CfE3h6QqigMJcZl2jEiIm2x1D3nPnj106NABAH9/f6Kjo3Pe\n0+l0bNy4EZ1OR2JiIqqq4ujoaJM4cs5p06MLIcoEZ2dnGvo5ov4zT0TRpXF/My87RyWEla2mPaWk\npODq6przXK/XY7Hc7B/X6XRs3ryZ3r178+CDD9r8Fo4kZCEEAHPnjaRHn0zadUxl5GhPXh35rL1D\nEgKwXWEQo9FIamrqzfNYLOh0udNiQEAAO3bswGQy8cMPP9jk890gXdZClFOXLycy7+NVmDIs9Ozz\nIG3btmbux+PsHZYQpaZVq1Zs3bqVLl26sH//fvz8/HLeS0lJYcSIESxcuBCDwUDFihVtXnNfErIQ\n5VBGRgYvvfDBPyU1FTZvXsf8BXoeeMDf3qEJcRtbVdwKCAhg586dBAUFARAaGkp4eDjp6ekEBgbS\nq1cvBg0ahKOjI40aNaJ37962CeQfkpCFKIcOHIjmYJQR3T/f+K9c9mTTxkhJyEKTbDXKWlEUpkyZ\nkuu1unXr5vw7MDCQwMBAm5z7TiQhC1EOeXpWo6JzOpnplQBrSU1XN9cC9hLCPixlrCZ1UcmgLiHK\noTp16jLslYa4up1H7xhHh8euMmLEAHuHJcQdlZfFJaSFLEQ59cYbQ3jhhUTS09Px9va5bXSpEFoh\ntayFEPe8qlWr2TsEIcQ/JCELUYbs3XOQOR+Gk5pqpl27mowdN6TQUzEuXYojPHwr1atXo3v3J20+\nhUOIklLWup6LShKyEGVEeno6E8aHceakdf3og/vjcPdYy5Dn+xS477FjJ3ll2FecPe2Ng0MMO347\nzIz/vm7rkIUoEeUlIctNIyHKiAsXznPm1M3v0GazC4cPXyjUvou+/plzZ6xzji0WZ9b/EE98fLyt\nQhWiRNmqUpfWaCYhq6pKcHAwQUFBDBkyhJiYGHuHJISmVK/ujW/N7JznipJBvXqFvAf8ryaGCjl1\nq4XQOrUYj7JEMwn51mWwxo0bR2hoqL1DEkJTXFxcmDqtFy1aJ9KwUTzPPV+B4S/3L9S+Q14IwLfW\nBVRVRdGl0b1HNby8ZPEIUTZY1KI/yhLN3EPObxksIYRVx04P0bHTQ3e93333NeSbZa/y44ZteHpW\noU/fLjaITghRHJpJyHktgyVzI4UoGTVr1uCV/wy0dxhC3DWVsnUvuKg0k5ALswyWEEKI8qesdT0X\nlWYScn7LYN1JlSrO6PUOpRRd4Xh4SC3gvMi1yZ9cn7zJtclfebg+5SQfaych32kZrPwkJaWVRliF\n5uHhSkJCsr3D0CS5NvmLjT3HmNFfcTkhm4aNnJn94Wu4urrZOyxNkJ+d/Gnp+tjyi4G0kEvZnZbB\nEuXHX7vXkXT1DyzmKjzx2OsYDAZ7h1Rq3hjzNft2ewBw7oyFqe99zcxZUrRDiBvKST7WTkIW5deu\n35fjU3cm7Z/IJjNTZcU3JxjQb4G9wyoVqqpy8UJmznNF0RF3KcOOEQkh7EVGTQm7S0nbjl8ja8EL\nJycFb98oMjLKR1JSFIWGfsacIh2qasKvUWU7RyWEtsg8ZCFKiclU0Vqw4p/FDlKSK5arLuuFX7/B\n6FGfcDnBROMmVXnzrRftHZIQmlLG8mqRSUIWdvdg67Es/+YEzVud4Py5SlR1G1Guprx5enrw8bxx\n9g5DCM2y2DuAUiIJWdidp2cNenZdSWzsOVre746bWyV7hyT+ZcdvkWwI343BCV4fM4CqVavaOyRR\njkgLWYhSkpmZyeRJn3H8WDJe1Q2ETHkRLy8Pe4cl/vHHH3sZM3oDSYkeqKpK1L7/sXxVME5OTvYO\nTZQT0kIWopRMCf6clcsUFKUKqqqSlrqAxUvftXdY4h8/b9pDUqL1C5KiKETtc+bwob9p2aqFnSMT\n4t4iCVnY3enTKSiKtRCGoiicOZ1u54jErYxuBlQ1HUWxVsZzdsnAw7OQyz4KUQLKy0qhkpCF3Xn7\nVEBVLSiKdSCXT43yM8K6LBg5MoiofTP4facZZ+dsXhzWBF/fmvYOS5QjtuqyVlWVkJAQjh49isFg\nYNq0adSsefNnOzw8nCVLlqDX6/Hz8yMkJMRGkVhJQhZ2N+W9oaSnfcrJk2l4eel57/0X7B2SuIWT\nkxNfL57EhQvncXFxoUoVGdAlSpetGsgRERGYTCbCwsKIiooiNDSU+fPnA9axLXPnziU8PByDwcC4\ncePYunUrjz32mI2ikYQsNMDV1Y1PF7xp7zBEPnQ6nbSKhd3YqoW8Z88eOnToAIC/vz/R0dE57xkM\nBsLCwnJqImRnZ9t8IKMkZCGEEJpmq4SckpKCq+vNRTH0en3O0r+KouRM71u6dCnp6ek88sgjNork\nn/Pb9OhCCCGERhmNRlJTU3Oe30jGN6iqysyZMzl79izz5s2zeTzlpxySEEKIMkktxiM/rVq1Ytu2\nbQDs378fPz+/XO9PmjSJrKws5s+fXyrlfKWFLIQQQtNs1WUdEBDAzp07CQoKAiA0NJTw8HDS09Np\n2rQpq1evpnXr1gwePBhFURgyZAhPPvmkjaKRhCyEEELjVBuNs1YUhSlTpuR6rW7dujn/Pnz4sE3O\nmxdJyEIIITRNSmcKIYQQGlBOCnXJoC4hhBBCC6SFLIQQQtOky1oIIYTQAFUpH53W0mUtRBkRExPD\nb9t3kZKSYu9QhChVlmI8yhJpIQtRBny18Hs+/GA/KckuNGi4gfkLhtKwYT17hyVEqShribWopIUs\nhMaZzWa++jKStJTq6BRXTp3w4ZN56+wdlhClRi3Gf2WJJGQhNM5sNpORmfs1U2bZ+kMjhCiYJGQh\nNM5gMNCxowdgzcpG10S6dfe3b1BClCK5hyyE0Iz/zR5L4yariI9LpkOnznTs+JC9QxKi1JS1ruei\nkoQsRBmg0+kY/nJ/e4chhF2UtZZuUUlCFkIIoWmqYu8ISockZCGEEJpmKSdd1jKoSwghhNAAzbSQ\nO3bsSJ06dQBo2bIlY8eOtW9AQgghNEHuIZeic+fO0bRpUz799FN7hyKEEEJjyssoa010WUdHRxMX\nF8eQIUN45ZVXOH36tL1DEkIIoREyD9lGVq1axeLFi3O9FhwczCuvvELnzp3Zs2cPEyZMYNWqVaUd\nmhBCCA0qL4O6FFVV7f5JMzIycHBwwNHREYBOnTqxbdu2fPfJzjaj1zuURnhCCCHsqId+SZH3Dc8e\nUoKR2JYm7iHPmzePypUrM2zYMI4cOYK3t3eB+yQlpZVCZIXn4eFKQkKyvcPQJLk2+ZPrkze5NvnT\n0vXx8HC1dwhlniYS8ssvv8yECRPYtm0ber2e0NBQe4ckhBBCI8pLl7UmErKbmxsLFiywdxhCCCE0\nyFajrFVVJSQkhKNHj2IwGJg2bRo1a9bMtU16ejovvfQS06dPp27dujaJ4wZNjLIWQggh8mKrUdYR\nERGYTCbCwsIYN27cbb2z0dHRDBo0iJiYmJL8OHmShCyEEELTLKhFfuRnz549dOjQAQB/f3+io6Nz\nvZ+VlcX8+fOpV6+ezT7brTTRZS2EEELkxVZ3kFNSUnB1vTkYTa/XY7FY0OmsbdWWLVtaz19Kk5Gk\nhSyEEKJcMhqNpKam5jy/NRnbgyRkIYQQmmZR1CI/8tOqVaucmhf79+/Hz8+vND5OnqTLWgghhKbZ\natpTQEAAO3fuJCgoCIDQ0FDCw8NJT08nMDAwZztFKZ0FmSUhCyGE0DRb3cFVFIUpU6bkeu1OU5uW\nLCl6pbC7IQlZCCGEpklhECGEEEIDyktClkFdQgghhAZIC1kIIYSmlbV1jYtKErIQQghNs1Uta62R\nhCyEEELTyss9ZEnIQgghNK2gAh/3CknIQgghNK283EOWUdZCCCGEBkgLWQghhKbJPWQhhBBCA2SU\ntRBCCKEB0kIWQgghNEASshBCCKEB5SUhyyhrIYQQQgOkhSyEEELTyksLWRKyEEIITbMo9o6gdEhC\nFkIIoWnSQhZCCCE0QBKyEEIIoQHmcpKQZZS1EEIIoQHSQhZCCKFp0mUthBBCaEB5Sch267LevHkz\n48aNy3keFRVF//79GThwIPPmzbNXWEIIITTGrFiK/MiPqqoEBwcTFBTEkCFDiImJyfX+li1b6Nev\nH0FBQaxcudKWHxGwU0KeNm0aH374Ya7XgoODmT17Nt999x0HDhzgyJEj9ghNCCGExphRi/zIT0RE\nBCaTibCwMMaNG0doaGjOe9nZ2cyYMYNFixaxdOlSli9fzpUrV2z6Oe2SkFu1akVISEjO85SUFLKy\nsvD19QWgffv27Nq1yx6hCSGE0BhbJeQ9e/bQoUMHAPz9/YmOjs557+TJk9SuXRuj0YijoyOtW7cm\nMjLSpp/TpveQV61axeLFi3O9FhoaSteuXfnrr79yXktNTcVoNOY8d3FxITY21pahCSGEKOdSUlJw\ndXXNea7X67FYLOh0utvec3FxITk52abx2DQh9+vXj379+hW4nYuLCykpKTnPU1NTcXNzy3cfDw/X\nfN+3By3GpBVybfIn1ydvcm3yVx6uT1LGmzY5rtFoJDU1Nef5jWR84727zUvFpYl5yEajEYPBQExM\nDKqqsmPHDlq3bm3vsIQQQtzDWrVqxbZt2wDYv38/fn5+Oe/Vr1+fs2fPcv36dUwmE5GRkbRo0cKm\n8Whm2tOUKVMYP348FouFdu3a0bx5c3uHJIQQ4h4WEBDAzp07CQoKAqy3VMPDw0lPTycwMJC3336b\nl156CVVVCQwMxNPT06bxKKqqlo8JXkIIIYSGaaLLWgghhCjvJCELIYQQGiAJWQghhNAASchCCCGE\nBkhCFkIIITRAErIQQgihAZKQhRBCCA2QhCyEEEJowP8DNI+uKfFJX58AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119ddc0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 200\n",
    "treat = np.r_[np.ones(int(n/2)), np.zeros(int(n/2))]\n",
    "x = np.random.normal(100, 15, size=n)\n",
    "y1 = 5*(treat==1) + 0.1*x + np.random.normal(0, 5, size=n)\n",
    "data = pd.DataFrame(dict(x=x, y1=y1, treat=treat))\n",
    "data.plot.scatter('x', 'y1', c='treat', cmap='plasma')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "L2 = 0.7 * (treat == 1) + .05 * (x - 100)\n",
    "y2 = (np.random.rand(n) <= 1 / (1 + np.exp(-L2))).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>y1</td>        <th>  R-squared:         </th> <td>   0.220</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.212</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   27.74</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 02 Jun 2016</td> <th>  Prob (F-statistic):</th> <td>2.43e-11</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:50:56</td>     <th>  Log-Likelihood:    </th> <td> -612.35</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   200</td>      <th>  AIC:               </th> <td>   1231.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   197</td>      <th>  BIC:               </th> <td>   1241.</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>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>    1.7556</td> <td>    2.812</td> <td>    0.624</td> <td> 0.533</td> <td>   -3.790     7.302</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x</th>         <td>    0.0818</td> <td>    0.027</td> <td>    3.029</td> <td> 0.003</td> <td>    0.029     0.135</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>treat</th>     <td>    5.1258</td> <td>    0.738</td> <td>    6.949</td> <td> 0.000</td> <td>    3.671     6.580</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.216</td> <th>  Durbin-Watson:     </th> <td>   2.083</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.898</td> <th>  Jarque-Bera (JB):  </th> <td>   0.108</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.055</td> <th>  Prob(JB):          </th> <td>   0.948</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.030</td> <th>  Cond. No.          </th> <td>    784.</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                     y1   R-squared:                       0.220\n",
       "Model:                            OLS   Adj. R-squared:                  0.212\n",
       "Method:                 Least Squares   F-statistic:                     27.74\n",
       "Date:                Thu, 02 Jun 2016   Prob (F-statistic):           2.43e-11\n",
       "Time:                        13:50:56   Log-Likelihood:                -612.35\n",
       "No. Observations:                 200   AIC:                             1231.\n",
       "Df Residuals:                     197   BIC:                             1241.\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      1.7556      2.812      0.624      0.533        -3.790     7.302\n",
       "x              0.0818      0.027      3.029      0.003         0.029     0.135\n",
       "treat          5.1258      0.738      6.949      0.000         3.671     6.580\n",
       "==============================================================================\n",
       "Omnibus:                        0.216   Durbin-Watson:                   2.083\n",
       "Prob(Omnibus):                  0.898   Jarque-Bera (JB):                0.108\n",
       "Skew:                           0.055   Prob(JB):                        0.948\n",
       "Kurtosis:                       3.030   Cond. No.                         784.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit1 = smf.ols(formula='y1 ~ x + treat', data=data).fit()\n",
    "fit1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Generalized Linear Model Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>y2</td>        <th>  No. Observations:  </th>  <td>   200</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                 <td>GLM</td>       <th>  Df Residuals:      </th>  <td>   197</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model Family:</th>       <td>Binomial</td>     <th>  Df Model:          </th>  <td>     2</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Link Function:</th>        <td>logit</td>      <th>  Scale:             </th>    <td>1.0</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>IRLS</td>       <th>  Log-Likelihood:    </th> <td> -122.91</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>           <td>Thu, 02 Jun 2016</td> <th>  Deviance:          </th> <td>  245.83</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>               <td>13:50:58</td>     <th>  Pearson chi2:      </th>  <td>  200.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Iterations:</th>         <td>6</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>z</th>      <th>P>|z|</th> <th>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   -4.7577</td> <td>    1.274</td> <td>   -3.733</td> <td> 0.000</td> <td>   -7.255    -2.260</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x</th>         <td>    0.0482</td> <td>    0.012</td> <td>    3.908</td> <td> 0.000</td> <td>    0.024     0.072</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>treat</th>     <td>    0.7157</td> <td>    0.310</td> <td>    2.308</td> <td> 0.021</td> <td>    0.108     1.324</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                 Generalized Linear Model Regression Results                  \n",
       "==============================================================================\n",
       "Dep. Variable:                     y2   No. Observations:                  200\n",
       "Model:                            GLM   Df Residuals:                      197\n",
       "Model Family:                Binomial   Df Model:                            2\n",
       "Link Function:                  logit   Scale:                             1.0\n",
       "Method:                          IRLS   Log-Likelihood:                -122.91\n",
       "Date:                Thu, 02 Jun 2016   Deviance:                       245.83\n",
       "Time:                        13:50:58   Pearson chi2:                     200.\n",
       "No. Iterations:                     6                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     -4.7577      1.274     -3.733      0.000        -7.255    -2.260\n",
       "x              0.0482      0.012      3.908      0.000         0.024     0.072\n",
       "treat          0.7157      0.310      2.308      0.021         0.108     1.324\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit2 = smf.glm(formula='y2 ~ x + treat', data=data, family=sm.families.Binomial()).fit()\n",
    "fit2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Specify Stan model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = \"\"\"\n",
    "data {\n",
    "    int n;\n",
    "    vector[n] x;\n",
    "    real y1[n];\n",
    "    int y2[n];\n",
    "    vector[n] treat;\n",
    "    vector<lower=0>[2] sigma_b;\n",
    "    vector[2] Zero;\n",
    "}\n",
    "\n",
    "parameters {\n",
    "    vector[2] alpha;\n",
    "    vector[2] beta;\n",
    "    vector[2] mu;\n",
    "    real<lower=0> sigma;\n",
    "    corr_matrix[2] Omega_b; \n",
    "}\n",
    "\n",
    "\n",
    "transformed parameters {\n",
    "    vector[n] theta1;\n",
    "    vector[n] theta2;\n",
    "    cov_matrix[2] Sigma; \n",
    "    \n",
    "    Sigma <- quad_form_diag(Omega_b, sigma_b); \n",
    "    \n",
    "    theta1 <- mu[1] + alpha[1]*x + beta[1]*treat;\n",
    "    theta2 <- mu[2] + alpha[2]*x + beta[2]*treat;\n",
    "}\n",
    "\n",
    "model {\n",
    "    beta ~ multi_normal(Zero, Sigma); \n",
    "    Omega_b ~ lkj_corr(1);\n",
    "\n",
    "    sigma ~ cauchy(0, 5);\n",
    "    \n",
    "    y1 ~ normal(theta1, sigma);\n",
    "    y2 ~ bernoulli_logit(theta2);\n",
    "}\n",
    "\n",
    "generated quantities {\n",
    "    real A;\n",
    "    real B;\n",
    "    real A_or_B;\n",
    "    real A_and_B;\n",
    "\n",
    "    A <- if_else(beta[1] > 2, 1, 0);\n",
    "    B <- if_else(exp(beta[2]) > 1.25, 1, 0);\n",
    "    \n",
    "    A_or_B <- if_else(A || B, 1, 0);\n",
    "    A_and_B <- if_else(A && B, 1, 0);\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "fit = pystan.stan(model_code=model, \n",
    "                  data=dict(x=x, y1=y1, y2=y2, treat=treat, n=n, sigma_b=(2, 1.5), Zero=(0,0)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.40912301,  0.72588719])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit['beta'].mean(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.1757017242076957"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(fit['beta'][:,1]).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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rg9FoxLe//W1YrVZs2LBB7WYRQmQkaw9/+/btiEajaGlpwb59+7Bx40Y888wz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119b32e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit.plot(pars=['beta']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Probability of A or B being true is essentially one, while the probability of both is 65%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sample = fit.extract(pars=['A_or_B', 'A_and_B'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0, 0.94825000000000004]"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[sample[s].mean(0) for s in sample]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Correlation between betas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.16257258],\n",
       "       [ 0.16257258,  1.        ]])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit['Omega_b'].mean(0)"
   ]
  }
 ],
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