6-3-logistic回归.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 第 3 节　logistic 回归\n",
    "## 第 6 章　广义线性模型｜用 Python 动手学统计学\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 10. 环境准备"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# 用于数值计算的库\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "from scipy import stats\n",
    "\n",
    "# 用于绘图的库\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "\n",
    "# 用于估计统计模型的库 (部分版本会报出警告信息)\n",
    "import statsmodels.formula.api as smf\n",
    "import statsmodels.api as sm\n",
    "\n",
    "# 设置浮点数打印精度\n",
    "%precision 3\n",
    "# 在 Jupyter Notebook 里显示图形\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 11. 实现：读取数据并可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   hours  result\n",
      "0      0       0\n",
      "1      0       0\n",
      "2      0       0\n"
     ]
    }
   ],
   "source": [
    "# 读取数据\n",
    "test_result = pd.read_csv(\"6-3-1-logistic-regression.csv\")\n",
    "print(test_result.head(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1506159ea20>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1505d7cef60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 可视化\n",
    "sns.barplot(x = \"hours\",y = \"result\", \n",
    "            data = test_result, palette='gray_r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       result\n",
      "hours        \n",
      "0         0.0\n",
      "1         0.0\n",
      "2         0.1\n",
      "3         0.1\n",
      "4         0.4\n",
      "5         0.4\n",
      "6         0.9\n",
      "7         0.8\n",
      "8         0.9\n",
      "9         1.0\n"
     ]
    }
   ],
   "source": [
    "# 学习时间与合格率的关系\n",
    "print(test_result.groupby(\"hours\").mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 12. 实现：logistic 回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 建模\n",
    "mod_glm = smf.glm(formula = \"result ~ hours\", \n",
    "                  data = test_result, \n",
    "                  family=sm.families.Binomial()).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 参考: 指定联系函数\n",
    "logistic_reg = smf.glm(formula = \"result ~ hours\", \n",
    "                       data = test_result, \n",
    "                       family=sm.families.Binomial(link=sm.families.links.logit)).fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 13. 实现：logistic 回归的结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Generalized Linear Model Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>result</td>      <th>  No. Observations:  </th>  <td>   100</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                 <td>GLM</td>       <th>  Df Residuals:      </th>  <td>    98</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model Family:</th>       <td>Binomial</td>     <th>  Df Model:          </th>  <td>     1</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Link Function:</th>        <td>logit</td>      <th>  Scale:             </th>    <td>1.0</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>IRLS</td>       <th>  Log-Likelihood:    </th> <td> -34.014</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>           <td>Thu, 15 Mar 2018</td> <th>  Deviance:          </th> <td>  68.028</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>               <td>15:27:16</td>     <th>  Pearson chi2:      </th>  <td>  84.9</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Iterations:</th>         <td>6</td>        <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   -4.5587</td> <td>    0.901</td> <td>   -5.061</td> <td> 0.000</td> <td>   -6.324</td> <td>   -2.793</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>hours</th>     <td>    0.9289</td> <td>    0.174</td> <td>    5.345</td> <td> 0.000</td> <td>    0.588</td> <td>    1.270</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                 Generalized Linear Model Regression Results                  \n",
       "==============================================================================\n",
       "Dep. Variable:                 result   No. Observations:                  100\n",
       "Model:                            GLM   Df Residuals:                       98\n",
       "Model Family:                Binomial   Df Model:                            1\n",
       "Link Function:                  logit   Scale:                             1.0\n",
       "Method:                          IRLS   Log-Likelihood:                -34.014\n",
       "Date:                Thu, 15 Mar 2018   Deviance:                       68.028\n",
       "Time:                        15:27:16   Pearson chi2:                     84.9\n",
       "No. Iterations:                     6                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     -4.5587      0.901     -5.061      0.000      -6.324      -2.793\n",
       "hours          0.9289      0.174      5.345      0.000       0.588       1.270\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 打印估计的结果\n",
    "mod_glm.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 14. 实现：模型选择"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 空模型\n",
    "mod_glm_null = smf.glm(\n",
    "    \"result ~ 1\", data = test_result, \n",
    "    family=sm.families.Binomial()).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "空模型　　　： 139.989\n",
      "学习时间模型： 72.028\n"
     ]
    }
   ],
   "source": [
    "# 对比 AIC\n",
    "print(\"空模型　　　：\", mod_glm_null.aic.round(3))\n",
    "print(\"学习时间模型：\", mod_glm.aic.round(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 15. 实现：回归曲线"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x2d7327032b0>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ymr+zZ2/d+1VRbF16v92TJGAhtsPtVrvjxYYN5bzzztsA7LWXxpFHjlISV3q/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\n+p5xQrQmCVgkld/vV7bTBcC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oCXr1b0wwGMTn8+L1+vD5vAmdpxsTDofR9R/54ovP+eqr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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d7328b5ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 用 lmplot 绘制 logistic 回归曲线\n",
    "sns.lmplot(x = \"hours\", y = \"result\",\n",
    "           data = test_result, \n",
    "           logistic = True,\n",
    "           scatter_kws = {\"color\": \"black\"},\n",
    "           line_kws    = {\"color\": \"black\"},\n",
    "           x_jitter = 0.1, y_jitter = 0.02)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 16. 实现：预测成功概率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0.010367\n",
       "1    0.025836\n",
       "2    0.062920\n",
       "3    0.145291\n",
       "4    0.300876\n",
       "5    0.521427\n",
       "6    0.733929\n",
       "7    0.874741\n",
       "8    0.946467\n",
       "9    0.978147\n",
       "dtype: float64"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 0~9 上公差为 1 的等差数列\n",
    "exp_val = pd.DataFrame({\n",
    "    \"hours\": np.arange(0, 10, 1)\n",
    "})\n",
    "# 成功概率的预测值\n",
    "pred = mod_glm.predict(exp_val)\n",
    "pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 19. logistic 回归的系数与优势比的关系"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 学习时间为 1 小时的合格率\n",
    "exp_val_1 = pd.DataFrame({\"hours\": [1]})\n",
    "pred_1 = mod_glm.predict(exp_val_1)\n",
    "\n",
    "# 学习时间为 2 小时的合格率\n",
    "exp_val_2 = pd.DataFrame({\"hours\": [2]})\n",
    "pred_2 = mod_glm.predict(exp_val_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.929])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 优势\n",
    "odds_1 = pred_1 / (1 - pred_1)\n",
    "odds_2 = pred_2 / (1 - pred_2)\n",
    "\n",
    "# 对数优势比\n",
    "sp.log(odds_2 / odds_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.929"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 系数\n",
    "mod_glm.params[\"hours\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.532"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 补充: 系数为 e 的指数时，其结果就是优势比\n",
    "sp.exp(mod_glm.params[\"hours\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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