{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "3fb7b88f-08d6-47b5-9c0a-a5a881c70a06",
   "metadata": {},
   "source": [
    "# 多項ロジットモデル"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "f1f520d5-7de8-4f5c-9467-83c42cfab30b",
   "metadata": {},
   "source": [
    "**多項ロジットモデル（multinomial logt model）**\n",
    "多項ロジットモデルは、被説明変数が取りうる値が3つ以上で、それらに順序がない場合に適用します。\n",
    "\n",
    "例えば、移動手段（バス・自動車・電車・徒歩・自転車・その他）を選択肢から選ぶ場合や、消費者が購入する商品を、ブランドA、ブランドB、ブランドCから選択する場合などに適用することができます。\n",
    "\n",
    "\n",
    "`statsmodels`を用いて推定します。\n",
    " \n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "97dfb2ec-0a0c-4f07-bb9a-9a71d8f245f1",
   "metadata": {},
   "source": [
    "ここではスマートフォンを用いて収集されたセンサーデータから、スマートフォンユーザーの移動手段を推定する例を考えます。\n",
    "\n",
    "このデータは、13人のボランティア（男性10名、女性3名）のスマートフォンから収集したデータで、徒歩、車、静止状態、電車、バスの5クラスで構成されています。\n",
    "\n",
    "データ出典: http://cs.unibo.it/projects/us-tm2017/index.html\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "59fda80a-e557-4340-8ac0-e3d04ea3e211",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "a7d69837-c602-4a12-8b61-9b70e00df5ad",
   "metadata": {},
   "source": [
    "まずはデータをダウンロードします。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b708a515-40a5-44a2-a68f-3388d77e4614",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dataset_5secondWindow.csv</th>\n",
       "      <th>id</th>\n",
       "      <th>time</th>\n",
       "      <th>activityrecognition#0</th>\n",
       "      <th>activityrecognition#1</th>\n",
       "      <th>android.sensor.accelerometer#mean</th>\n",
       "      <th>android.sensor.accelerometer#min</th>\n",
       "      <th>android.sensor.accelerometer#max</th>\n",
       "      <th>android.sensor.accelerometer#std</th>\n",
       "      <th>android.sensor.game_rotation_vector#mean</th>\n",
       "      <th>android.sensor.game_rotation_vector#min</th>\n",
       "      <th>android.sensor.game_rotation_vector#max</th>\n",
       "      <th>android.sensor.game_rotation_vector#std</th>\n",
       "      <th>android.sensor.gravity#mean</th>\n",
       "      <th>android.sensor.gravity#min</th>\n",
       "      <th>android.sensor.gravity#max</th>\n",
       "      <th>android.sensor.gravity#std</th>\n",
       "      <th>android.sensor.gyroscope#mean</th>\n",
       "      <th>android.sensor.gyroscope#min</th>\n",
       "      <th>android.sensor.gyroscope#max</th>\n",
       "      <th>android.sensor.gyroscope#std</th>\n",
       "      <th>android.sensor.gyroscope_uncalibrated#mean</th>\n",
       "      <th>android.sensor.gyroscope_uncalibrated#min</th>\n",
       "      <th>android.sensor.gyroscope_uncalibrated#max</th>\n",
       "      <th>android.sensor.gyroscope_uncalibrated#std</th>\n",
       "      <th>android.sensor.light#mean</th>\n",
       "      <th>android.sensor.light#min</th>\n",
       "      <th>android.sensor.light#max</th>\n",
       "      <th>android.sensor.light#std</th>\n",
       "      <th>android.sensor.linear_acceleration#mean</th>\n",
       "      <th>android.sensor.linear_acceleration#min</th>\n",
       "      <th>android.sensor.linear_acceleration#max</th>\n",
       "      <th>android.sensor.linear_acceleration#std</th>\n",
       "      <th>android.sensor.magnetic_field#mean</th>\n",
       "      <th>android.sensor.magnetic_field#min</th>\n",
       "      <th>android.sensor.magnetic_field#max</th>\n",
       "      <th>android.sensor.magnetic_field#std</th>\n",
       "      <th>android.sensor.magnetic_field_uncalibrated#mean</th>\n",
       "      <th>android.sensor.magnetic_field_uncalibrated#min</th>\n",
       "      <th>android.sensor.magnetic_field_uncalibrated#max</th>\n",
       "      <th>android.sensor.magnetic_field_uncalibrated#std</th>\n",
       "      <th>android.sensor.orientation#mean</th>\n",
       "      <th>android.sensor.orientation#min</th>\n",
       "      <th>android.sensor.orientation#max</th>\n",
       "      <th>android.sensor.orientation#std</th>\n",
       "      <th>android.sensor.pressure#mean</th>\n",
       "      <th>android.sensor.pressure#min</th>\n",
       "      <th>android.sensor.pressure#max</th>\n",
       "      <th>android.sensor.pressure#std</th>\n",
       "      <th>android.sensor.proximity#mean</th>\n",
       "      <th>android.sensor.proximity#min</th>\n",
       "      <th>android.sensor.proximity#max</th>\n",
       "      <th>android.sensor.proximity#std</th>\n",
       "      <th>android.sensor.rotation_vector#mean</th>\n",
       "      <th>android.sensor.rotation_vector#min</th>\n",
       "      <th>android.sensor.rotation_vector#max</th>\n",
       "      <th>android.sensor.rotation_vector#std</th>\n",
       "      <th>android.sensor.step_counter#mean</th>\n",
       "      <th>android.sensor.step_counter#min</th>\n",
       "      <th>android.sensor.step_counter#max</th>\n",
       "      <th>android.sensor.step_counter#std</th>\n",
       "      <th>sound#mean</th>\n",
       "      <th>sound#min</th>\n",
       "      <th>sound#max</th>\n",
       "      <th>sound#std</th>\n",
       "      <th>speed#mean</th>\n",
       "      <th>speed#min</th>\n",
       "      <th>speed#max</th>\n",
       "      <th>speed#std</th>\n",
       "      <th>target</th>\n",
       "      <th>user</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>16170.0</td>\n",
       "      <td>78.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>100.0</td>\n",
       "      <td>9.811476</td>\n",
       "      <td>9.758895</td>\n",
       "      <td>9.849411</td>\n",
       "      <td>0.014626</td>\n",
       "      <td>0.029340</td>\n",
       "      <td>0.029014</td>\n",
       "      <td>0.029526</td>\n",
       "      <td>0.000119</td>\n",
       "      <td>9.806650</td>\n",
       "      <td>9.806649</td>\n",
       "      <td>9.806651</td>\n",
       "      <td>4.780692e-07</td>\n",
       "      <td>0.001651</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.003533</td>\n",
       "      <td>0.000737</td>\n",
       "      <td>0.016221</td>\n",
       "      <td>0.014172</td>\n",
       "      <td>0.018695</td>\n",
       "      <td>0.000982</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.020978</td>\n",
       "      <td>0.002495</td>\n",
       "      <td>0.05241</td>\n",
       "      <td>0.011045</td>\n",
       "      <td>57.099638</td>\n",
       "      <td>56.690387</td>\n",
       "      <td>57.575950</td>\n",
       "      <td>0.177549</td>\n",
       "      <td>51.363566</td>\n",
       "      <td>51.199707</td>\n",
       "      <td>51.539208</td>\n",
       "      <td>0.080899</td>\n",
       "      <td>354.286933</td>\n",
       "      <td>353.598335</td>\n",
       "      <td>354.942707</td>\n",
       "      <td>0.245676</td>\n",
       "      <td>1004.090261</td>\n",
       "      <td>1004.05540</td>\n",
       "      <td>1004.12790</td>\n",
       "      <td>0.017416</td>\n",
       "      <td>8.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.050413</td>\n",
       "      <td>0.044777</td>\n",
       "      <td>0.056351</td>\n",
       "      <td>0.002109</td>\n",
       "      <td>28966.0</td>\n",
       "      <td>28966.0</td>\n",
       "      <td>28966.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>Still</td>\n",
       "      <td>U12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>15871.0</td>\n",
       "      <td>145.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>100.0</td>\n",
       "      <td>9.939207</td>\n",
       "      <td>7.707437</td>\n",
       "      <td>17.146631</td>\n",
       "      <td>1.775944</td>\n",
       "      <td>0.999925</td>\n",
       "      <td>0.999903</td>\n",
       "      <td>0.999946</td>\n",
       "      <td>0.000030</td>\n",
       "      <td>9.806624</td>\n",
       "      <td>9.806624</td>\n",
       "      <td>9.806624</td>\n",
       "      <td>6.474977e-07</td>\n",
       "      <td>0.036326</td>\n",
       "      <td>0.011669</td>\n",
       "      <td>0.059388</td>\n",
       "      <td>0.020290</td>\n",
       "      <td>0.039023</td>\n",
       "      <td>0.014132</td>\n",
       "      <td>0.085494</td>\n",
       "      <td>0.018629</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.879220</td>\n",
       "      <td>0.641117</td>\n",
       "      <td>1.18581</td>\n",
       "      <td>0.278730</td>\n",
       "      <td>29.351288</td>\n",
       "      <td>28.172505</td>\n",
       "      <td>30.386017</td>\n",
       "      <td>0.921547</td>\n",
       "      <td>82.767760</td>\n",
       "      <td>82.409890</td>\n",
       "      <td>83.125630</td>\n",
       "      <td>0.506105</td>\n",
       "      <td>332.695577</td>\n",
       "      <td>330.461054</td>\n",
       "      <td>339.108607</td>\n",
       "      <td>1.705816</td>\n",
       "      <td>1008.274660</td>\n",
       "      <td>1008.27466</td>\n",
       "      <td>1008.27466</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.999981</td>\n",
       "      <td>0.999963</td>\n",
       "      <td>0.999999</td>\n",
       "      <td>0.000026</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>89.20021</td>\n",
       "      <td>89.065143</td>\n",
       "      <td>89.335277</td>\n",
       "      <td>0.191013</td>\n",
       "      <td>16.539349</td>\n",
       "      <td>16.539349</td>\n",
       "      <td>16.539349</td>\n",
       "      <td>0.628595</td>\n",
       "      <td>Car</td>\n",
       "      <td>U12</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   dataset_5secondWindow.csv       id   time  activityrecognition#0  \\\n",
       "0                        0.0  16170.0   78.0                    NaN   \n",
       "1                        1.0  15871.0  145.0                    NaN   \n",
       "\n",
       "   activityrecognition#1  android.sensor.accelerometer#mean  \\\n",
       "0                  100.0                           9.811476   \n",
       "1                  100.0                           9.939207   \n",
       "\n",
       "   android.sensor.accelerometer#min  android.sensor.accelerometer#max  \\\n",
       "0                          9.758895                          9.849411   \n",
       "1                          7.707437                         17.146631   \n",
       "\n",
       "   android.sensor.accelerometer#std  android.sensor.game_rotation_vector#mean  \\\n",
       "0                          0.014626                                  0.029340   \n",
       "1                          1.775944                                  0.999925   \n",
       "\n",
       "   android.sensor.game_rotation_vector#min  \\\n",
       "0                                 0.029014   \n",
       "1                                 0.999903   \n",
       "\n",
       "   android.sensor.game_rotation_vector#max  \\\n",
       "0                                 0.029526   \n",
       "1                                 0.999946   \n",
       "\n",
       "   android.sensor.game_rotation_vector#std  android.sensor.gravity#mean  \\\n",
       "0                                 0.000119                     9.806650   \n",
       "1                                 0.000030                     9.806624   \n",
       "\n",
       "   android.sensor.gravity#min  android.sensor.gravity#max  \\\n",
       "0                    9.806649                    9.806651   \n",
       "1                    9.806624                    9.806624   \n",
       "\n",
       "   android.sensor.gravity#std  android.sensor.gyroscope#mean  \\\n",
       "0                4.780692e-07                       0.001651   \n",
       "1                6.474977e-07                       0.036326   \n",
       "\n",
       "   android.sensor.gyroscope#min  android.sensor.gyroscope#max  \\\n",
       "0                      0.000000                      0.003533   \n",
       "1                      0.011669                      0.059388   \n",
       "\n",
       "   android.sensor.gyroscope#std  android.sensor.gyroscope_uncalibrated#mean  \\\n",
       "0                      0.000737                                    0.016221   \n",
       "1                      0.020290                                    0.039023   \n",
       "\n",
       "   android.sensor.gyroscope_uncalibrated#min  \\\n",
       "0                                   0.014172   \n",
       "1                                   0.014132   \n",
       "\n",
       "   android.sensor.gyroscope_uncalibrated#max  \\\n",
       "0                                   0.018695   \n",
       "1                                   0.085494   \n",
       "\n",
       "   android.sensor.gyroscope_uncalibrated#std  android.sensor.light#mean  \\\n",
       "0                                   0.000982                        0.0   \n",
       "1                                   0.018629                        0.0   \n",
       "\n",
       "   android.sensor.light#min  android.sensor.light#max  \\\n",
       "0                       0.0                       0.0   \n",
       "1                       0.0                       0.0   \n",
       "\n",
       "   android.sensor.light#std  android.sensor.linear_acceleration#mean  \\\n",
       "0                       0.0                                 0.020978   \n",
       "1                       NaN                                 0.879220   \n",
       "\n",
       "   android.sensor.linear_acceleration#min  \\\n",
       "0                                0.002495   \n",
       "1                                0.641117   \n",
       "\n",
       "   android.sensor.linear_acceleration#max  \\\n",
       "0                                 0.05241   \n",
       "1                                 1.18581   \n",
       "\n",
       "   android.sensor.linear_acceleration#std  android.sensor.magnetic_field#mean  \\\n",
       "0                                0.011045                           57.099638   \n",
       "1                                0.278730                           29.351288   \n",
       "\n",
       "   android.sensor.magnetic_field#min  android.sensor.magnetic_field#max  \\\n",
       "0                          56.690387                          57.575950   \n",
       "1                          28.172505                          30.386017   \n",
       "\n",
       "   android.sensor.magnetic_field#std  \\\n",
       "0                           0.177549   \n",
       "1                           0.921547   \n",
       "\n",
       "   android.sensor.magnetic_field_uncalibrated#mean  \\\n",
       "0                                        51.363566   \n",
       "1                                        82.767760   \n",
       "\n",
       "   android.sensor.magnetic_field_uncalibrated#min  \\\n",
       "0                                       51.199707   \n",
       "1                                       82.409890   \n",
       "\n",
       "   android.sensor.magnetic_field_uncalibrated#max  \\\n",
       "0                                       51.539208   \n",
       "1                                       83.125630   \n",
       "\n",
       "   android.sensor.magnetic_field_uncalibrated#std  \\\n",
       "0                                        0.080899   \n",
       "1                                        0.506105   \n",
       "\n",
       "   android.sensor.orientation#mean  android.sensor.orientation#min  \\\n",
       "0                       354.286933                      353.598335   \n",
       "1                       332.695577                      330.461054   \n",
       "\n",
       "   android.sensor.orientation#max  android.sensor.orientation#std  \\\n",
       "0                      354.942707                        0.245676   \n",
       "1                      339.108607                        1.705816   \n",
       "\n",
       "   android.sensor.pressure#mean  android.sensor.pressure#min  \\\n",
       "0                   1004.090261                   1004.05540   \n",
       "1                   1008.274660                   1008.27466   \n",
       "\n",
       "   android.sensor.pressure#max  android.sensor.pressure#std  \\\n",
       "0                   1004.12790                     0.017416   \n",
       "1                   1008.27466                          NaN   \n",
       "\n",
       "   android.sensor.proximity#mean  android.sensor.proximity#min  \\\n",
       "0                            8.0                           8.0   \n",
       "1                            NaN                           NaN   \n",
       "\n",
       "   android.sensor.proximity#max  android.sensor.proximity#std  \\\n",
       "0                           8.0                           NaN   \n",
       "1                           NaN                           NaN   \n",
       "\n",
       "   android.sensor.rotation_vector#mean  android.sensor.rotation_vector#min  \\\n",
       "0                             0.050413                            0.044777   \n",
       "1                             0.999981                            0.999963   \n",
       "\n",
       "   android.sensor.rotation_vector#max  android.sensor.rotation_vector#std  \\\n",
       "0                            0.056351                            0.002109   \n",
       "1                            0.999999                            0.000026   \n",
       "\n",
       "   android.sensor.step_counter#mean  android.sensor.step_counter#min  \\\n",
       "0                           28966.0                          28966.0   \n",
       "1                               NaN                              NaN   \n",
       "\n",
       "   android.sensor.step_counter#max  android.sensor.step_counter#std  \\\n",
       "0                          28966.0                              NaN   \n",
       "1                              NaN                              NaN   \n",
       "\n",
       "   sound#mean  sound#min  sound#max  sound#std  speed#mean  speed#min  \\\n",
       "0         NaN        NaN        NaN        NaN    0.000000   0.000000   \n",
       "1    89.20021  89.065143  89.335277   0.191013   16.539349  16.539349   \n",
       "\n",
       "   speed#max  speed#std target user  \n",
       "0   0.000000   0.000000  Still  U12  \n",
       "1  16.539349   0.628595    Car  U12  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "url = \"http://cs.unibo.it/projects/us-tm2017/static/dataset/extension/5second/csv/dataset_5secondWindow.tar.gz\"\n",
    "df = pd.read_csv(url, compression='gzip', header=0, sep=',', quotechar='\"', on_bad_lines='warn')\n",
    "#最初の数行を表示させます\n",
    "pd.set_option('display.max_columns', 100) # すべての列がNotebook上で表示されるように、オプション設定を変更します。\n",
    "df.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "11bf306d-555e-4f55-aef2-25d62b82f30f",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/x2/7ss5kcb12n1gtlpc8p2mtjtw0000gn/T/ipykernel_65166/2509734072.py:2: FutureWarning: The default value of regex will change from True to False in a future version.\n",
      "  df.columns = df.columns.str.replace('android.sensor.','').str.replace('#','_')\n"
     ]
    }
   ],
   "source": [
    "# カラム名をわかりやすさのため変更します\n",
    "df.columns = df.columns.str.replace('android.sensor.','').str.replace('#','_')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "bbeb12c2-a2f1-487d-a18c-d8bbeca0558d",
   "metadata": {},
   "source": [
    "ここでは、移動手段（Car, Still, Train, Bus, Walking）を次の変数を用いて推定するモデルを考えます。\n",
    "\n",
    "* `accelerometer_mean`\n",
    "* `game_rotation_vector_mean`\n",
    "* `gyroscope_mean`\n",
    "* `linear_acceleration_mean`\n",
    "* `orientation_mean` \n",
    "* `pressure_mean`\n",
    "* `rotation_vector_mean`\n",
    "* `sound_mean`\n",
    "\n",
    "上の変数の欠損している行を分析から除外します。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "745f5be0-27f3-43df-9a91-47e0c8bec2aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df[[\n",
    "    'target','accelerometer_mean','game_rotation_vector_mean',\n",
    "    'gyroscope_mean','linear_acceleration_mean','orientation_mean', \n",
    "    'pressure_mean','rotation_vector_mean','sound_mean'\n",
    "]]\n",
    "df = df.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "15726ede-4eac-4f13-95a7-303d678b2b24",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>accelerometer_mean</th>\n",
       "      <th>game_rotation_vector_mean</th>\n",
       "      <th>gyroscope_mean</th>\n",
       "      <th>linear_acceleration_mean</th>\n",
       "      <th>orientation_mean</th>\n",
       "      <th>pressure_mean</th>\n",
       "      <th>rotation_vector_mean</th>\n",
       "      <th>sound_mean</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1255.000000</td>\n",
       "      <td>1255.000000</td>\n",
       "      <td>1255.000000</td>\n",
       "      <td>1255.000000</td>\n",
       "      <td>1255.000000</td>\n",
       "      <td>1255.000000</td>\n",
       "      <td>1255.000000</td>\n",
       "      <td>1255.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>9.996223</td>\n",
       "      <td>0.732083</td>\n",
       "      <td>0.325744</td>\n",
       "      <td>1.507555</td>\n",
       "      <td>208.533199</td>\n",
       "      <td>1020.577142</td>\n",
       "      <td>0.768484</td>\n",
       "      <td>75.202876</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.720097</td>\n",
       "      <td>0.246679</td>\n",
       "      <td>0.496171</td>\n",
       "      <td>1.890074</td>\n",
       "      <td>92.273671</td>\n",
       "      <td>15.173493</td>\n",
       "      <td>0.224416</td>\n",
       "      <td>12.239499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>7.369055</td>\n",
       "      <td>0.042684</td>\n",
       "      <td>0.001164</td>\n",
       "      <td>0.009447</td>\n",
       "      <td>17.135360</td>\n",
       "      <td>946.339840</td>\n",
       "      <td>0.120813</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>9.738144</td>\n",
       "      <td>0.570153</td>\n",
       "      <td>0.027239</td>\n",
       "      <td>0.272564</td>\n",
       "      <td>135.326907</td>\n",
       "      <td>1011.055625</td>\n",
       "      <td>0.668633</td>\n",
       "      <td>71.869349</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>9.830731</td>\n",
       "      <td>0.763646</td>\n",
       "      <td>0.083699</td>\n",
       "      <td>0.707634</td>\n",
       "      <td>206.208459</td>\n",
       "      <td>1020.669000</td>\n",
       "      <td>0.813465</td>\n",
       "      <td>77.707224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>10.049428</td>\n",
       "      <td>0.969717</td>\n",
       "      <td>0.512946</td>\n",
       "      <td>2.083757</td>\n",
       "      <td>291.281798</td>\n",
       "      <td>1029.123300</td>\n",
       "      <td>0.959668</td>\n",
       "      <td>82.794433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>14.661139</td>\n",
       "      <td>0.999999</td>\n",
       "      <td>3.268860</td>\n",
       "      <td>18.141770</td>\n",
       "      <td>396.133498</td>\n",
       "      <td>1058.609900</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>90.308734</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       accelerometer_mean  game_rotation_vector_mean  gyroscope_mean  \\\n",
       "count         1255.000000                1255.000000     1255.000000   \n",
       "mean             9.996223                   0.732083        0.325744   \n",
       "std              0.720097                   0.246679        0.496171   \n",
       "min              7.369055                   0.042684        0.001164   \n",
       "25%              9.738144                   0.570153        0.027239   \n",
       "50%              9.830731                   0.763646        0.083699   \n",
       "75%             10.049428                   0.969717        0.512946   \n",
       "max             14.661139                   0.999999        3.268860   \n",
       "\n",
       "       linear_acceleration_mean  orientation_mean  pressure_mean  \\\n",
       "count               1255.000000       1255.000000    1255.000000   \n",
       "mean                   1.507555        208.533199    1020.577142   \n",
       "std                    1.890074         92.273671      15.173493   \n",
       "min                    0.009447         17.135360     946.339840   \n",
       "25%                    0.272564        135.326907    1011.055625   \n",
       "50%                    0.707634        206.208459    1020.669000   \n",
       "75%                    2.083757        291.281798    1029.123300   \n",
       "max                   18.141770        396.133498    1058.609900   \n",
       "\n",
       "       rotation_vector_mean   sound_mean  \n",
       "count           1255.000000  1255.000000  \n",
       "mean               0.768484    75.202876  \n",
       "std                0.224416    12.239499  \n",
       "min                0.120813     0.000000  \n",
       "25%                0.668633    71.869349  \n",
       "50%                0.813465    77.707224  \n",
       "75%                0.959668    82.794433  \n",
       "max                1.000000    90.308734  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f965f6cc-5f51-46a6-8839-ab6cae3e6c25",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = df.drop('target', axis=1)\n",
    "y = df['target']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e4680aed-a229-40b5-860c-f3ea05910bf9",
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.441453</td>\n",
       "      <td>0.043532</td>\n",
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       "      <th>gyroscope_mean</th>\n",
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       "      <td>1.000000</td>\n",
       "      <td>0.732075</td>\n",
       "      <td>0.050534</td>\n",
       "      <td>-0.032837</td>\n",
       "      <td>0.169035</td>\n",
       "      <td>0.017961</td>\n",
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       "      <th>linear_acceleration_mean</th>\n",
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       "      <td>0.732075</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.096761</td>\n",
       "      <td>-0.099997</td>\n",
       "      <td>0.226298</td>\n",
       "      <td>0.072577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>orientation_mean</th>\n",
       "      <td>0.043532</td>\n",
       "      <td>0.215494</td>\n",
       "      <td>0.050534</td>\n",
       "      <td>0.096761</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.007241</td>\n",
       "      <td>-0.007124</td>\n",
       "      <td>0.016743</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pressure_mean</th>\n",
       "      <td>-0.045848</td>\n",
       "      <td>-0.144826</td>\n",
       "      <td>-0.032837</td>\n",
       "      <td>-0.099997</td>\n",
       "      <td>0.007241</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.288926</td>\n",
       "      <td>0.054731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rotation_vector_mean</th>\n",
       "      <td>0.081403</td>\n",
       "      <td>0.488242</td>\n",
       "      <td>0.169035</td>\n",
       "      <td>0.226298</td>\n",
       "      <td>-0.007124</td>\n",
       "      <td>-0.288926</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.010011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sound_mean</th>\n",
       "      <td>0.138451</td>\n",
       "      <td>0.179971</td>\n",
       "      <td>0.017961</td>\n",
       "      <td>0.072577</td>\n",
       "      <td>0.016743</td>\n",
       "      <td>0.054731</td>\n",
       "      <td>-0.010011</td>\n",
       "      <td>1.000000</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           accelerometer_mean  game_rotation_vector_mean  \\\n",
       "accelerometer_mean                   1.000000                   0.129695   \n",
       "game_rotation_vector_mean            0.129695                   1.000000   \n",
       "gyroscope_mean                       0.500263                   0.297029   \n",
       "linear_acceleration_mean             0.441453                   0.395925   \n",
       "orientation_mean                     0.043532                   0.215494   \n",
       "pressure_mean                       -0.045848                  -0.144826   \n",
       "rotation_vector_mean                 0.081403                   0.488242   \n",
       "sound_mean                           0.138451                   0.179971   \n",
       "\n",
       "                           gyroscope_mean  linear_acceleration_mean  \\\n",
       "accelerometer_mean               0.500263                  0.441453   \n",
       "game_rotation_vector_mean        0.297029                  0.395925   \n",
       "gyroscope_mean                   1.000000                  0.732075   \n",
       "linear_acceleration_mean         0.732075                  1.000000   \n",
       "orientation_mean                 0.050534                  0.096761   \n",
       "pressure_mean                   -0.032837                 -0.099997   \n",
       "rotation_vector_mean             0.169035                  0.226298   \n",
       "sound_mean                       0.017961                  0.072577   \n",
       "\n",
       "                           orientation_mean  pressure_mean  \\\n",
       "accelerometer_mean                 0.043532      -0.045848   \n",
       "game_rotation_vector_mean          0.215494      -0.144826   \n",
       "gyroscope_mean                     0.050534      -0.032837   \n",
       "linear_acceleration_mean           0.096761      -0.099997   \n",
       "orientation_mean                   1.000000       0.007241   \n",
       "pressure_mean                      0.007241       1.000000   \n",
       "rotation_vector_mean              -0.007124      -0.288926   \n",
       "sound_mean                         0.016743       0.054731   \n",
       "\n",
       "                           rotation_vector_mean  sound_mean  \n",
       "accelerometer_mean                     0.081403    0.138451  \n",
       "game_rotation_vector_mean              0.488242    0.179971  \n",
       "gyroscope_mean                         0.169035    0.017961  \n",
       "linear_acceleration_mean               0.226298    0.072577  \n",
       "orientation_mean                      -0.007124    0.016743  \n",
       "pressure_mean                         -0.288926    0.054731  \n",
       "rotation_vector_mean                   1.000000   -0.010011  \n",
       "sound_mean                            -0.010011    1.000000  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3119e062-fcbc-41d0-b4cc-47480da6aaa9",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Walking</th>\n",
       "      <td>346</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Train</th>\n",
       "      <td>311</td>\n",
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       "    <tr>\n",
       "      <th>Car</th>\n",
       "      <td>310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bus</th>\n",
       "      <td>220</td>\n",
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       "      <th>Still</th>\n",
       "      <td>68</td>\n",
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      "text/plain": [
       "         target\n",
       "Walking     346\n",
       "Train       311\n",
       "Car         310\n",
       "Bus         220\n",
       "Still        68"
      ]
     },
     "execution_count": 9,
     "metadata": {},
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    }
   ],
   "source": [
    "y.value_counts().to_frame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fd3977f6-1f98-4ffe-af57-0f5d1f576bbf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.488472\n",
      "         Iterations 11\n",
      "                          MNLogit Regression Results                          \n",
      "==============================================================================\n",
      "Dep. Variable:                 target   No. Observations:                 1255\n",
      "Model:                        MNLogit   Df Residuals:                     1219\n",
      "Method:                           MLE   Df Model:                           32\n",
      "Date:                Wed, 17 May 2023   Pseudo R-squ.:                  0.6764\n",
      "Time:                        11:16:00   Log-Likelihood:                -613.03\n",
      "converged:                       True   LL-Null:                       -1894.5\n",
      "Covariance Type:            nonrobust   LLR p-value:                     0.000\n",
      "=============================================================================================\n",
      "               target=Car       coef    std err          z      P>|z|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------------------\n",
      "accelerometer_mean           -1.3405      0.326     -4.117      0.000      -1.979      -0.702\n",
      "game_rotation_vector_mean    -2.8793      0.932     -3.088      0.002      -4.707      -1.052\n",
      "gyroscope_mean               -1.2694      0.827     -1.535      0.125      -2.890       0.351\n",
      "linear_acceleration_mean     -0.3871      0.224     -1.730      0.084      -0.826       0.052\n",
      "orientation_mean             -0.0100      0.002     -4.722      0.000      -0.014      -0.006\n",
      "pressure_mean                -0.2423      0.022    -11.012      0.000      -0.285      -0.199\n",
      "rotation_vector_mean         -6.5886      1.024     -6.433      0.000      -8.596      -4.581\n",
      "sound_mean                    0.1831      0.023      8.124      0.000       0.139       0.227\n",
      "const                       255.7548     23.220     11.014      0.000     210.244     301.266\n",
      "---------------------------------------------------------------------------------------------\n",
      "             target=Still       coef    std err          z      P>|z|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------------------\n",
      "accelerometer_mean           -2.3018      1.406     -1.638      0.101      -5.057       0.453\n",
      "game_rotation_vector_mean    -1.4923      1.166     -1.280      0.201      -3.778       0.793\n",
      "gyroscope_mean                2.0263      1.769      1.145      0.252      -1.441       5.494\n",
      "linear_acceleration_mean     -6.1539      1.390     -4.427      0.000      -8.879      -3.429\n",
      "orientation_mean             -0.0112      0.003     -3.412      0.001      -0.018      -0.005\n",
      "pressure_mean                -0.1061      0.031     -3.456      0.001      -0.166      -0.046\n",
      "rotation_vector_mean         -3.7290      1.312     -2.843      0.004      -6.300      -1.158\n",
      "sound_mean                   -0.1043      0.025     -4.151      0.000      -0.154      -0.055\n",
      "const                       144.7582     35.347      4.095      0.000      75.479     214.037\n",
      "---------------------------------------------------------------------------------------------\n",
      "             target=Train       coef    std err          z      P>|z|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------------------\n",
      "accelerometer_mean           -0.4580      0.518     -0.883      0.377      -1.474       0.558\n",
      "game_rotation_vector_mean     0.9464      0.830      1.140      0.254      -0.681       2.574\n",
      "gyroscope_mean                0.0587      0.632      0.093      0.926      -1.180       1.298\n",
      "linear_acceleration_mean     -1.7283      0.255     -6.766      0.000      -2.229      -1.228\n",
      "orientation_mean             -0.0237      0.002    -11.086      0.000      -0.028      -0.019\n",
      "pressure_mean                 0.0276      0.011      2.432      0.015       0.005       0.050\n",
      "rotation_vector_mean         -8.2604      0.901     -9.171      0.000     -10.026      -6.495\n",
      "sound_mean                    0.1133      0.020      5.724      0.000       0.075       0.152\n",
      "const                       -20.3954     13.175     -1.548      0.122     -46.217       5.426\n",
      "---------------------------------------------------------------------------------------------\n",
      "           target=Walking       coef    std err          z      P>|z|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------------------\n",
      "accelerometer_mean            0.1972      0.211      0.934      0.350      -0.216       0.611\n",
      "game_rotation_vector_mean     8.2232      1.216      6.762      0.000       5.840      10.607\n",
      "gyroscope_mean                3.3952      0.576      5.897      0.000       2.267       4.524\n",
      "linear_acceleration_mean      0.8137      0.132      6.149      0.000       0.554       1.073\n",
      "orientation_mean             -0.0108      0.002     -4.662      0.000      -0.015      -0.006\n",
      "pressure_mean                 0.0122      0.015      0.817      0.414      -0.017       0.042\n",
      "rotation_vector_mean         -6.9962      1.184     -5.908      0.000      -9.317      -4.675\n",
      "sound_mean                   -0.0786      0.016     -4.811      0.000      -0.111      -0.047\n",
      "const                        -9.8708     15.770     -0.626      0.531     -40.779      21.037\n",
      "=============================================================================================\n"
     ]
    }
   ],
   "source": [
    "x = sm.add_constant(x, prepend = False)\n",
    "mnlogit_mod = sm.MNLogit(y, x,\n",
    "                         # method=\"bfgs\", \n",
    "                         # maxiter=250\n",
    "                        )\n",
    "mnlogit_fit = mnlogit_mod.fit()\n",
    "print (mnlogit_fit.summary())"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "07724620-5ad7-4e8c-a625-57fae1a67f67",
   "metadata": {},
   "source": [
    "多項ロジットモデルでは、選択肢の数をkとするとk-1個のモデルを推定します。\n",
    "上の出力を見ると、5つの選択肢のうちBusがベース（参照グループ）として設定されているため、出力された結果を見る際には、パラメーターの推定値は、参照グループであるバスに対する相対的なものとなります。\n",
    "\n",
    "多項ロジットモデルでの一般的な解釈は、説明変数の単位変化に対して、参照グループに対して、モデル内の他の変数が一定である場合、パラメーター推定値の分だけ変化すると期待されることになります。\n",
    "\n",
    "上の結果で`target=Car`の出力結果では、バスと車の相対比較を示しています。\n",
    "\n",
    "`accelerometer_mean`の推定された係数は`-1.340`で、モデル内の他の変数が一定である場合、バスに対する車の`accelerometer_mean`の値が1単位増えると、バスより車である可能性は1.340減少すると解釈できます。\n",
    "\n",
    "同様に、`game_rotation_vector_mean`が1単位増えると、モデル内の他の変数が一定である場合、ユーザーの移動手段はバスであるよりも車である可能性が2.8793減少する可能性があると解釈できます。"
   ]
  }
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