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+{
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+ "cells": [
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+ {
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+ "cell_type": "code",
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+ "execution_count": 1,
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+ "metadata": {},
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+ "outputs": [
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+ {
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+ "data": {
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+ "text/html": [
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+ "<div>\n",
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+ "<style scoped>\n",
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+ " .dataframe tbody tr th:only-of-type {\n",
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+ " vertical-align: middle;\n",
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+ " }\n",
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+ "\n",
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+ " .dataframe tbody tr th {\n",
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+ " vertical-align: top;\n",
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+ " }\n",
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+ "\n",
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+ " .dataframe thead th {\n",
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+ " text-align: right;\n",
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+ " }\n",
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+ "</style>\n",
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+ "<table border=\"1\" class=\"dataframe\">\n",
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+ " <thead>\n",
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+ " <tr style=\"text-align: right;\">\n",
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+ " <th></th>\n",
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+ " <th>x1</th>\n",
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+ " <th>x2</th>\n",
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+ " <th>x3</th>\n",
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+ " </tr>\n",
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+ " </thead>\n",
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+ " <tbody>\n",
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+ " <tr>\n",
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+ " <th>0</th>\n",
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+ " <td>0</td>\n",
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+ " <td>0</td>\n",
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+ " <td>0.894992</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>1</th>\n",
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+ " <td>0</td>\n",
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+ " <td>1</td>\n",
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+ " <td>0.596078</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>2</th>\n",
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+ " <td>0</td>\n",
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+ " <td>2</td>\n",
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+ " <td>0.435564</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>3</th>\n",
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+ " <td>1</td>\n",
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+ " <td>0</td>\n",
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+ " <td>1.153073</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>4</th>\n",
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+ " <td>1</td>\n",
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+ " <td>1</td>\n",
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+ " <td>1.340793</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>5</th>\n",
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+ " <td>1</td>\n",
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+ " <td>2</td>\n",
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+ " <td>1.621597</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>6</th>\n",
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+ " <td>2</td>\n",
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+ " <td>0</td>\n",
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+ " <td>2.139849</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>7</th>\n",
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+ " <td>2</td>\n",
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+ " <td>1</td>\n",
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+ " <td>2.488654</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>8</th>\n",
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+ " <td>2</td>\n",
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+ " <td>2</td>\n",
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+ " <td>2.049478</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>9</th>\n",
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+ " <td>0</td>\n",
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+ " <td>0</td>\n",
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+ " <td>0.564523</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>10</th>\n",
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+ " <td>0</td>\n",
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+ " <td>1</td>\n",
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+ " <td>0.270165</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>11</th>\n",
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+ " <td>0</td>\n",
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+ " <td>2</td>\n",
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+ " <td>0.596075</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>12</th>\n",
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+ " <td>1</td>\n",
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+ " <td>0</td>\n",
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+ " <td>1.291240</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>13</th>\n",
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+ " <td>1</td>\n",
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+ " <td>1</td>\n",
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+ " <td>1.251871</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>14</th>\n",
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+ " <td>1</td>\n",
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+ " <td>2</td>\n",
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+ " <td>1.110560</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>15</th>\n",
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+ " <td>2</td>\n",
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+ " <td>0</td>\n",
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+ " <td>2.805694</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>16</th>\n",
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+ " <td>2</td>\n",
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+ " <td>1</td>\n",
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+ " <td>2.465100</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>17</th>\n",
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+ " <td>2</td>\n",
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+ " <td>2</td>\n",
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+ " <td>2.258865</td>\n",
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+ " </tr>\n",
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+ " </tbody>\n",
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+ "</table>\n",
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+ "</div>"
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+ ],
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+ "text/plain": [
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+ " x1 x2 x3\n",
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+ "0 0 0 0.894992\n",
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+ "1 0 1 0.596078\n",
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+ "2 0 2 0.435564\n",
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+ "3 1 0 1.153073\n",
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+ "4 1 1 1.340793\n",
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+ "5 1 2 1.621597\n",
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+ "6 2 0 2.139849\n",
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+ "7 2 1 2.488654\n",
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+ "8 2 2 2.049478\n",
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+ "9 0 0 0.564523\n",
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+ "10 0 1 0.270165\n",
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+ "11 0 2 0.596075\n",
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+ "12 1 0 1.291240\n",
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+ "13 1 1 1.251871\n",
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+ "14 1 2 1.110560\n",
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+ "15 2 0 2.805694\n",
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+ "16 2 1 2.465100\n",
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+ "17 2 2 2.258865"
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+ ]
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+ },
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+ "execution_count": 1,
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+ "metadata": {},
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+ "output_type": "execute_result"
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+ }
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+ ],
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+ "source": [
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+ "import numpy as np\n",
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+ "import pandas as pd\n",
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+ "\n",
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+ "\n",
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+ "\n",
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+ "# 生成模型数据，其中x1，x2为不相关的变量；x1，x3强相关\n",
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+ "data = []\n",
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+ "n = 2\n",
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+ "np.random.seed(2046)\n",
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+ "for i in range(0, 3):\n",
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+ " for j in range(0, 3):\n",
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+ " # x1，x2为不相关的变量\n",
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+ " data.append({\"x1\": i, \"x2\": j})\n",
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+ "data = pd.DataFrame(data * n)\n",
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+ "# 生成强相关自变量\n",
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+ "data[\"x3\"] = data[\"x1\"] + np.random.random(9 * n)\n",
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+ "data"
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+ ]
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+ },
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+ {
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+ "cell_type": "code",
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+ "execution_count": 2,
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+ "metadata": {},
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+ "outputs": [
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+ {
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+ "data": {
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+ "text/html": [
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+ "<div>\n",
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+ "<style scoped>\n",
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+ " .dataframe tbody tr th:only-of-type {\n",
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+ " vertical-align: middle;\n",
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+ " }\n",
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+ "\n",
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+ " .dataframe tbody tr th {\n",
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+ " vertical-align: top;\n",
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+ " }\n",
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+ "\n",
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+ " .dataframe thead th {\n",
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+ " text-align: right;\n",
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+ " }\n",
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+ "</style>\n",
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+ "<table border=\"1\" class=\"dataframe\">\n",
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+ " <thead>\n",
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+ " <tr style=\"text-align: right;\">\n",
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+ " <th></th>\n",
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+ " <th>const</th>\n",
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+ " <th>x1</th>\n",
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+ " <th>x2</th>\n",
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+ " <th>x3</th>\n",
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+ " </tr>\n",
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+ " </thead>\n",
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+ " <tbody>\n",
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+ " <tr>\n",
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+ " <th>0</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>0</td>\n",
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+ " <td>0</td>\n",
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+ " <td>0.894992</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>1</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>0</td>\n",
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+ " <td>1</td>\n",
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+ " <td>0.596078</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>2</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>0</td>\n",
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+ " <td>2</td>\n",
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+ " <td>0.435564</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>3</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>1</td>\n",
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+ " <td>0</td>\n",
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+ " <td>1.153073</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>4</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>1</td>\n",
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+ " <td>1</td>\n",
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+ " <td>1.340793</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>5</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>1</td>\n",
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+ " <td>2</td>\n",
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+ " <td>1.621597</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>6</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>2</td>\n",
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+ " <td>0</td>\n",
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+ " <td>2.139849</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>7</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>2</td>\n",
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+ " <td>1</td>\n",
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+ " <td>2.488654</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>8</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>2</td>\n",
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+ " <td>2</td>\n",
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+ " <td>2.049478</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>9</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>0</td>\n",
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+ " <td>0</td>\n",
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+ " <td>0.564523</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>10</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>0</td>\n",
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+ " <td>1</td>\n",
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+ " <td>0.270165</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>11</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>0</td>\n",
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+ " <td>2</td>\n",
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+ " <td>0.596075</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>12</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>1</td>\n",
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+ " <td>0</td>\n",
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+ " <td>1.291240</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>13</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>1</td>\n",
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+ " <td>1</td>\n",
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+ " <td>1.251871</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>14</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>1</td>\n",
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+ " <td>2</td>\n",
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+ " <td>1.110560</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>15</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>2</td>\n",
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+ " <td>0</td>\n",
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+ " <td>2.805694</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
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+ " <th>16</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>2</td>\n",
|
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+ " <td>1</td>\n",
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+ " <td>2.465100</td>\n",
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+ " </tr>\n",
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+ " <tr>\n",
|
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+ " <th>17</th>\n",
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+ " <td>1.0</td>\n",
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+ " <td>2</td>\n",
|
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+ " <td>2</td>\n",
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+ " <td>2.258865</td>\n",
|
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+ " </tr>\n",
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+ " </tbody>\n",
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+ "</table>\n",
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+ "</div>"
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+ ],
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+ "text/plain": [
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+ " const x1 x2 x3\n",
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+ "0 1.0 0 0 0.894992\n",
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+ "1 1.0 0 1 0.596078\n",
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+ "2 1.0 0 2 0.435564\n",
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+ "3 1.0 1 0 1.153073\n",
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+ "4 1.0 1 1 1.340793\n",
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+ "5 1.0 1 2 1.621597\n",
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+ "6 1.0 2 0 2.139849\n",
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+ "7 1.0 2 1 2.488654\n",
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+ "8 1.0 2 2 2.049478\n",
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+ "9 1.0 0 0 0.564523\n",
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+ "10 1.0 0 1 0.270165\n",
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+ "11 1.0 0 2 0.596075\n",
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+ "12 1.0 1 0 1.291240\n",
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+ "13 1.0 1 1 1.251871\n",
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+ "14 1.0 1 2 1.110560\n",
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+ "15 1.0 2 0 2.805694\n",
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+ "16 1.0 2 1 2.465100\n",
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+ "17 1.0 2 2 2.258865"
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+ ]
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+ },
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+ "execution_count": 2,
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+ "metadata": {},
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+ "output_type": "execute_result"
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+ }
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+ ],
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+ "source": [
|
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+ "import statsmodels.api as sm\n",
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+ "\n",
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+ "\n",
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+ "# 在数据中加入常数项（如果无）\n",
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+ "X = sm.add_constant(data[[\"x1\", \"x2\", \"x3\"]])\n",
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+ "X"
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+ ]
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+ },
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+ {
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+ "cell_type": "code",
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+ "execution_count": 3,
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+ "metadata": {},
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+ "outputs": [
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+ {
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+ "name": "stdout",
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+ "output_type": "stream",
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+ "text": [
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+ "variance inflation factor, VIF, for one exogenous variable\n",
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+ "\n",
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+ " The variance inflation factor is a measure for the increase of the\n",
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+ " variance of the parameter estimates if an additional variable, given by\n",
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+ " exog_idx is added to the linear regression. It is a measure for\n",
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+ " multicollinearity of the design matrix, exog.\n",
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+ "\n",
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+ " One recommendation is that if VIF is greater than 5, then the explanatory\n",
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+ " variable given by exog_idx is highly collinear with the other explanatory\n",
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+ " variables, and the parameter estimates will have large standard errors\n",
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+ " because of this.\n",
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+ "\n",
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+ " Parameters\n",
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+ " ----------\n",
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+ " exog : ndarray\n",
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+ " design matrix with all explanatory variables, as for example used in\n",
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+ " regression\n",
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+ " exog_idx : int\n",
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+ " index of the exogenous variable in the columns of exog\n",
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+ "\n",
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+ " Returns\n",
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+ " -------\n",
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+ " vif : float\n",
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+ " variance inflation factor\n",
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+ "\n",
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+ " Notes\n",
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+ " -----\n",
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+ " This function does not save the auxiliary regression.\n",
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+ "\n",
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+ " See Also\n",
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+ " --------\n",
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+ " xxx : class for regression diagnostics TODO: doesn't exist yet\n",
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+ "\n",
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+ " References\n",
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+ " ----------\n",
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+ " http://en.wikipedia.org/wiki/Variance_inflation_factor\n",
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+ "\n",
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+ " \n"
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+ ]
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+ }
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+ ],
|
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+ "source": [
|
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+ "from statsmodels.stats.outliers_influence import variance_inflation_factor\n",
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+ "\n",
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+ "\n",
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+ "print(variance_inflation_factor.__doc__)"
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+ ]
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+ },
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+ {
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+ "cell_type": "code",
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+ "execution_count": 4,
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+ "metadata": {},
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+ "outputs": [
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+ {
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+ "data": {
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+ "text/html": [
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+ "<div>\n",
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+ "<style scoped>\n",
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+ " .dataframe tbody tr th:only-of-type {\n",
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+ " vertical-align: middle;\n",
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+ " }\n",
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+ "\n",
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+ " .dataframe tbody tr th {\n",
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+ " vertical-align: top;\n",
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+ " }\n",
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+ "\n",
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+ " .dataframe thead th {\n",
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+ " text-align: right;\n",
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+ " }\n",
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+ "</style>\n",
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+ "<table border=\"1\" class=\"dataframe\">\n",
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+ " <thead>\n",
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+ " <tr style=\"text-align: right;\">\n",
|
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+ " <th></th>\n",
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+ " <th>VIF Factor</th>\n",
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+ " <th>features</th>\n",
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+ " </tr>\n",
|
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+ " </thead>\n",
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+ " <tbody>\n",
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+ " <tr>\n",
|
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+ " <th>0</th>\n",
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+ " <td>11.049590</td>\n",
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+ " <td>const</td>\n",
|
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+ " </tr>\n",
|
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+ " <tr>\n",
|
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+ " <th>1</th>\n",
|
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+ " <td>12.907932</td>\n",
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+ " <td>x1</td>\n",
|
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+ " </tr>\n",
|
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+ " <tr>\n",
|
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+ " <th>2</th>\n",
|
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+ " <td>1.061102</td>\n",
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+ " <td>x2</td>\n",
|
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+ " </tr>\n",
|
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+ " <tr>\n",
|
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+ " <th>3</th>\n",
|
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+ " <td>12.969034</td>\n",
|
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+ " <td>x3</td>\n",
|
|
|
+ " </tr>\n",
|
|
|
+ " </tbody>\n",
|
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+ "</table>\n",
|
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+ "</div>"
|
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+ ],
|
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+ "text/plain": [
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+ " VIF Factor features\n",
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+ "0 11.049590 const\n",
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+ "1 12.907932 x1\n",
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+ "2 1.061102 x2\n",
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+ "3 12.969034 x3"
|
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+ ]
|
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+ },
|
|
|
+ "execution_count": 4,
|
|
|
+ "metadata": {},
|
|
|
+ "output_type": "execute_result"
|
|
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+ }
|
|
|
+ ],
|
|
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+ "source": [
|
|
|
+ "vif = pd.DataFrame()\n",
|
|
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+ "vif[\"VIF Factor\"] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])]\n",
|
|
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+ "vif[\"features\"] = X.columns\n",
|
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+ "vif"
|
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|
+ ]
|
|
|
+ }
|
|
|
+ ],
|
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+ "metadata": {
|
|
|
+ "kernelspec": {
|
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+ "display_name": "Python 3",
|
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+ "language": "python",
|
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+ "name": "python3"
|
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+ },
|
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+ "language_info": {
|
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+ "codemirror_mode": {
|
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+ "name": "ipython",
|
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+ "version": 3
|
|
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+ },
|
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+ "file_extension": ".py",
|
|
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+ "mimetype": "text/x-python",
|
|
|
+ "name": "python",
|
|
|
+ "nbconvert_exporter": "python",
|
|
|
+ "pygments_lexer": "ipython3",
|
|
|
+ "version": "3.6.6"
|
|
|
+ }
|
|
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+ },
|
|
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+ "nbformat": 4,
|
|
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+ "nbformat_minor": 2
|
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+}
|
Gen TANG