{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction: Understanding Logistic Regression Outputs\n",
    "\n",
    "The purpose of this notebook is to understand the outputs of logistic regression: logits, probabilities, odds, and classifications. Logistic regression is simple because it's a linear classification model, but that doesn't always mean something is simple to understand! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-24T20:51:31.827250Z",
     "start_time": "2019-02-24T20:51:31.793310Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "x = %load_ext autoreload"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-24T20:54:24.473784Z",
     "start_time": "2019-02-24T20:54:24.439451Z"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'get_config' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-21-f3c508c65698>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mget_config\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'get_config' is not defined"
     ]
    }
   ],
   "source": [
    "\n",
    "get_config()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-25T14:04:49.865346Z",
     "start_time": "2019-02-25T14:04:49.605290Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'autoreload', 'ipywidgets', 'storemagic'}"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython import get_ipython\n",
    "ipython = get_ipython()\n",
    "ex = ipython.extension_manager\n",
    "ex.loaded"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-25T14:04:56.277816Z",
     "start_time": "2019-02-25T14:04:56.218916Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script><script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window._Plotly) {require(['plotly'],function(plotly) {window._Plotly=plotly;});}</script>"
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     "data": {
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       "<script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script><script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window._Plotly) {require(['plotly'],function(plotly) {window._Plotly=plotly;});}</script>"
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       "<script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script><script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window._Plotly) {require(['plotly'],function(plotly) {window._Plotly=plotly;});}</script>"
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import sys\n",
    "sys.path.append('../..')\n",
    "\n",
    "# Options for pandas\n",
    "pd.options.display.max_columns = 20\n",
    "pd.options.display.max_rows = 10\n",
    "\n",
    "# Display all cell outputs\n",
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = 'all'\n",
    "\n",
    "import plotly.plotly as py\n",
    "import plotly.graph_objs as go\n",
    "from plotly.offline import iplot, init_notebook_mode\n",
    "init_notebook_mode(connected=True)\n",
    "\n",
    "import cufflinks as cf\n",
    "cf.go_offline(connected=True)\n",
    "cf.set_config_file(theme='pearl')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-25T14:04:58.048984Z",
     "start_time": "2019-02-25T14:04:58.007948Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
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     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
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     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def logits_to_probs(logits):\n",
    "    return 1 / (1 + np.exp(-logits))\n",
    "\n",
    "def logits_to_odds(logits):\n",
    "    return np.exp(logits)\n",
    "\n",
    "def probs_to_odds(probs):\n",
    "    return probs / (1 - probs)\n",
    "\n",
    "def odds_to_probs(odds):\n",
    "    return odds / (1 + odds)\n",
    "\n",
    "logits_to_probs(1)\n",
    "logits_to_probs(2) \n",
    "logits_to_probs(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-25T14:08:41.778381Z",
     "start_time": "2019-02-25T14:08:41.601221Z"
    }
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   ],
   "source": [
    "df = pd.DataFrame({'logits': np.arange(-10, 10, 0.01)})\n",
    "df['odds'] = logits_to_odds(df['logits'])\n",
    "\n",
    "df['probs'] = odds_to_probs(df['odds'])\n",
    "df['class'] = df['probs'].round()\n",
    "\n",
    "df.iplot(kind='scatter', x='logits', y='probs', secondary_y='odds', \n",
    "         xTitle='Log Odds', yTitle='Probability', secondary_y_title='Odds',\n",
    "        title='Probability and Odds vs Log Odds', \n",
    "         hline=[dict(y=0.5, dash='dash', width=1, color='black')])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-25T14:09:24.131430Z",
     "start_time": "2019-02-25T14:09:23.971161Z"
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   },
   "outputs": [
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   "source": [
    "coef0 = -0.5 \n",
    "coef1 = 0.2\n",
    "\n",
    "xrange = np.arange(-2, 5, 0.01)\n",
    "logits = coef0 + coef1 * xrange\n",
    "odds = logits_to_odds(logits)\n",
    "probs = logits_to_probs(logits)\n",
    "classes = np.round(probs)\n",
    "\n",
    "df = pd.DataFrame(dict(logits=logits, odds=odds, probs=probs, classes=classes)).set_index(xrange)\n",
    "df.iplot()"
   ]
  },
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   "cell_type": "code",
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     "end_time": "2019-02-25T14:20:29.790185Z",
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    "logits_to_odds(2)\n",
    "logits_to_odds(3)"
   ]
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     "end_time": "2019-02-25T14:20:53.897654Z",
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    "logits_to_odds(3)\n",
    "logits_to_odds(4)"
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   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-25T14:22:08.385723Z",
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       "2.718281828459045"
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   ],
   "source": [
    "logits_to_odds(4) / logits_to_odds(3)\n",
    "logits_to_odds(3) / logits_to_odds(2)"
   ]
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   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
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     "end_time": "2019-02-25T14:31:01.721576Z",
     "start_time": "2019-02-25T14:31:01.667899Z"
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     "execution_count": 50,
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   "source": [
    "100 * np.exp(2)"
   ]
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   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-25T14:49:51.398006Z",
     "start_time": "2019-02-25T14:49:51.345912Z"
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     "data": {
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       "1.718281828459045"
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     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
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       "1.718281828459045"
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     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(logits_to_odds(4) - logits_to_odds(3)) / logits_to_odds(3)\n",
    "(logits_to_odds(3) - logits_to_odds(2)) / logits_to_odds(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-25T14:55:42.725137Z",
     "start_time": "2019-02-25T14:55:42.668987Z"
    }
   },
   "outputs": [],
   "source": [
    "def gauge_effect(c, x0, intercept=0):\n",
    "    initial_log_odds = c * x0 + intercept\n",
    "    initial_odds = np.exp(initial_log_odds)\n",
    "    initial_probability = 1 / (1 + np.exp(-initial_log_odds))\n",
    "    \n",
    "    updated_log_odds = c * (x0 + 1) + intercept\n",
    "    updated_odds = np.exp(updated_log_odds)\n",
    "    updated_probability = 1 / (1 + np.exp(-updated_log_odds))\n",
    "    \n",
    "    change_in_odds_ratio = 100 * (updated_odds - initial_odds) / initial_odds\n",
    "    change_in_probability = 100 * (updated_probability - initial_probability) / initial_probability\n",
    "    \n",
    "    \n",
    "#    print(updated_odds, initial_odds)\n",
    "    print(f'Change in odds ratio: {change_in_odds_ratio:0.2f}%.')\n",
    "    print(f'Change in probability: {change_in_probability:0.2f}%.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-25T14:55:43.314190Z",
     "start_time": "2019-02-25T14:55:43.263844Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Change in odds ratio: 348.17%.\n",
      "Change in probability: 16.51%.\n",
      "Change in odds ratio: 348.17%.\n",
      "Change in probability: 0.86%.\n"
     ]
    }
   ],
   "source": [
    "gauge_effect(1.5, 1)\n",
    "gauge_effect(1.5, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-25T14:55:51.252280Z",
     "start_time": "2019-02-25T14:55:51.196779Z"
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     "execution_count": 60,
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    "np.exp(1.5)"
   ]
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   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-11T13:50:07.225368Z",
     "start_time": "2019-02-11T13:50:07.191131Z"
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   "outputs": [
    {
     "data": {
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     "execution_count": 26,
     "metadata": {},
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    }
   ],
   "source": [
    "probs_to_odds(logits_to_probs(0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-11T13:49:55.279633Z",
     "start_time": "2019-02-11T13:49:55.247997Z"
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   "source": [
    "logits_to_odds(0.5)"
   ]
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   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-11T13:48:54.113628Z",
     "start_time": "2019-02-11T13:48:54.079034Z"
    }
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      ]
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     "execution_count": 23,
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   ],
   "source": [
    "odds_to_probs(10) - odds_to_probs(10.15)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-11T13:48:39.556904Z",
     "start_time": "2019-02-11T13:48:39.526284Z"
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     "execution_count": 22,
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    "odds_to_probs(1.15) - odds_to_probs(1.3)"
   ]
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   ],
   "source": [
    "probs_to_odds(logits_to_probs(1))\n",
    "logits_to_probs(2) \n",
    "logits_to_probs(4)"
   ]
  },
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   "cell_type": "code",
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    "logits_to_probs(9)\n",
    "logits_to_probs(10) "
   ]
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   ],
   "source": [
    "np.exp(1) / np.exp(0)\n",
    "np.exp(3) / np.exp(2)"
   ]
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    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}