risk.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Risk assessment\n",
    "\n",
    "This notebook presents an exploration of different ways to assess the risk of recidivism based on a risk score.\n",
    "\n",
    "Copyright 2015 Allen Downey\n",
    "\n",
    "MIT License: http://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import thinkbayes2\n",
    "import thinkplot\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Read the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>score</th>\n",
       "      <th>10-yr recidivate</th>\n",
       "      <th>recid</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   score  10-yr recidivate  recid\n",
       "0     -2                 0      0\n",
       "1     -2                 0      0\n",
       "2     -1                 0      0\n",
       "3     -1                 0      0\n",
       "4     -1                 0      0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_excel('helmus10yrfixed.xlsx')\n",
    "df['recid'] = df['10-yr recidivate']\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last row of the table is the total, so we have to drop it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>score</th>\n",
       "      <th>10-yr recidivate</th>\n",
       "      <th>recid</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>699</th>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>700</th>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>701</th>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>702</th>\n",
       "      <td>11</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>703</th>\n",
       "      <td>NaN</td>\n",
       "      <td>204</td>\n",
       "      <td>204</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     score  10-yr recidivate  recid\n",
       "699     10                 1      1\n",
       "700     10                 1      1\n",
       "701     10                 1      1\n",
       "702     11                 0      0\n",
       "703    NaN               204    204"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Done."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>score</th>\n",
       "      <th>10-yr recidivate</th>\n",
       "      <th>recid</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>698</th>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>699</th>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>700</th>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>701</th>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>702</th>\n",
       "      <td>11</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     score  10-yr recidivate  recid\n",
       "698     10                 1      1\n",
       "699     10                 1      1\n",
       "700     10                 1      1\n",
       "701     10                 1      1\n",
       "702     11                 0      0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.dropna()\n",
    "df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###Logistic regression\n",
    "\n",
    "Start with a logistic regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>recid</td>      <th>  No. Observations:  </th>  <td>   703</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>               <td>Logit</td>      <th>  Df Residuals:      </th>  <td>   701</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>MLE</td>       <th>  Df Model:          </th>  <td>     1</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Fri, 13 Nov 2015</td> <th>  Pseudo R-squ.:     </th>  <td>0.03919</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>09:56:23</td>     <th>  Log-Likelihood:    </th> <td> -406.84</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>           <td>True</td>       <th>  LL-Null:           </th> <td> -423.43</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th> </th>                      <td> </td>        <th>  LLR p-value:       </th> <td>8.371e-09</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>   -1.8129</td> <td>    0.194</td> <td>   -9.335</td> <td> 0.000</td> <td>   -2.194    -1.432</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>score</th>     <td>    0.2048</td> <td>    0.037</td> <td>    5.534</td> <td> 0.000</td> <td>    0.132     0.277</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:                  recid   No. Observations:                  703\n",
       "Model:                          Logit   Df Residuals:                      701\n",
       "Method:                           MLE   Df Model:                            1\n",
       "Date:                Fri, 13 Nov 2015   Pseudo R-squ.:                 0.03919\n",
       "Time:                        09:56:23   Log-Likelihood:                -406.84\n",
       "converged:                       True   LL-Null:                       -423.43\n",
       "                                        LLR p-value:                 8.371e-09\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     -1.8129      0.194     -9.335      0.000        -2.194    -1.432\n",
       "score          0.2048      0.037      5.534      0.000         0.132     0.277\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "formula = 'recid ~ score'\n",
    "model = smf.logit(formula, data=df)\n",
    "results = model.fit(disp=False)\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the model to predict probabilities for each score:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores = range(-3, 13)\n",
    "scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3 0.0811230553353\n",
      "-2 0.0977539746983\n",
      "-1 0.117358915927\n",
      "0 0.140284367251\n",
      "1 0.166841660229\n",
      "2 0.197272884005\n",
      "3 0.231710970071\n",
      "4 0.270137790771\n",
      "5 0.312346491893\n",
      "6 0.357916109828\n",
      "7 0.406206803608\n",
      "8 0.456381885955\n",
      "9 0.507458085398\n",
      "10 0.558379071389\n",
      "11 0.608101233976\n",
      "12 0.655677299314\n"
     ]
    }
   ],
   "source": [
    "def make_predictions(results, scores):\n",
    "    columns = ['score']\n",
    "    new = pd.DataFrame(scores, columns=columns)\n",
    "    return results.predict(new)\n",
    "\n",
    "ps = make_predictions(results, scores)\n",
    "for score, p in zip(scores, ps):\n",
    "    print(score, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's what that looks like graphically:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6ttaHniISEYV6GXF3ln+9kakzFjBtxkK+3bS1yH4N6h/PRee3ocf5bTil4Yll\nXKWIxDuFeilb981mps1YyNQZC1i15rsi+5xwfHW6dW1Nj66tadmsgfZfEZGjplCPspycXL5YtpaP\n5ixj1uylrFy1sch+1apV5oLOZ9Lj/Da0OaORFgeJSFQo1KNg1+69zJ63nJmfZvHx3C+L3EAL8p4g\n1KXTafQ4vzUd2zWjYkX97xeR6FKqHKX1G7fkhficZcxb9DU52TlF9kuumExq26ZclNaG8zqeRuVj\nKpVxpSJSnkQU6mbWExgOJAHPu/sjhc63BF4E2gL3ufvfo11o0HJyclmUtZpZs/OGVVavLXp8HOC4\nWtU4t0MLzuvYkrPbnKqnB4lImSk21M0sCXgK6A6sB+aY2QR3z8rXbTNwEzCgVKoMyI6de/h03lfM\nmr2UT+Z+yfYduw/bt3nT+nTu0JJzO7SgZbMG2tZWRAIRyZ16KrDc3VcBmNlooD8QDnV33wRsMrNL\nSqPIsrR63aa8Dzk/XcqCJavIzTl0eT5ApUoVaX/WqXRObck57ZtT50TNIxeR4EUS6g2AtfmO1wEd\nS6ecsrf5hx18vuhrPl+4krkLV7Ju/feH7XvC8dXpnNqSczu0pH2bJhyj8XERiTGRhLoX3yUyGRkZ\n4a/T0tJIS0uL1ltHbOu2Xcxf/DWfLVzJvIUrDzt3/Ectm51E59QWdE5tSfNT62sOuYiUqszMTDIz\nM4/69eZ+5Mw2s05Ahrv3DB3fA+QW/rA0dG4osLOoD0rNzIu7VmnYvmM38xevYt6ivBBf8XXR88Z/\nlJJSiQ5tTw3dkbfghOP0pCARCY6Z4e4R301Gcqc+F2hmZo2ADcBgIP1w14/0wqVl56694RD/fNFK\nvlzxzSFPBcovKTmJM1o0pF2rxrRr3YQzW55MSkrFMqxYRCR6ir1TBzCzXhyc0jjS3YeZ2Q0A7j7C\nzOoCc4DqQC6wAzjd3Xfme49SuVPftXsvC5esYd7CvBBfunxDkXuP/ygpOYnTmjWgXesmtG3VhFan\nnay54yISs0p6px5RqEdDNEN97oIVzJ2/gnkLV5L11brDzlCBvGd1ntasAW1bNaZtqya0OeMUzRsX\nkbhRGsMvMefZf08m68t1RZ80o/mp9WjXqgntWjfhrDMbUbXKMWVboIhIQOIy1Nu1blIg1Js2qUe7\n1k1o16oxbc5oRPVqVQKsTkQkOHEZ6ud1PI29+w7QLjSkUqO6QlxEBOJ0TF1EpLwo6Zi6NigREUkg\nCnURkQRrumXWAAAFVklEQVSiUBcRSSAKdRGRBKJQFxFJIAp1EZEEolAXEUkgCnURkQSiUBcRSSAK\ndRGRBKJQFxFJIAp1EZEEolAXEUkgCnURkQSiUBcRSSAKdRGRBKJQFxFJIAp1EZEEUmyom1lPM1tq\nZl+Z2V2H6fNk6PwCM2sb/TJFRCQSRwx1M0sCngJ6AqcD6WZ2WqE+vYGm7t4MuB54ppRqLROZmZlB\nlxAR1Rk98VAjqM5oi5c6S6q4O/VUYLm7r3L3A8BooH+hPv2AlwDc/VOgppnViXqlZSRe/qJVZ/TE\nQ42gOqMtXuosqeJCvQGwNt/xulBbcX1O+umliYhISRUX6h7h+9hRvk5ERKLI3A+fv2bWCchw956h\n43uAXHd/JF+fZ4FMdx8dOl4KnO/u3xZ6LwW9iMhRcPfCN86HlVzM+blAMzNrBGwABgPphfpMAIYA\no0M/BLYWDvSSFiUiIkfniKHu7tlmNgSYDCQBI909y8xuCJ0f4e4Tzay3mS0HdgG/KvWqRUSkSEcc\nfhERkfhS5itKzew2M8s1s+PK+tqRMLO/mVlWaCHVG2ZWI+ia8otkMVjQzKyhmU03sy/MbLGZ3Rx0\nTUdiZklm9rmZvR10LYdjZjXNbGzoe3NJaKgz5pjZPaG/90Vm9qqZpcRATS+Y2bdmtihf23FmNtXM\nvjSzKWZWM8gaQzUVVWeJ86hMQ93MGgI9gNVled0SmgKc4e5tgC+BewKuJyySxWAx4gBwq7ufAXQC\nfh+jdf7oD8ASYnvW1hPARHc/DWgNZAVczyFCn71dB7Rz91bkDdleEWRNIS+S928mv7uBqe7eHHg/\ndBy0ouoscR6V9Z36P4A7y/iaJeLuU909N3T4KbE15z6SxWCBc/eN7j4/9PVO8gKofrBVFc3MTgJ6\nA89z6NTcmBC6O+vi7i9A3mdd7r4t4LKKsp28H+hVzCwZqAKsD7YkcPf/AT8Uag4vmgz9d0CZFlWE\nouo8mjwqs1A3s/7AOndfWFbXjIJrgYlBF5FPJIvBYkro7q0ted+Qsehx4A4gt7iOAWoMbDKzF81s\nnpn9y8yqBF1UYe6+Bfg7sIa82XJb3X1asFUdVp18s/S+BeJhFXxEeRTVUA+NUS0q4k8/8n5tGJq/\nezSvXRJHqLNvvj73Afvd/dWg6ixCLA8PHMLMjgXGAn8I3bHHFDPrA3zn7p8To3fpIclAO+Bpd29H\n3iyzWBguKMDMTgVuARqR95vZsWb280CLioDnzRaJ6X9bJcmj4uapl4i79zhMQWeSd7exwMwg71eI\nz8ws1d2/i2YNkThcnT8ys1+S9yt5tzIpKHLrgYb5jhuSd7cec8ysIjAO+K+7jw+6nsM4F+gX2pTu\nGKC6mb3s7r8IuK7C1pH3W+6c0PFYYjDUgfbAR+6+GcDM3iDv//ErgVZVtG/NrK67bzSzekCZ51Ck\nSppHZTL84u6L3b2Ouzd298bkfZO2CyLQi2NmPcn7dby/u+8Nup5CwovBzKwSeYvBJgRc0yEs7yf3\nSGCJuw8Pup7Dcfd73b1h6HvyCuCDGAx03H0jsNbMmoeaugNfBFjS4SwFOplZ5dD3QHfyPoCORROA\na0JfXwPE5I3H0eRRUA/JiOVfdf4JHAtMDU1zezrogn7k7tnkrd6dTN4/ljHuHnOzIIDOwFXABaH/\nh5+HvjljXSx/X94EvGJmC8ib/fKXgOs5hLsvAF4m7+bjx8/OnguuojxmNgr4CGhhZmvN7FfAX4Ee\nZvYlcGHoOFBF1HktR5FHWnwkIpJA9Dg7EZEEolAXEUkgCnURkQSiUBcRSSAKdRGRBKJQFxFJIAp1\nEZEEolAXEUkg/x+fY6gWIEjbFgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79eb3fb090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Plot(scores, ps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Equivalently, we could get the fitted values from the results, which are in the form of log-odds, and convert to probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0.097754\n",
       "1    0.097754\n",
       "2    0.117359\n",
       "3    0.117359\n",
       "4    0.117359\n",
       "dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "odds = np.exp(results.fittedvalues)\n",
    "ps = odds / (1 + odds)\n",
    "ps.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To show confidence intervals on the estimated probabilities, we could transform the confidence intervals on the estimated parameters, but I prefer to do it by resampling.\n",
    "\n",
    "Here's a simple version that plots 200 estimated lines to show uncertainty visually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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w67WF64kzAlapG4aRYK3Iou7q7PV63lIB4KvxKIr8BhR6wwvOXQEQ23aOdgvf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\nInokpR4R0SMp9YiIHvkND9xL0x6MzJQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79eb671310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_regression_lines(df, scores):\n",
    "    columns = ['score']\n",
    "    new = pd.DataFrame(scores, columns=columns)\n",
    "\n",
    "    formula = 'recid ~ score'\n",
    "\n",
    "    for i in range(200):\n",
    "        sample = df.sample(len(df), replace=True)\n",
    "        model = smf.logit(formula, data=sample)\n",
    "        results = model.fit(disp=False)\n",
    "        ps = results.predict(new)\n",
    "        thinkplot.Plot(scores, ps, color='gray', alpha=0.05)\n",
    "        \n",
    "plot_regression_lines(df, scores)\n",
    "\n",
    "ps = make_predictions(results, scores)\n",
    "thinkplot.Plot(scores, ps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a more complicated version that plots the median of the resampled estimates in each column, and a 95% confidence interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/downey/anaconda/lib/python2.7/site-packages/matplotlib/axes/_axes.py:475: UserWarning: No labelled objects found. Use label='...' kwarg on individual plots.\n",
      "  warnings.warn(\"No labelled objects found. \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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EPht9/supfrYxW8nI7Ah97r64TU3NzmZanC0pv0cwHOSV7ld4ve/1uPGbmm7i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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79e5556690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def run_regressions(df, scores, iters=1000, formula='recid ~ score', color='gray'):\n",
    "    columns = ['score']\n",
    "    new = pd.DataFrame(scores, columns=columns)\n",
    "    new['score2'] = new.score**2\n",
    "    \n",
    "    array = np.zeros((iters, len(scores)))\n",
    "\n",
    "    for i in range(iters):\n",
    "        sample = df.sample(len(df), replace=True)\n",
    "        model = smf.logit(formula, data=sample)\n",
    "        results = model.fit(disp=False)\n",
    "        ps = results.predict(new)\n",
    "        array[i,] = ps\n",
    "\n",
    "    array = np.sort(array, axis=0)    \n",
    "    percents = [2.5, 50, 97.5]\n",
    "    rows = [thinkbayes2.PercentileRow(array, p) for p in percents]\n",
    "    return rows\n",
    "    \n",
    "def plot_regressions(df, iters=1000, formula='recid ~ score', color='gray'):\n",
    "    scores = range(-3, 13)\n",
    "    rows = run_regressions(df, scores, iters, formula, color)\n",
    "    thinkplot.Plot(scores, rows[0], color=color, alpha=0.2)\n",
    "    thinkplot.Plot(scores, rows[1], color=color, alpha=0.5)\n",
    "    thinkplot.Plot(scores, rows[2], color=color, alpha=0.2)\n",
    "    \n",
    "plot_regressions(df, iters=1000, color='green')\n",
    "thinkplot.Config(xlabel='score', ylabel='10 year prob of recidivism', xlim=[-4, 13])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian logistic regression\n",
    "\n",
    "This turns out not to be particularly useful, so feel free to skip it.\n",
    "\n",
    "An alternative is Bayesian regression.  To demonstrate how it works, I'll use the parameters estimated by logistic regression to compute the likelihood of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.20475163024127738, -1.8129301177982706)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "slope, inter = (results.params['score'], results.params['Intercept'])\n",
    "slope, inter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the parameters to compute log-odds, convert to probabilities, then compute the probability of each actual outcome."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0.902246\n",
       "1    0.902246\n",
       "2    0.882641\n",
       "3    0.882641\n",
       "4    0.882641\n",
       "dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_odds = df.score * slope + inter\n",
    "odds = np.exp(log_odds)\n",
    "ps = odds / (1 + odds)\n",
    "likes = ps * df.recid + (1-ps) * (1-df.recid)\n",
    "likes.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The product of these likelihoods is the likelihood of the data.  The log-likelihood we get is the same as the output of the logistic regression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-406.83547329540573, -406.83547329540579)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(np.prod(likes)), results.llf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now here's a Bayesian suite that computes this likelihood function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class BLogit(thinkbayes2.Suite, thinkbayes2.Joint):\n",
    "    \n",
    "    def Likelihood(self, df, hypo):\n",
    "        \"\"\"The likelihood of the data under the hypothesis.\n",
    "        \n",
    "        df: DataFrame with score and recid\n",
    "        hypo: slope, intercept pair\n",
    "        \n",
    "        returns: float\n",
    "        \"\"\"\n",
    "        slope, inter = hypo\n",
    "        log_odds = df.score * slope + inter\n",
    "        odds = np.exp(log_odds)\n",
    "        ps = odds / (1 + odds)\n",
    "        likes = ps * df.recid + (1-ps) * (1-df.recid)\n",
    "        like = np.prod(likes)\n",
    "        return like"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can confirm again that it yields the same likelihood, given the parameters estimated by logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-406.83547329540573, -406.83547329540579)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hypo = (slope, inter)\n",
    "blogit = BLogit()\n",
    "like = blogit.Likelihood(df, hypo)\n",
    "np.log(like), results.llf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can generate the Bayesian estimate of the parameters by generating a suite of hypothesis and computing the likelihood of the data under each.\n",
    "\n",
    "I'll start with a uniform distribution for both parameters (using the confidence intervals from logistic regression to choose the bounds)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "hypos = [(slope, inter) for slope in np.linspace(0, 0.4, 101)\n",
    "                        for inter in np.linspace(-3, 0, 101)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialize the suite:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "blogit = BLogit(hypos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And update with the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-410.95822860613788"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "like = blogit.Update(df)\n",
    "np.log(like)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The marginal distribution of the slope parameter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.13600000000000001, 0.28000000000000003)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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38SkpzGXBvEJOn+vBN6zUt3Sydslsr8MySaquro66urqEXzdWcmgDql371fhr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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79e584e310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_slope = blogit.Marginal(0)\n",
    "thinkplot.Pdf(pmf_slope)\n",
    "pmf_slope.CredibleInterval(95)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And for the intercept parameter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.2199999999999998, -1.4399999999999999)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gT8q+XSnb29O89qFp106mbd+Fq1zuHwagua6azau01k4+bFzaxLy6aq4NjXK5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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79e5b1f210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_inter = blogit.Marginal(1)\n",
    "thinkplot.Pdf(pmf_inter)\n",
    "pmf_inter.CredibleInterval(95)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's the joint distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/downey/anaconda/lib/python2.7/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  if self._edgecolors == str('face'):\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79e5a05f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Contour(blogit, pcolor=True, contour=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the posterior distribution of the parameters, we can generate a predictive distribution of probability for each score:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_predictive(blogit, score):\n",
    "    pmf = thinkbayes2.Pmf()\n",
    "    for (slope, inter), prob in blogit.Items():\n",
    "        x = score * slope + inter\n",
    "        o = np.exp(x)\n",
    "        p = o / (1+o)\n",
    "        pmf[p] = prob\n",
    "    return pmf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the posterior predictive distributions look like for a range of scores."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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J40xJPSsX5qCU4uGTbybtNyO59/Ts75P2dZRvN34gAlMQxn0FRsdn8Km/fJDb53E7VZ2D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\nu0AgEBQgwrgLBAJBASKMu0AgEBQg/x/uJAV2E2ELFAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79e56c6550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scores = [-1, 1, 3, 5, 7, 9, 11]\n",
    "thinkplot.PrePlot(len(scores))\n",
    "for score in scores:\n",
    "    pmf = make_predictive(blogit, score)\n",
    "    thinkplot.Cdf(pmf.MakeCdf())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also plot the results with a line plot and 95% credible intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cdfs = [make_predictive(blogit, score).MakeCdf() for score in scores]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extracting the medians and credible intervals from the posterior predictive distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "medians = np.array([cdf.Percentile(50) for cdf in cdfs])\n",
    "cis = np.array([cdf.CredibleInterval(95) for cdf in cdfs])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's what they look like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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e/vHAC8CVwN+4+z/HO+ilVFWH+LSsCIBefVIYN6ZfXYmPGdlbJzdFpF2JWepm\nlgosBG4ByoBNZrbG3QujhlUAfwrMapGUDRgyqDtjhmXTq3tf/vkH/ejYMeF/+RARabbGTGOnAsXu\nvtfdq4GlwMzoAe5+1N03A9UtkLFBZsaYYdn06z1IhS4i7V5jSn0oUBK1XRp5TURE2pjGlLrHHiIi\nIm1BY45XlAGZUduZhGfrTbYgau1ebm4uubm5zXkbEZGklZeXR15eXrO/39wbnoibWRqwA7gZOABs\nBObVO1H6+dgFwOmLrX4xM4/1Wc2VyM8oFRFpiJnh7o1eix1zpu7uNWb2BLCe8JLG59290Mwei+xf\nZGaDgE1AD6DWzL4HTHD3ymb9vxARkWZp1HIRd18HrKv32qKorw9x4SEaEREJgK7MERFJIip1EZEk\nolIXEUkiMVe/xO2DWnD1i4hIsmrq6hfN1EVEkohKXUQkiajURUSSiEpdRCSJqNRFRJKISl1EJImo\n1EVEkohKXUQkiajURUSSiEpdRCSJqNRFRJKISl1EJImo1EVEkohKXUQkiajURUSSSMxSN7PpZlZk\nZrvM7C8vMeb/RfZvMbMr4x9TREQao8FSN7NUYCEwHZgAzDOzK+qNuQMY4+5ZwB8BP2qhrIHKy8sL\nOsJlSeT8iZwdlD9oiZ6/qWLN1KcCxe6+192rgaXAzHpj7gJ+CuDuHwC9zGxg3JMGLNF/MBI5fyJn\nB+UPWqLnb6pYpT4UKInaLo28FmtMxuVHExGRpopV6o19qGj95+fpYaQiIgFo8MHTZnYNsMDdp0e2\nnwRq3f3pqDH/CeS5+9LIdhFwo7sfrvdeKnoRkWZoyoOn02Ls3wxkmdkI4AAwB5hXb8wa4AlgaeQf\ngRP1C72poUREpHkaLHV3rzGzJ4D1QCrwvLsXmtljkf2L3H2tmd1hZsXAGeA7LZ5aREQuqsHDLyIi\nklha9YpSM/snMyuMXKS0ysx6tubnN0djLr5qq8ws08zeNrPtZrbNzP570Jmaw8xSzexjM3s96CxN\nZWa9zGxF5Oe+IHKIMmGY2ZORn598M3vZzDoGnelSzOzHZnbYzPKjXutjZm+a2U4z+5WZ9QoyY0Mu\nkb/Jndnatwn4FZDt7pOBncCTrfz5TdKYi6/auGrgf7p7NnAN8HiC5f/c94ACEnNV1b8Ba939CiAH\nKAw4T6NFzqV9F7jK3ScRPgQ7N8hMMbxA+L/VaH8FvOnuY4FfR7bbqovlb3Jntmqpu/ub7l4b2fyA\ntr+evTG51gGMAAACn0lEQVQXX7VZ7n7I3T+JfF1JuFCGBJuqacwsA7gDWMyXl862aZFZ1dfc/ccQ\nPkfl7icDjtUUpwhPDLqYWRrQBSgLNtKlufvvgOP1Xq67ODLyv7NaNVQTXCx/czozyBt6/QGwNsDP\nb4zGXHyVECKzrisJ/2Akkn8F/hyojTWwDRoJHDWzF8zsIzN7zsy6BB2qsdz9GPDPwH7Cq99OuPtb\nwaZqsoFRq/EOA4l8tXujOjPupR45fpV/kT93Ro35G6DK3V+O9+fHWSL+uv8lZtYNWAF8LzJjTwhm\n9i3giLt/TILN0iPSgKuA/3D3qwivDmvLv/5fwMxGA/8DGEH4N7xuZvZAoKEug4dXhSTkf9NN6cxY\n69SbzN1vbWi/mX2b8K/TN8f7s1tAGZAZtZ1JeLaeMMysA7ASeNHdfx50nia6DrgrctO4TkAPM/uZ\nuz8ccK7GKgVK3X1TZHsFCVTqwNXABnevADCzVYT/Tl4KNFXTHDazQe5+yMwGA0eCDtRUTe3M1l79\nMp3wr9Iz3f2z1vzsZqq7+MrM0glffLUm4EyNZmYGPA8UuPszQedpKnf/a3fPdPeRhE/Q/SaBCh13\nPwSUmNnYyEu3ANsDjNRURcA1ZtY58rN0C+ET1olkDfBI5OtHgISa2DSnM1t1nbqZ7QLSgWORl95z\n9z9ptQDNYGbfBJ7hi4uv/jHgSI1mZjcAvwW28sWvnU+6+xvBpWoeM7sR+N/uflfQWZrCzCYTPsmb\nDuwGvpNIJ0vN7C8Il2Et8BHwaGTRQJtjZq8ANwL9CB8//ztgNbAMGAbsBe539xNBZWzIRfJ/n/Bq\nlyZ1pi4+EhFJInqcnYhIElGpi4gkEZW6iEgSUamLiCQRlbqISBJRqYuIJBGVuohIElGpi4gkkf8P\nh8fNnIBIZLQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79f9865fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_bayesian_regression(scores, medians, cis):\n",
    "    for score, (low, high) in zip(scores, cis):\n",
    "        plt.vlines(score, low, high, color='blue', alpha=0.5, linewidth=2)\n",
    "    thinkplot.PrePlot(1)\n",
    "    thinkplot.plot(scores, medians, linewidth=2)\n",
    "\n",
    "scores = [-1, 1, 3, 5, 7, 9, 11]\n",
    "plot_bayesian_regression(scores, medians, cis)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we superimpose the lines from the logistic regression, we can compare them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gzPQVj8eJRqPEYrFBdXIYf/3+lAiwh61bi0/v3LE7ys+fChBPCK0t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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79e7bb0d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_regressions(df)\n",
    "\n",
    "scores = [-1, 1, 3, 5, 7, 9, 11]\n",
    "plot_bayesian_regression(scores, medians, cis)\n",
    "thinkplot.Config(xlabel='score', ylabel='10 year prob of recidivism', xlim=[-4, 13])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Bayesian and logistic regressions agree about the median values.  And the credible intervals for the Bayesian regression are the same as the confidence intervals for the logistic regression.\n",
    "\n",
    "So if you don't have an informative prior, and all you want is the median of the posterior distribution and a measure of precision, the Bayesian method has no real advantage."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###Categorical\n",
    "\n",
    "Next we can explore another way to estimate risk for each group.  This one turns out to be bad, so feel free to skip it.\n",
    "\n",
    "If we treat score as a categorical variable, we can estimate risk for each score separately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.0 2\n",
      "-1.0 24\n",
      "0.0 31\n",
      "1.0 56\n",
      "2.0 42\n",
      "3.0 82\n",
      "4.0 130\n",
      "5.0 133\n",
      "6.0 83\n",
      "7.0 61\n",
      "8.0 32\n",
      "9.0 17\n",
      "10.0 9\n",
      "11.0 1\n"
     ]
    }
   ],
   "source": [
    "grouped = df.groupby('score')\n",
    "for name, group in grouped:\n",
    "    print(name, len(group))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'll use a Beta distribution for each group."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def MakeBeta(group):\n",
    "    yes = sum(group.recid == 1)\n",
    "    no = sum(group.recid==0)\n",
    "    beta = thinkbayes2.Beta(yes+1, no+1)\n",
    "    return beta\n",
    "\n",
    "betas = {}\n",
    "for name, group in grouped:\n",
    "    betas[name] = MakeBeta(group)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then extract the median and 95% credible interval from each posterior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rows=[]\n",
    "for name, beta in sorted(betas.items()):\n",
    "    cdf = beta.MakeCdf()\n",
    "    low = cdf.Percentile(2.5)\n",
    "    mean = beta.Mean()\n",
    "    high = cdf.Percentile(97.5)\n",
    "    rows.append((low, mean, high))\n",
    "    \n",
    "array = np.array(rows).transpose()\n",
    "scores = sorted(betas)\n",
    "lows = array[0,]\n",
    "means = array[1,]\n",
    "highs = array[2,]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is kind of a mess, with credible intervals much wider than the CIs from logistic regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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yjnOd2Xz4/UYO6r2/e4m2Dt+EvstsJR3hDyulnoq/idXmH575oNFopoWBgQE6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\nzrmU+T/rC6EBvWeUXgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79e58ee5d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_regressions(df)\n",
    "\n",
    "for score, low, high in zip(scores, lows, highs):\n",
    "        plt.vlines(score, low, high, color='blue', alpha=0.5, linewidth=2)\n",
    "        \n",
    "thinkplot.PrePlot(1)\n",
    "thinkplot.plot(scores, means, linewidth=2)\n",
    "thinkplot.Config(xlabel='score', ylabel='10 year prob of recidivism', xlim=[-4, 13])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Logistic regression with a quadratic model\n",
    "\n",
    "One last option to consider is a quadratic model of risk.\n",
    "\n",
    "Here the linear model again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>recid</td>      <th>  No. Observations:  </th>  <td>   703</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>               <td>Logit</td>      <th>  Df Residuals:      </th>  <td>   701</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>MLE</td>       <th>  Df Model:          </th>  <td>     1</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Fri, 13 Nov 2015</td> <th>  Pseudo R-squ.:     </th>  <td>0.03919</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>09:56:55</td>     <th>  Log-Likelihood:    </th> <td> -406.84</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>           <td>True</td>       <th>  LL-Null:           </th> <td> -423.43</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th> </th>                      <td> </td>        <th>  LLR p-value:       </th> <td>8.371e-09</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>   -1.8129</td> <td>    0.194</td> <td>   -9.335</td> <td> 0.000</td> <td>   -2.194    -1.432</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>score</th>     <td>    0.2048</td> <td>    0.037</td> <td>    5.534</td> <td> 0.000</td> <td>    0.132     0.277</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:                  recid   No. Observations:                  703\n",
       "Model:                          Logit   Df Residuals:                      701\n",
       "Method:                           MLE   Df Model:                            1\n",
       "Date:                Fri, 13 Nov 2015   Pseudo R-squ.:                 0.03919\n",
       "Time:                        09:56:55   Log-Likelihood:                -406.84\n",
       "converged:                       True   LL-Null:                       -423.43\n",
       "                                        LLR p-value:                 8.371e-09\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     -1.8129      0.194     -9.335      0.000        -2.194    -1.432\n",
       "score          0.2048      0.037      5.534      0.000         0.132     0.277\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "formula = 'recid ~ score'\n",
    "model = smf.logit(formula, data=df)\n",
    "results = model.fit(disp=False)\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's the quadratic version."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>recid</td>      <th>  No. Observations:  </th>  <td>   703</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>               <td>Logit</td>      <th>  Df Residuals:      </th>  <td>   700</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>MLE</td>       <th>  Df Model:          </th>  <td>     2</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Fri, 13 Nov 2015</td> <th>  Pseudo R-squ.:     </th>  <td>0.04235</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>09:56:55</td>     <th>  Log-Likelihood:    </th> <td> -405.49</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>           <td>True</td>       <th>  LL-Null:           </th> <td> -423.43</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th> </th>                      <td> </td>        <th>  LLR p-value:       </th> <td>1.626e-08</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>   -2.1210</td> <td>    0.288</td> <td>   -7.354</td> <td> 0.000</td> <td>   -2.686    -1.556</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>score</th>     <td>    0.3820</td> <td>    0.119</td> <td>    3.209</td> <td> 0.001</td> <td>    0.149     0.615</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>score2</th>    <td>   -0.0193</td> <td>    0.012</td> <td>   -1.601</td> <td> 0.109</td> <td>   -0.043     0.004</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:                  recid   No. Observations:                  703\n",
       "Model:                          Logit   Df Residuals:                      700\n",
       "Method:                           MLE   Df Model:                            2\n",
       "Date:                Fri, 13 Nov 2015   Pseudo R-squ.:                 0.04235\n",
       "Time:                        09:56:55   Log-Likelihood:                -405.49\n",
       "converged:                       True   LL-Null:                       -423.43\n",
       "                                        LLR p-value:                 1.626e-08\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     -2.1210      0.288     -7.354      0.000        -2.686    -1.556\n",
       "score          0.3820      0.119      3.209      0.001         0.149     0.615\n",
       "score2        -0.0193      0.012     -1.601      0.109        -0.043     0.004\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['score2'] = df.score**2\n",
    "\n",
    "formula = 'recid ~ score + score2'\n",
    "model = smf.logit(formula, data=df)\n",
    "results = model.fit(disp=False)\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The square term is not significant.\n",
    "\n",
    "Also if we plot the predictions of the two models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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dDAK7XC7GxsZwOp0ope8u6mI/jH5r6wm+w+EgEAjg9XqN4G8hvQj/d5VSnwP+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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79e7bb9610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_regressions(df, formula='recid ~ score')\n",
    "plot_regressions(df, formula='recid ~ score + score2', color='blue')\n",
    "thinkplot.Config(xlabel='score', ylabel='10 year prob of recidivism', xlim=[-4, 13])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The quadratic model is getting pulled down by the low recidivism rates in the highest groups, which are based on small sample sizes.  So this model is likely overfit to the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###PTPP\n",
    "\n",
    "Another approach is to pose a different question: if we choose a threshold on the score, and consider a score at or above the threshold to be a \"positive test\", and recidivism to be a \"condition of interest\", what can we say about the specificity, sensitivity, and post-test probabilities?\n",
    "\n",
    "I'll run an example with a threshold of 6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "testpos = df.score >= 6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the cross tabulation of test outcome and recidivism:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>recid</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>score</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>False</th>\n",
       "      <td>381</td>\n",
       "      <td>119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>118</td>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "recid    0    1\n",
       "score          \n",
       "False  381  119\n",
       "True   118   85"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tab = pd.crosstab(testpos, df.recid)\n",
    "tab"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sensitivity (fraction of recidivists the test detects)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.41666666666666669"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sens = tab[1][True] / sum(tab[1])\n",
    "sens"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Specificity (fraction of non-recidivists who test negative)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.76352705410821642"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spec = tab[0][False] / sum(tab[0])\n",
    "spec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Post-test probability of recidivism given positive test (PTPP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.41871921182266009"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ptpp = tab[1][True] / sum(testpos)\n",
    "ptpp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Post-test probability of non-recidivism given negative test (PTPN)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.76200000000000001"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ptpn = tab[0][False] / sum(testpos == False)\n",
    "ptpn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each of these quantities is a proportion estimated based on a ratio of frequencies, so if the prior distribution is Beta, the posterior distribution is also Beta.\n",
    "\n",
    "Following Crawford et al, I'll uses a prior distribution with $\\alpha = \\beta = 0$ (although I don't buy their justification for this choice)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def MakeBeta(yes, no, alpha=0, beta=0):\n",
    "    return thinkbayes2.Beta(yes+alpha, no+beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can make a posterior distribution for sensitivity, and confirm that the posterior mean is the same as the observed proportion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.41666666666666669"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sens_dist = MakeBeta(tab[1][True], tab[1][False])\n",
    "sens_dist.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And likewise for specificity:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.76352705410821642"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spec_dist = MakeBeta(tab[0][False], tab[0][True])\n",
    "spec_dist.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And PTPP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.41871921182266009"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ptpp_dist = MakeBeta(tab[1][True], tab[0][True])\n",
    "ptpp_dist.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the posterior distribution looks like for PTPP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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q6YuEFPqSKoW+SLYU+pKqtGfvwMjQ1/COdDqFvqTGPfsxffX0pdMp9CU1774LZ88G7UmT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\nFxHpIAp9EZEOotAXEekgCn0RkQ7y/wFOoX29VaTzdgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79e573e610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pdf(ptpp_dist.MakePmf())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's the symmetric 95% credible interval.  There is a 95% chance that the actual value falls in this interval (subject to the validity of the data as a representative sample)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.35185214,  0.48710358])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "symm_ci = ptpp_dist.Percentile([2.5, 97.5])\n",
    "symm_ci"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the 95th percentile, which could be consider a sort of upper bound."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.47600745])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "low_ci = ptpp_dist.Percentile([0, 95])\n",
    "low_ci"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the 5th percentile, a sort of lower bound."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.36234389,  1.        ])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "high_ci = ptpp_dist.Percentile([5, 100])\n",
    "high_ci"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'll wrap this process up in a function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.41871921182266009, [0.3518521419235516, 0.48710358239969676])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def estimate_ptpp(df, thresh):\n",
    "    testpos = df.score >= thresh\n",
    "    tab = pd.crosstab(testpos, df.recid)\n",
    "    ptpp_dist = MakeBeta(tab[1][True], tab[0][True])\n",
    "    est = ptpp_dist.Mean()\n",
    "    ci = ptpp_dist.Percentile([2.5, 97.5])\n",
    "    return est, ci.tolist()\n",
    "\n",
    "estimate_ptpp(df, 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now we can try it out with difference choices for the threshold:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2 (0.29018492176386912, [0.257238685423252, 0.32426188788597143])\n",
      "-1 (0.29101283880171186, [0.25799004591947694, 0.32516511391927216])\n",
      "0 (0.2983751846381093, [0.2645132327072705, 0.33336546689622504])\n",
      "1 (0.30804953560371517, [0.27305246225166213, 0.3441723583875195])\n",
      "2 (0.32881355932203388, [0.29150490164753645, 0.36722150461892855])\n",
      "3 (0.32846715328467152, [0.289792273616399, 0.36832796975593507])\n",
      "4 (0.33905579399141633, [0.2967986471722945, 0.3826214938883786])\n",
      "5 (0.36904761904761907, [0.31830277635205195, 0.4212691852755268])\n",
      "6 (0.41871921182266009, [0.3518521419235516, 0.48710358239969676])\n",
      "7 (0.44166666666666665, [0.3542685323315231, 0.5309072169144622])\n",
      "8 (0.40677966101694918, [0.2859632642550582, 0.5335854545353503])\n",
      "9 (0.44444444444444442, [0.26587121742295106, 0.6308196190760335])\n",
      "10 (0.40000000000000002, [0.1369956622651665, 0.7007049437914596])\n"
     ]
    }
   ],
   "source": [
    "for thresh in range(-2, 11):\n",
    "    print(thresh, estimate_ptpp(df, thresh))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the goal is to chose the threshold that maximizes PTPP, 7 is the best choice.\n",
    "\n",
    "In that case we could say that of all people who score 7 or more, 44% of them will be charged with a new crime within 10 years (that's the definition of recidivism the data are based on).\n",
    "\n",
    "But within that group, people with different scores have different probabilities of recidivism.  From the logistic regression model\n",
    "\n",
    "    score     prob\n",
    "    7         0.406206803608\n",
    "    8         0.456381885955\n",
    "    9         0.507458085398\n",
    "    10        0.558379071389\n",
    "    11        0.608101233976\n",
    "    \n",
    "So lumping everone above 6 into a single category might be generous to the 11s and harsh to the 7s.\n",
    "\n",
    "If the goal of the analysis is to estimate the probability of recidivism for an individual, the logistic regression model is an appropriate choice.\n",
    "\n",
    "If the goal is to choose a threshold and compute some of the consequences of applying that threshold, the PTPP analysis is appropriate.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZYGURdGhoiImJCdu7eW5GPp8vB/zKc3tFBLfbjd/v75rfTmwL/CLiAD4J3A/MAc+JyBPG\nmOmaW79pjHmfXeNQSrVOvUPRfT5f8WD01qjXXE1EOHToEHfddVfXLeAWCgVisRjJZLIq4APlgG/X\nbuXNsnM0p4FZY8wlABF5HHgQqA383fW3qJSqq96h6IFAoKULq4lEgjNnztQsFg9yzz2nWvrm0gqF\nQoF4PE4ikVgV8AcHB/H7/V17uIudgf8AcLXi8TXgvpp7DPA2EXkZ67eCf2GMOWPjmJRSm1B7Pi5A\nMBjE6/W25PWNMdy4cYPZ2dmq2nzYAxwnEOieGXOhUCCRSJBIJGrGapWxBgKBrt9LYOefpln/Fl4E\nxowxSRF5N/B54Hi9Gx+uKDKenJxkcnKyBUNUSq0nl8sRDoerDkUPBoMt22jUqDZ/fHycqalRuiUp\nUJrhJ5PJVQHf6XQSCAQ6vvYwNTXF1NTUuvfZGfjngLGKx2NYs/4yY0ys4usnReRTIjJsjAlT4+Gt\n7C5RSm1KvfNxh4aGWnZyVb3afK/Xy6lTp1r228RW5fP58gy/NqXjdDrx+Xxdc5JX7aT4kUceqXuf\nnYH/eWBcRA4B14EPAg9V3iAie4HbxhgjIqcBqRf0lVLtZ+f5uMYYrly5wqVLl6qCaTfV5ufz+fIM\nv9sD/kbZFviNMTkR+SjwFFY556eNMdMi8pHi848C/wj4ZRHJAUngQ3aNRynVPDuPSkyn00xPT7O0\ntFS+1k21+esFfL/fXzzNa/uydcXEGPMk8GTNtUcrvv4T4E/sHINSO00reuusxc6jEhcWFpiZmamq\nDAoGg0xMTHQ8mOZyOeLx+Ko6fLAWbX0+X8fH2Crds1SulOq42gNUWnVqVqO++XfffTeHDh3qaG3+\negHf7/d3fNG21TTwK6WA+geoDA8PbznoN+qbPzExQSgU2tJrb0WptcLy8vKqgO9yufD5fDsu4Jdo\n4FdKAQmWlqr74bTi1Kxbt25x7ty5qsNGRkZGOHnyZAc3N2VZXIyv6qUDVsD3+/1dX4e/VRr4lep5\nseKHpRUHqOTzec6dO8etW7fK10SEo0ePdqxvvrWuEAOWqY35g4OD+Hy+HR/wSzTwK9XDotEo0OoD\nVGI8//yZqhm12+3m1KlTth8pWE+jbpnQ/a0V7KKBX6keZIxhaWmpKhi6XC6Ghzd/gIqVJ58DXiOV\nWsmZj46OMj4+3vba/LXKMt1uNz6fr+cCfokGfqV6TL0Om+BmeHho00E/k8kwMzMDrOy/dDgcHD9+\nnL17925twBu0VvM066AYP6FQbwb8Eg38SvWQes3WwAsE2WzaPRwOMzMzU/VG4vf7mZiYaMvB4SXG\nmHLAr+2lU1q0hd7I4a9HA79SPSKbzRIOh6sqbKxWx5trq1woFLh48SJXr16teWaMe+453LZTpowx\nJJNJYrFY3W6ZO7EOf6s08CvVA9LpNIuLi1V9d7bSbK1RbT6cBIZpRcwPh+H8eejrg0QC6vVsKwX8\nyjcz2DmtFeyigV+pHa52Y1ZfXx8+3zAXLw5w5gw89xz4fDA/D+u1yjHGcPPmTWZnZ6uC7fDwMCdP\nnuRv/3brqZR4HL75TXjhBZibs6598pPwYz8Gb3oTiFg7jGOxWE3Kytp/4Pf7t23ztHbRwK/UDhaL\nxYjFrBr95WW4fNnFjRtDXLzooNQuJ5GwPj71KTh1Cn7kR2DPntWvlcvlOHfuHLdv3y5fa2Vt/vIy\nfPvb8PTTUNHKB4BUCr7wBXj++Sxvf3uEQCBT9bzD4cDn8+HxeLruaMZupIFfqR3IGEMkEmFhIclr\nr/Vz/ryTq1cHGBhwN8y9GwPf/771UXoDKBXkRCIRpqenWV5eLt/v8Xg4derUlo9ezOXg2WfhW99i\n1caqYBDSaWtROp1OMzOT59y5Ae67D06fzjAw0IfP58Pr9WrA34CGgV9E3MD/DhwDXsFqq5xrdL9S\nqjtEowWefTbKmTOGq1d9FApCf38/g4ODVcFx924rwC8swPXr1a9x5oz1ceKE4ejRa6RSF6pKI/ft\n28exY8e2VJtfKMDLL8M3vgHRaPVzo6PwrneBMVkKhRive53hhRecgFAoCE8/7eLSJS8//dMuRkfb\ns4i8k6w14/8MkAH+HngPcAr41XYMSim1MdEoTE/D975X4OzZFPn8SkB2Op24XC5EhH37YGLCCvi7\ndlnPf/ObMDICH/6w9fXZs9b1XC7H1NQ8Tz2VZ2xsN2984xKjo4Ut9803BmZm4Otft9YVKoVC8M53\nwsREnlgsikgKhwN++Ifh5MksX/3qIHfuDDIwMEA83sdnPgP33gs/+qOgaf3mrRX4J4wxrwcQkceA\n59ozJKVUMxYXrWB/5gxcu2aVV9buUh0YGODoUVc52K/VDHP/fnjoIbhxA774xShPP71UrgK6etXD\n7dsh3vrWEQ4d2vwC7qVL8NWvWuOt5PVaqaV77imQSsWZn6/efCUiHDo0yK/+qp8XX3Twta9BadvA\niy9ab1bvfje87nVsej9CL1kr8JfTOsXTtNowHKXUWrJZuHIFbt+GT3xi5Xoulyu3FxYxHDhQ4N57\nB3nTm1wEg82/fj6fJxqdZXz8BiMjTl5+eYjLl70MDQ0RDAa5fFl47DE4dswK1GNj678mWG8mX/sa\nzM5WX3e54G1vg7e+1ZDNJlhYiK+qxYdBdu8OlNtD33ef9VvLl75k/eYA1uL0Zz8L3/0uvPe9a7/B\nqbUD/xtEJFbx2F3x2BhjAjaOS6kdo1UnZl2/Dp/7HFy4UH09m82SySwzNpbj+PEcx48XOHhwaMOb\nluLxOGfOnCGZTAIwPJzl3e+OsWvXGN/9boDvf99K04AVwGdn4cgR6w3g7rvrv2Y4bOXwX321+rrD\nAadPw9vfDpBkaWl1Lb61LyAADFB7JEAgAB/6kPUbz5NPrqwRzM5a1UmTk/AP/gEt2U+wEzUM/MaY\nzp92rJSiUID/+T+tAFo5GXY4YP/+ZcbGohw9msftNjgcDoaHhzfYfMxqrvbCC69VpVf27NnD8ePH\n6e/vL8/w/+7v4HvfW3kDuHDB+jh82Hq+pLIWv3LMIvDGN8I73gGDg2mi0WjVMYxg1eIHAoGmNl9N\nTFhvPl/7mrUfwRjrt6KvfMV6s/nJn4QDBzbwR9EjmqnqOQq8yiaqekTkAeDjWIetP2aM+ViD+94C\nPA18wBjzuY18D6V2sqUla5Z/5crKNYfDCnYf/nCEfD5Rvu50OhkeHt5QpY3VX8dqrlYK5g6Hg2PH\njjE6OrqqCuinf9oK8N/6FrzyysobwMWL1sdLL1mz8U98YnUt/smT1sJtKJQlGo2ysJCuet7hcJQ3\nX20ktexywXveA294A/zN30DpCICbN+Gxx6zfLN75Tus+ZbGtqkdEHMAngfuxerU+JyJPGGOm69z3\nMeDLgC4kKIUVUF95xcpjpyvi48GD8OY3G9zuRfL5lZp6l8tFKBTaUH+cO3fucPbsWWAlQvt8Pk6d\nOrVmc7Vdu+Af/sOVN4CXX16Z1Uci1sfRoyv333033H8/7Ntn9cWfn68u1u/r68Pr9eLz+bZUi3/w\noFWZ9J3vwNSU9cZjDDzzjJUSes97Nv3SO46dVT2ngVljzKXiazwOPAhM19z3K8Bngbds8PWV2pFS\nKfjiF62NVCV9fVagfdvb8vze7y1izcksHo+HYDDYdNDM5/PMzs5y48aNqutjY2McPtx8c7XhYXjw\nQavU8lvfshZWK+3dawX8I0cKxOMx5ueTqyp1PB4Pfr+/ZQ3dHA74oR+yKpi++EV47TXrejQKjz9u\npanGx1vyrbY1O6t6DgCVbfuuAfdV3iAiB7DeDN6JFfhrm2cr1VMuXIDPf756Q9PwMPzUT8Hu3WnC\n4SVgZRHU7/dv6FSrejtwrVbFJzl6dHhTYw6F4H3vs94Azp61Kmx+6qfgB37AkEwmmJ9fXanjdrvx\n+/1bPsh9rTH97M9agf7LX7bGBHDnjlUG++qr8PrX2/KttwU7q3qaCeIfB37LGGPEemdp+O7ycEVJ\nxOTkJJOTk028vFLbQy5nbWj69rerr//gD8KP/zik0zHC4XjFjFkYGgo23e++UChw+fJlLl++XHXd\n2oh1HNj6wSRDQyuz6WPHkszPr67Uaedh5iJWcD92zFrsffFF63o+bzWl24mmpqaYmppa9761Av+g\nMSa7xvPrmQMqq3zHsGb9lX4QeLz428Qu4N0ikjXGPFH7Yg9vtRZOqS5165a1gFtxLjkejzWLPn68\nwNLSUs0M3QEM4fE0t1qZSCSYnp6uaqHc39/P+Pg4e/bsobVLa8tAlKWl6jqQTrZJdrutP8s3vMHq\nCRQIWFVIO1HtpPiRRx6pe99agf8Z4N4tjOF5YFxEDgHXgQ8CD1XeYIw5UvpaRP4C+Jt6QV+pnai0\n8PjVr1oz/pLxcSt3PjCQYX5+sWrWbNXmD2EF//Ve3zA3N8eFCxeqUi1DQ0OcPHmypUE4nU4Xu4Cu\n7prp9/vbehJXI4cOwZvfXF1e2qvWCvxbmgYU1wU+CjyF9VP6aWPMtIh8pPj8o1t5faW2s2jUyuVX\nbsbq77d6zr/lLZBIxFlYiFUthm4kn291spxhcXGxfK2vr4/Dhw9z8ODBlnWyzGQyxGIx0unq0kyr\n53/3dc3s69NNXbB24N8tIr9G/TcAY4z54/Ve3BjzJPBkzbW6Ad8Y84vrvZ5SO8GZM1a9eWUL4n37\nrAXRkZECi4vVqZ2+vj5CoVDTO3Fv377NuXPnqg4p8fl8TExM4K13jNUmZLNZYrFYTQoKrHDhZc8e\nX9uOXlQbt1bgdwDNlwsotYO0qs1CpXTaai9QWfYoYpUfvuMdUChkuXNnsSpgDwwMEAqFmtqUlc1m\nOX/+fNVBKQB33XUXhw4dakkgzuVyxONxUqlU3dJM6/xeh86qu9xagf+mMab+yoBSakMiEfizP7NK\nCUuCQWuWf/fd1gJsNBqtCqY+nw+/399UqmRxcZGZmZmqlMvg4CAnT55kaGhoy+PP5/PE4/FV3T/B\n/tJM1Xr6N6WUjWIxaxPR1atUdcl8wxusnaQul2FxcYlURd6nr6+PoaGhphZf8/k8Fy9e5FpNn+PR\n0VGOHTu25WBcKBSIx+MkEolVAX9wcBC/37/BvkCqG6z1U/FeEfnn6AlcSm2IMVa/+WeesfL5Vyu2\nMQ4Owk/8BPzAD1ipmfn56tSO0+kkFAo1FbBjsRjT09Plbpql//748eNbOijF+n8w5YBfu/mqnbX4\nyh5r/XR9HD2BS9mk1Tl0O3LyG5XNWjtFn33W6j9f6/BheP/7rZl/MpkkEolUzaK9Xi+BQKCJ1I4B\nrvDii5eq/vuRkRFOnDixpYBsjCGRSBCPr95tOzAwgN/v33C7Z9V99AQupbYoErFaAr/4IlRMvsuC\nQas18M/9HIBhaSlSNUvv6+sjGAzibuLsQOu/mwGi5c6YfX19HDt2jH379m2hdNKQTKaIxVbvtu3k\n5itlDz2BS6lNMMY6RvDZZ61ToGrS3/T3W3n806etRV2AfD7H4uJiVf/5ZlM7xhiuXbvGxYsXgZWZ\neCAQYGJioqk3jcZSQGzVbtv+/v5ym2S1s+gJXEptQCZjtUt+9lnr+MNaQ0PWBqx77rHaLqxIcedO\npCp90mxXzUQiwczMTHFnbIlw+PAh7rrrrk3P8tNp6yCUyrbMYO229fl8eDyertp8pVpHT+BSqgnh\nsJXOeeklWLVnCetglNOn4fjx6p2hVg4+CiTKrQJEhGBw/QZrhUKBq1evcunSpZqKGh9wgrvv3tw2\nm2zWOgilVPr54Q9b17t1t61qPS3nVKoBY6wzXJ99Fs6fX53OGRiwjhE8fdo6napWOp0mEolQkTWl\nv7+fUCi0bglkLBbj7NmzVY3VRIRDhw7xwz88tqnNWNZB6tGq0lFYOQjF6/XqbtseoYFfqQq5nLXJ\n6to1mJuzdtbWGh62gv2b3mSVZ9YqFArEYjESiUTVdbfbzdDQ0Jqz6VL75CtXrqzq03Py5MlNtVxo\nVItvx0EoanvQwK+a0g3lkq1ijNUkbWHB+rhzZ+XrpaWVmX6t8XEr4B87Vv8NAaxZ/tLSUk1lTB8Q\nJBRae5E0Go0yMzOzquJns43V1irN1N22vU3/1tWOlUqtBPTKIB8Orz4IvBGXy1qofctbYGSk8X2F\nQoFoNFos6PykAAAb8klEQVQVtIFiCWSQtdoo5/N5Ll26xNXKnV5AMBjkxIkTm2ppnEwm65ZmDgwM\nEAgEdPNVj9PAr9ounYb5eevzd76zMnsWqf663rVGz9+6Zb3eF76wEuDr1dSvR8Squx8etgL9r/+6\nlctfy/LyMpFIpCrINlubv7S0xNmzZ6vy7g6HgyNHjrB///4Nz/KXl5eJxWJVJaNgrS0EAgGtxVeA\nBv4drZvSMwsLcO6c9XHlyspB4l/+cmtef3ra+vzSS83d7/FYgX1kBHbtWvl6eNiqwV9asu5bK+gX\nCgUikciqxVK3200wGFwzb57L5bhw4QLXr1+vuh4KhThx4sSGA3SjvvjddBCK6h4a+JUt8nm4fHkl\n2IfD7R9Df/9KQK8N8lvdk5RKpYhEquvyHQ4HwWBw3aAdDoc5e/ZsVZDu7+/n6NGjjI6ObmiWn8vl\niMVidSt1tDRTNaKBfwt2Yr+ZrYjFrLLH8+etjpSZTON7fT4rpXLffStlkpWf17tW+/yZM+B0Wh0v\nSwE+EGi8CLtZ+XyeSCSy6gASj8dDIBBYd5Y/OzvLzZs3q66PjIxw/PjxDfXAKVUO1bZJ1kod1QwN\n/GrTjIHr160Z/fnz1teNDAxYm5zGx62PPy6e3/bud7dmLK++an0+fbo1r1dPMpkkGo2umuUPDQ01\nEbTv8Oyz58hUvBs6nU6OHTvGnj17mp6Vr9U1Uyt1VLP0J0RtSDptzebPnbNKHiv2F60SClk7WY8f\ntw4b2a7xqNEsv5lumul0mg984DVu375d9RvQ7t27GR8f31B1TaNKHZfLRSAQ0L74qmm2/lMUkQew\n2js7gMeMMR+ref5B4P/G6jpVAP6lMebrdo5JNadQsLpOLi5a+fnXXrNSOX/4h1b+vp6+PrjrrpVg\nPzLS+lRLu9Wb5ff39xMMBtec5RcKBebm5rh06VJVoB4YGGB8fHxD/fIbVeo4nU4CgYC2SVYbZlvg\nFxEH8EngfmAOeE5EnjDGTFfc9lVjzBeK978e+B9YB7+oNshmrcBeCu6VnxcXoTKTUCoxrw36Xq+1\noen4cTh6tP5O1u0pB0RYWlpZgBURvF7vuschLi4ucv78+VU1/Xv37uXYsWNNz8xre+qUaKWO2io7\nZ/yngVljzCUAEXkceBAoB35jTOWedh9wx8bx9KRs1mo9UBvYw2FrBr8Z+/ZZefrjx2H/fnbUwdql\n3a4QwzrwxNLf38/Q0NCaqZl0Os3s7Czz8/NV1z0eD+Pj44RCoabGkM/nywu3lbRSR7WKnYH/AFC5\nFfEacF/tTSLyfuAPgH3Aj9k4nh2lUIBEwmo9EItZH7Vf//3fW71nNpv69fmsPP3wsNV73u2GX/s1\nq1pmpzHGkEwmicfjVamZZmb5hUKBa9eucfny5ar/1uFwcOjQIQ4cONBUhY321FHtYmfgN+vfAsaY\nzwOfF5G3A/8FOFHvvocrahwnJyeZnJzc+gi7kDHWAmopiDcK7PF4dSqmntw6JyT39a3sUi0F+MrP\nlZPbl1+2Pu+0oN8o4Fuc7No1tGZqJhwOc/78+VV19Hv27OHo0aNN5d9LY4jFYqsqdQYHBwkEAlqp\no5oyNTXF1NTUuvfZ+dM0B4xVPB7DmvXXZYz5loj0i8iIMWah9vmHu6y4PRKxaseNgb/6KysIG7O1\nz08/bQXrP/iD1o2zrw/27Kkf3INBcPTwqQulgJ+reYd0OBz8xm9YJ081muUvLy8zOzvLnTvV2Umv\n18v4+DhDQ0NNjSGVso47rB2D9tRRm1E7KX7kkUfq3mdn4H8eGBeRQ8B14IPAQ5U3iMhR4IIxxojI\nvQD1gn43SqdXTmCanl773o285kZ4PNYM3O+3Pmq/zmSsNM8//aetGV8rdfJ9vFGwbebkqdLhKJcv\nX15Vz3/48GH279/fVDomk8kQjUar6vpBjztU7WFb4C+e0/tR4Cmscs5PG2OmReQjxecfBX4a+DkR\nyQJx4EN2jafV7FxbczrrB/LKr32+9evie2my2MwbSaOyyGaPGlxYWGB2dnZVWmfv3r0cPXq0qdn5\nWi0WSpU6unCr7GZr4tAY8yTwZM21Ryu+/kPgD+0cg10CAZiYsN4APvABK6UisrXPy8tW6uV3fmf7\n1793k0YBv9kqmVQqxezsLAsL1b+M+nw+xsfHCQaD645hrRYLXq8Xn8+3IxZuuywjqxrQFaNNcrlg\n717r61OnWvOapRp4DfqtkU6nicViq9IpzR41mM/nuXr1KleuXFm1gauU1llvdr7eYSiBQABHLy+0\nqI7QwK92nEYtijcyu75z5w6zs7Or2jSMjo5y5MiRptI62mJBdSsN/GrHaEXAj8fjXLhwgXBNH2mf\nz8fx48cJNFHPqoehqG6ngV81pZtzt5lMhng8vmp2Xtr45PP51k2nLC8vc/HiRW7dulV1vb+/nyNH\njrBv37510zraYkFtFxr41bZkjCGVSpFIJFbNrEWk3KJ4vYCfzWa5cuUKc3Nzq3Lw+/bt48iRI+um\nZNaq1Cn9pqGVOqqbaODfwbp5lr5Z+XyeZDJZtx+9iDA4ONhUT/pS98zLly+vqucfGRnhyJEjeL3e\ndV9DD0Ox1078Ge4GGvjVtpDJZEgkEiwvL1cFWVgJtF6vd92Ab4zh9u3bXLx4cVVqyO/3c/To0XV3\n3a5XqaOHoahupz+dW9Dq2YjObqqtlc4BK//u8XjweDxNzazD4TAXLlwgXnN6jNvt5vDhw+zevXvd\nlMxalTp+v19bLKhtQQO/6jprpXPACrJer7fp6ph4PM5rr73G4uJi1XWn08ndd9/dVJuF5eVlotHo\nqrSQ0+nE7/drpY7aVjTwq67RTDrH4/E0Xf/eqFKnr6+PsbExxsbG1k3JNOqpo5U6ajvTwK86qtXp\nHFi/UufQoUPrtkteq1JHD0NR250GftURrU7ngFbqKNUsDfyqbQqFAsvLy6RSKTKZTEvSOWD91nDr\n1i0uXry4avNUs5U6YDVji0ajqxZutVJH7TT6k6xsZYwhnU6TSqXq5u7Bypd7vd4NpXNKrz0/P8+l\nS5dWnU+7kUqdXC5HJBJZ9aahPXXUTqWBX9kik8mQSqVIpVJ1UzkiwsDAwIbTObB2wHc6nRw6dIh9\n+/at+yZijCEWi60649bhcBAIBPQwFLVjaeBXLZPL5crBvjbHXuJ0OnG73bjd7g23I14r4DscDg4e\nPNhUpQ5YFT+RSGTDB6srtRNo4Fdbks/ny8G+XlUOWJU5pWC/mTx5MwH/4MGDTaVk1krrBINBzeOr\nnqA/5WrDSiWYjRZpwSp7LAX7ze5mbWXAN8YQj8eJx+Oa1lE9TwO/akozi7SlJmlutxuXy7XpdEkr\nAz7U33Wr5Zmql9ke+EXkAeDjWAeuP2aM+VjN8z8D/AYgQAz4ZWPMK3aPS63PGMPy8jLLy8uk0+k1\nF2ndbjeDg4NbCqKtDvj5fJ5IJLKqGdvAwADBYFCrdVTPsjXwi4gD+CRwPzAHPCciTxhjpituuwD8\nsDEmUnyT+I/AW+0cl2qsVGtfCvb1ZvawtUXaWq0O+KXumbFYrGr8fX19BAIBbbOgep7dM/7TwKwx\n5hKAiDwOPAiUA78x5umK+58BDto8JlUjn8+Xg32jnD1Yi7SDg4N4PJ6WLIK2OuCDdcB6JBJZVVVU\nqtbRtI5S9gf+A8DVisfXgPvWuP9/Bb5k64gUYPWzKQX7RtU4YM3sBwcHGRwcbFlqpFAocOfOnZYG\n/Hw+TzQaXdVbx+l0EgwGtV2yUhXsDvz1p451iMg7gF8Cfqje8w9XNKufnJxkcnJyi0PrPZlMphzs\nG9XZi0g5jTM4OLjlNE6lbDbL9evXuX79et1zaTcT8BsditLX14ff71+3N49SO8nU1BRTU1Pr3ieN\nfq1vBRF5K/CwMeaB4uPfBgp1FnjfAHwOeMAYM1vndYyd49ypjDHlHbTpdHpVD5oSEcHlcpVn9q1O\nh8Tjcebm5rh169aqBeLNBnxofCiKx+MhEAhoWketUpo/9sqhRyKCMWZVeZ3dM/7ngXEROQRcBz4I\nPFQzsLuwgv7P1gv6amNyuRzpdJp0Ok0mk6lbiQPWjLgy2Ld6p6oxhoWFBa5du8bS0tKq551OJwcO\nHODAgQMbDvjpdJpoNLoqRaVpHaWaY2vgN8bkROSjwFNY5ZyfNsZMi8hHis8/CvxfQAj402LwyRpj\nTts5rp2kUCiQyWTKwb5RCges2XUp0A8MDNjSliCXy3Hjxg3m5uZWlVEC+Hw+Dh48yJ49ezY8I89m\ns0Sj0bppIj0URanm2V7Hb4x5Eniy5tqjFV//E+Cf2D2OnaQy0Gez2YZVOLBSiVMK9nZJJpPMzc1x\n8+bNVakXEWHXrl0cPHiQQCCw4TecRgu3fX19eL1efD6f9tZRagN05+42kM/ny4G+0Uaqkr6+PgYG\nBnC5XLhcLlt7zxhjWFxc5Nq1a4TD4VXP9/f3s3//fvbv37+pM2kLhQLxeHxV90zddavU1mjg70Kl\n9gjNpG9KVTilQO90Om2f/ebzeW7evMnc3NyqckywauYPHDjA3r17N1UVZIwpL9zWvskNDg4SCAS0\nmZpSW6D/erpENputWpRdK33jcDjKgd7lcrVt1ptKpcrpnHpvRiMjIxw8eJChoaFNv/mkUilisdiq\n1x8YGCAQCOjCrVItoIG/Q0qLsqXWCI1KLWGl3LId6Zt641xYWODmzZssLCyset7hcLBv3z4OHDiw\npQ6XmUyGaDRKJpOput7f34/f79fumUq1kAb+NtrIrL4yfWNXBU4jpRbGN2/e5NatW3Vn9263m4MH\nD7J3794tvRHlcjmi0eiqCqDSBiyPx6MLt0q1mAZ+G5Vy9c3M6ivr6gcGBlq6Y7ZZmUyGW7ducfPm\nTRKJRN17QqEQBw8eZHh4eEsBOZ/PE4/HSSaTqxZuS5U6unCrlD008LfYRmb1ldU3ncpdFwoFwuEw\nN27cIBwO1x3v4OAge/fuZXR0dMspl1wuRyKRqBvw3W43fr+/I296SvUSDfxbtNlZfTsXZeupTOXU\na9LW19fH7t27GR0d3dJibUk6nSaRSNTd1OVyuQgEAtofX6k20cC/CZlMpryJqplcfSnQd7oiJZvN\nllM58Xi87j3BYJDR0VF279695UXk0kEu8Xi87pvLwMAAfr8fl8u1pe+jlNoYDfxNyOVyVbtl19tA\nVUrf2NHwbKNKqZxSVU69NymXy8Xo6Ch79+5tSduDQqFAMpkkkUjU3cXrcrnw+XwdfyNUqldp4K9j\nI/1voLtm9WDNtGOxGPPz89y6dWtViSRYb1C7du1idHSUUCjUksqZ0oJtKpVa9eZY2m3r9Xp185VS\nHab/ArECZeWi7Hr9bzq1gWotxhii0Sjz8/PcuXOnbi4dIBAIMDo6yp49e1oWgDOZTDl/X/vn5nA4\n8Hq9eDyervhzUkr1cOBvtn0xtLf/zUYYY4hEIszPzzM/P193Zg9WLn10dJTR0dGWdrAs5e/rfV+n\n04nX68XtdmsdvlJdxtaDWFqlFQexlBYaS8F+vZ2y7e5/0yxjDEtLS+Vg3+jYxP7+fnbt2sXu3bu3\nXHNf+/1L+ft6KbBS/l4XbJXqvE4dxNJVlpaW1jxIvLKmvpvSEoVCgcXFRebn51lYWGgY7J1OZznY\nDw0NtfT/IZ/Pl+vv6+Xv3W43Pp+va34bUko11jP/SkWEgYGB8iEeldU3Lper6zYNlapxSsG+0QLz\nwMBAVbBv5W8mpd+SksnkqsNPYKUfvtfr7ao3SqXU2nom8IN1Fmtl+qbb5PP5qmDfKB3lcrnKwT4Y\nDLY8DZXJZEgmkywvL9dd++jv7y8v2HZLCkwp1byeyfF3I2MMiUSCxcVFwuEwkUik4SLz4OAgu3fv\nZvfu3fj9/pYH3Hw+TzKZJJVK1f3tolR/7/F4NnWoilKq/TqW4xeRB4CPY525+5gx5mM1z58E/gK4\nB/hXxph/Z/eYOimTyZQD/eLiYsNKHLA6YJaCvR3HCxpjSKVSpFKpuqkcsNYN3G43bre769JhSqnN\nsTXwi4gD+CRwPzAHPCciTxhjpituWwB+BXi/nWPplEKhQCQSKQf7Rq0SSjweTznYe71eW1Ip6XS6\nHPDr/SbV19eH2+3G4/F0ZUpMKbU1ds/4TwOzxphLACLyOPAgUA78xph5YF5E3mvzWNqiNIsOh8OE\nw2GWlpbW3CPQ399PKBRieHiYUChkWxoll8uRSqVIJpN11w4qUzkul0tz90rtYHYH/gPA1YrH14D7\nbP6ebZfNZllcXCzP6hulTcAKsIFAoBzo7cjXlxQKhXJVTqOUUimVoztrleoddgf+nbciixXoo9Fo\nOYUTi8XWvN/tdpdn9UNDQ7bWupeCfWmzmqZylFK17A78c8BYxeMxrFn/hj388MPlrycnJ5mcnNzK\nuJpWqmUvBfpIJNLwdKoSh8NRlb6x+7zYfD5fDvaN2kRrKkepnW9qaoqpqal177O1nFNE+oGzwLuA\n68CzwEM1i7ulex8GYvWqetpZzlk6b7YU5CORyJqVNyWV6ZtAIGB7YM1ms+Vg32gnL1ipHI/Hg9vt\n1lSOUj2mUTmn7XX8IvJuVso5P22M+QMR+QiAMeZRERkFngMCQAGIAaeMMfGK17At8Ofz+arZfDQa\nXbOPT3E8+Hw+gsEgwWCQoaEh21MmxhgymUw52DcaY6nP0ODgIIODg9pCQake1rHA3wqtDPyZTKZq\nNh+Px9dswQxW6qYU5IPBYNvOha081rHRLlpYSeOUgr3O7JVSoE3ayOVyvPDCC6RSqXXvdblcVYHe\nrnr6eppZnAVrgbYU6DVnr5TaiJ4J/P39/Q1nzF6vtyrQtzOQlk77Kn2sdQiMw+EoB/uBgQEN9kqp\nTemZwA/WQeJ37tzB7/eXg3wgEGhrSWM+n68K9LlcrqnD2gcHB7X0UinVEj2V489kMvT397c1B146\nqL0y0K9FF2eVUq2ii7ttks1mqwJ9MxVCTqeTgYGB8ocuziqlWqHnF3ftUDqkvTLQr9WXB1YOhKn8\n0Fy9UqqdNPA3qVAokM1myx+5XG7d/DysHNRe+uim83uVUr1JA38duVxuVZBfL2VT4nA4VgV6pZTq\nJj0d+AuFQlWQL33d7HqCiKwK9LoYq5Tqdj0TpUq7YGtTNc3q6+ujv78fp9OJ0+ksf61pG6XUdtMz\ngV9EWFxcbGo273A4VgV4nckrpXaKnopmTqezqtOmiNSdxWs5pVJqJ+upwO92u8t5+FKg11SNUqrX\n6AYupZTaoRpt4NKchlJK9RgN/Eop1WM08CulVI/RwK+UUj1GA79SSvUYWwO/iDwgIjMicl5EfrPB\nPf9v8fmXReQeO8ejlFLKxsAvIg7gk8ADwCngIRGZqLnnPcAxY8w48GHgT+0aj12mpqY6PYQ1dfP4\nunls0N3j07FtXjePr11js3PGfxqYNcZcMsZkgceBB2vueR/wGQBjzDPAkIjstXFMLdfNP0TQ3ePr\n5rFBd49Px7Z53Ty+nRD4DwBXKx5fK15b756DNo5JKaV6np2Bv9mttrW7ynSLrlJK2ci2lg0i8lbg\nYWPMA8XHvw0UjDEfq7jnz4ApY8zjxcczwI8YY27VvJa+GSil1Ca0+8zd54FxETkEXAc+CDxUc88T\nwEeBx4tvFEu1QR/qD1wppdTm2Bb4jTE5Efko8BTgAD5tjJkWkY8Un3/UGPMlEXmPiMwCCeAX7RqP\nUkopy7bozqmUUqp1ttXOXRH5dREpiMhwp8dSSUT+rYhMFzehfU5Egl0wpnU3z3WKiIyJyDdE5Psi\n8j0R+T87PaZaIuIQkZdE5G86PZZKIjIkIp8t/rydKaZIu4aI/Hbx7/VVEflvIuLq4Fj+k4jcEpFX\nK64Ni8hXROSciPytiAx12fjaEku2TeAXkTHgR4HLnR5LHX8LvM4Y80bgHPDbnRxMM5vnOiwL/HNj\nzOuAtwL/R5eND+BXgTN0X5XZJ4AvGWMmgDcA0x0eT1lxPe9/A+41xrweK8X7oQ4O6S+w/g1U+i3g\nK8aY48DXio87pd742hJLtk3gB/4Y+I1OD6IeY8xXjDGF4sNn6PxehGY2z3WMMeamMea7xa/jWMFr\nf2dHtUJEDgLvAR5jdblxxxRnf283xvwnsNbRjDGRDg+rUhTrTd0jIv2AB5jr1GCMMd8CFmsulzeN\nFj+/v62DqlBvfO2KJdsi8IvIg8A1Y8wrnR5LE34J+FKHx9DM5rmuUJwl3oP1Q94t/j3wL4HCeje2\n2WFgXkT+QkReFJE/FxFPpwdVYowJA/8OuIJVybdkjPlqZ0e1yt6KysFbQDd3CrAtlnRN4C/m3V6t\n8/E+rF93frfy9i4a309W3POvgIwx5r+1e3w1ui09UZeI+IDPAr9anPl3nIj8BHDbGPMSXTTbL+oH\n7gU+ZYy5F6sSrpOpiioichT4Z8AhrN/gfCLyMx0d1BqK57l25b8Vu2NJ1xy2boz50XrXReQHsGY6\nLxcPRj8IvCAip40xtzs9vhIR+QWs9MC72jKgtc0BYxWPx7Bm/V1DRJzAXwP/1Rjz+U6Pp8LbgPcV\nGwgOAgER+c/GmJ/r8LjA+ju8Zox5rvj4s3RR4AfeDHzbGLMAICKfw/rz/MuOjqraLREZNcbcFJF9\nQNtiSLPaEUu6ZsbfiDHme8aYvcaYw8aYw1g//Pe2M+ivR0QewEoNPGiMWe70eKjYPCciA1ib557o\n8JjKxHoH/zRwxhjz8U6Pp5Ix5neMMWPFn7UPAV/vkqCPMeYmcFVEjhcv3Q98v4NDqjUDvFVE3MW/\n4/uxFsi7yRPAzxe//nmgmyYdbYslXR/46+jGX83+A+ADvlIsAfxUJwdjjMlh7Yh+Cusf3l8ZY7qm\n+gP4IeBngXcU/7xeKv7Ad6Nu+3n7FeAvReRlrKqe3+/weMqMMS8D/xlr4lFaj/uPnRqPiPx34NvA\nCRG5KiK/CPwb4EdF5BzwzuLjbhnfL9GmWKIbuJRSqsdsxxm/UkqpLdDAr5RSPUYDv1JK9RgN/Eop\n1WM08CulVI/RwK+UUj1GA79SSvUYDfxK2aTYoVKprqOBX6kKIuIVkf9PRL5bbML3ARF5i4h8u3jt\nmeI9g8Uuma8UO2VOFv/7XxCRJ0Tka1i7Lz3FAzeeKd73vs7+HyrVRU3alOoSDwBzxpj3AohIAHgJ\n+IAx5oViR9FlrC6UeWPMG0TkBPC3FT107gFeb4xZEpHfB75mjPml4mlPz4jIV40xybb/nylVpDN+\npaq9gtXL5d+IyP8C3A3cMMa8ANbBMcaYPFa/of9avHYW62S441i9fb5ijFkqvt6PAb8lIi8B3wBc\nVHdOVartdMavVAVjzHkRuQd4L/CvsYJ1I4369SdqHv+UMeZ8K8anVCvojF+pCsUe7cvGmL8E/gjr\nGMtREXlz8Xl/8UzjbwE/U7x2HLgLqy1x7ZvBU0D5MPnim4pSHaUzfqWqvR74tyJSADLAL2NNkP6D\niLiBJFaf+U8BfyoirwA54OeNMVkRqT3V6f8BPl68rw+4gHXuq1Ido22ZlVKqx2iqRymleowGfqWU\n6jEa+JVSqsdo4FdKqR6jgV8ppXqMBn6llOoxGviVUqrHaOBXSqke8/8DDlHllw/AFFMAAAAASUVO\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79e5729dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_regressions(df)\n",
    "\n",
    "threshes = range(-2, 11)\n",
    "meds = []\n",
    "for thresh in threshes:\n",
    "    med, (low, high) = estimate_ptpp(df, thresh)\n",
    "    plt.vlines(thresh, low, high, color='blue', alpha=0.5, linewidth=2)\n",
    "\n",
    "    meds.append(med)\n",
    "    \n",
    "thinkplot.Plot(threshes, meds, color='blue', alpha=0.5)\n",
    "thinkplot.Config(xlabel='score', ylabel='PTPP', xlim=[-4, 13])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}