GBM_LCCM_Example.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GBM-LCCM Example\n",
    "The purpose of this notebook is to demonstrate how the Gaussian Bernoulli - Latent Class Choice Model (GBM-LCCM) code from Sfeir et al. (2020) could be used.\n",
    "\n",
    "The application is based on the \"London Dataset\" from Hillel et al.(2018) which is available online as a supplementary material to the paper.\n",
    "\n",
    "The dataset contains individual trip diaries of the London Travel Demand Survey (LTDS) from April 2012 to March 2015 with their corresponding modes alternatives extracted from a Google directions application programming interface (API) and corresponding estimates of car operating costs and public transport fares. The dataset consists of 81,086 trips, four modes (walke, cycle, public transport, and drive), and different trip purposes (e.g. Home-Based Work, Home-Based Education, etc.).\n",
    "\n",
    "The required steps to build a travel mode choie model and run the GBM-LCCM code successfully are listed below.\n",
    "\n",
    "##### References\n",
    "Sfeir, G., Abou-Zeid, M., Rodrigues, F., Pereira, F.C., & Kaysi, I. (2021). “Latent class choice model with a flexible class membership component: A mixture model approach.” Journal of Chocie Modelling, 41, 100320, https://doi.org/10.1016/j.jocm.2021.100320\n",
    "\n",
    "Hillel, T., Elshafie, M.Z.E.B., Jin, Y. (2018). \"Recreating passenger mode choice-sets for transport\n",
    "simulation: A case study of London, UK,\" in: Proceedings of the Institution of Civil Engineers - Smart Infrastructure and Construction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1: Import the GBM-LCCM Package and All other Necessary Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import GBM_LCCM\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pylogit as pl\n",
    "import warnings\n",
    "from collections import OrderedDict\n",
    "from sklearn import preprocessing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2: Load the Dataset\n",
    "The GBM-LCCM consists of two sub-models, a class memberhsip model and a class-specific choice model:\n",
    "\n",
    "- The class membership model is defined as a Gaussian Mixture Model to cluster individuals probabilistically to K clusters (latent classes)\n",
    "\n",
    "- Conditioned on the class membership of an individual, the class-specific choice model estimates the probability of choosing a specific alternative\n",
    "\n",
    "The class-specific choice model needs the data to be in \"long\" format while the class membership model requires a \"wide\" format.\n",
    "\n",
    "For more details regarding how to convert your data from wide to long format, you can refer to the following link: https://github.com/timothyb0912/pylogit/blob/master/examples/notebooks/Main%20PyLogit%20Example.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load the \"london\" dataset, which is available in wide format\n",
    "wide_london = pd.read_csv('dataset.csv')\n",
    "\n",
    "# the .copy() returns a copy of the dataset and ensures that modifications are made to a copy and not the original data\n",
    "wide_london = wide_london.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "       trip_id  household_id  person_n  trip_n travel_mode purpose  \\\n",
       "0            0             0         0       0       drive     HBO   \n",
       "1            1             0         0       1       drive     HBO   \n",
       "2            2             0         0       2       drive     HBO   \n",
       "3            3             0         0       3       drive     HBO   \n",
       "4            4             0         1       2       drive     HBO   \n",
       "...        ...           ...       ...     ...         ...     ...   \n",
       "81081    81081         17615         0       0       drive     HBO   \n",
       "81082    81082         17615         0       2       drive    NHBO   \n",
       "81083    81083         17615         0       3       drive     HBO   \n",
       "81084    81084         17615         1       0          pt     HBW   \n",
       "81085    81085         17615         1       1          pt     HBW   \n",
       "\n",
       "          fueltype faretype  bus_scale  survey_year  ...  dur_pt_int_total  \\\n",
       "0       Petrol_Car     full        1.0            1  ...          0.000000   \n",
       "1       Petrol_Car     full        1.0            1  ...          0.000000   \n",
       "2       Petrol_Car     full        1.0            1  ...          0.000000   \n",
       "3       Petrol_Car     full        1.0            1  ...          0.000000   \n",
       "4       Petrol_Car      dis        1.0            1  ...          0.000000   \n",
       "...            ...      ...        ...          ...  ...               ...   \n",
       "81081  Average_Car     full        1.0            3  ...          0.216667   \n",
       "81082  Average_Car     full        1.0            3  ...          0.183333   \n",
       "81083  Average_Car     full        1.0            3  ...          0.000000   \n",
       "81084  Average_Car     full        1.0            3  ...          0.250000   \n",
       "81085  Average_Car     full        1.0            3  ...          0.100000   \n",
       "\n",
       "       dur_pt_int_waiting  dur_pt_int_walking  pt_n_interchanges  dur_driving  \\\n",
       "0                0.000000            0.000000                  0     0.052222   \n",
       "1                0.000000            0.000000                  0     0.059444   \n",
       "2                0.000000            0.000000                  0     0.236667   \n",
       "3                0.000000            0.000000                  0     0.233333   \n",
       "4                0.000000            0.000000                  0     0.229167   \n",
       "...                   ...                 ...                ...          ...   \n",
       "81081            0.197222            0.019444                  2     0.859722   \n",
       "81082            0.160278            0.023056                  2     0.925833   \n",
       "81083            0.000000            0.000000                  0     0.112500   \n",
       "81084            0.230556            0.019444                  2     1.121944   \n",
       "81085            0.079167            0.020833                  1     0.941389   \n",
       "\n",
       "       cost_transit  cost_driving_total  cost_driving_fuel  \\\n",
       "0               1.5                0.14               0.14   \n",
       "1               1.5                0.15               0.15   \n",
       "2               1.5                0.79               0.79   \n",
       "3               1.5                0.78               0.78   \n",
       "4               1.5                0.78               0.78   \n",
       "...             ...                 ...                ...   \n",
       "81081           4.3                2.48               2.48   \n",
       "81082           4.3                2.53               2.53   \n",
       "81083           1.5                0.32               0.32   \n",
       "81084           4.4               12.88               2.38   \n",
       "81085           5.9                2.38               2.38   \n",
       "\n",
       "       cost_driving_con_charge  driving_traffic_percent  \n",
       "0                          0.0                 0.111702  \n",
       "1                          0.0                 0.112150  \n",
       "2                          0.0                 0.203052  \n",
       "3                          0.0                 0.160714  \n",
       "4                          0.0                 0.130909  \n",
       "...                        ...                      ...  \n",
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       "81082                      0.0                 0.503750  \n",
       "81083                      0.0                 0.234568  \n",
       "81084                     10.5                 0.760832  \n",
       "81085                      0.0                 0.652995  \n",
       "\n",
       "[81086 rows x 36 columns]"
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     "execution_count": 3,
     "metadata": {},
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   "source": [
    "wide_london"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for this application we will only use Home-Based Work (HBW) trips\n",
    "wide_london = wide_london[wide_london['purpose']== \"HBW\"]\n",
    "\n",
    "# reset index \n",
    "wide_london.reset_index(inplace=True, drop=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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     "text": [
      "/var/folders/m2/kskgzsyn6t9b8xsjgl711fv00000gp/T/ipykernel_4673/1317594267.py:10: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  wide_london['travel_mode_nb'] = wide_london['travel_mode'].map(mode_mapping)\n",
      "/var/folders/m2/kskgzsyn6t9b8xsjgl711fv00000gp/T/ipykernel_4673/1317594267.py:12: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  wide_london['walk_av'] = 1\n",
      "/var/folders/m2/kskgzsyn6t9b8xsjgl711fv00000gp/T/ipykernel_4673/1317594267.py:13: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  wide_london['cycle_av'] = 1\n",
      "/var/folders/m2/kskgzsyn6t9b8xsjgl711fv00000gp/T/ipykernel_4673/1317594267.py:14: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  wide_london['pt_av'] = 1\n",
      "/var/folders/m2/kskgzsyn6t9b8xsjgl711fv00000gp/T/ipykernel_4673/1317594267.py:15: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  wide_london['drive_av'] = 1\n"
     ]
    }
   ],
   "source": [
    "# Note that 5 columns need to be added to the original dataset:\n",
    "# - travel_mode_nb: 1 for walk, 2 for cycle, 3 for pt, and 4 for drive\n",
    "# - walk_av, cycle_av, pt_av, drive_av: to determine the availability of each mode (1 if available and 0 otherwise).\n",
    "# For simplicity, we assume that all modes are available for all individuals\n",
    "\n",
    "# Define mapping\n",
    "mode_mapping = {'walk': 1, 'cycle': 2, 'pt': 3, 'drive': 4}\n",
    "\n",
    "# Apply mapping\n",
    "wide_london['travel_mode_nb'] = wide_london['travel_mode'].map(mode_mapping)\n",
    "\n",
    "wide_london['walk_av'] = 1\n",
    "wide_london['cycle_av'] = 1\n",
    "wide_london['pt_av'] = 1\n",
    "wide_london['drive_av'] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>trip_id</th>\n",
       "      <td>17</td>\n",
       "      <td>125</td>\n",
       "      <td>139</td>\n",
       "      <td>140</td>\n",
       "      <td>141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>household_id</th>\n",
       "      <td>3</td>\n",
       "      <td>26</td>\n",
       "      <td>29</td>\n",
       "      <td>29</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>person_n</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>trip_n</th>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>travel_mode</th>\n",
       "      <td>pt</td>\n",
       "      <td>drive</td>\n",
       "      <td>pt</td>\n",
       "      <td>pt</td>\n",
       "      <td>pt</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>purpose</th>\n",
       "      <td>HBW</td>\n",
       "      <td>HBW</td>\n",
       "      <td>HBW</td>\n",
       "      <td>HBW</td>\n",
       "      <td>HBW</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fueltype</th>\n",
       "      <td>Average_Car</td>\n",
       "      <td>Petrol_Car</td>\n",
       "      <td>Petrol_Car</td>\n",
       "      <td>Petrol_Car</td>\n",
       "      <td>Petrol_Car</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>faretype</th>\n",
       "      <td>full</td>\n",
       "      <td>free</td>\n",
       "      <td>full</td>\n",
       "      <td>full</td>\n",
       "      <td>full</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bus_scale</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>survey_year</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>travel_year</th>\n",
       "      <td>2012</td>\n",
       "      <td>2012</td>\n",
       "      <td>2012</td>\n",
       "      <td>2012</td>\n",
       "      <td>2012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>travel_month</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>travel_date</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>day_of_week</th>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>start_time_linear</th>\n",
       "      <td>21.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>13.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>32</td>\n",
       "      <td>61</td>\n",
       "      <td>62</td>\n",
       "      <td>62</td>\n",
       "      <td>54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>female</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>driving_license</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>car_ownership</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>distance</th>\n",
       "      <td>1901</td>\n",
       "      <td>961</td>\n",
       "      <td>6161</td>\n",
       "      <td>6161</td>\n",
       "      <td>6161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dur_walking</th>\n",
       "      <td>0.512222</td>\n",
       "      <td>0.241667</td>\n",
       "      <td>2.361111</td>\n",
       "      <td>2.369167</td>\n",
       "      <td>2.361111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dur_cycling</th>\n",
       "      <td>0.141667</td>\n",
       "      <td>0.055</td>\n",
       "      <td>0.601667</td>\n",
       "      <td>0.561667</td>\n",
       "      <td>0.601667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dur_pt_total</th>\n",
       "      <td>0.4325</td>\n",
       "      <td>0.208333</td>\n",
       "      <td>0.638056</td>\n",
       "      <td>0.537222</td>\n",
       "      <td>0.638056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dur_pt_access</th>\n",
       "      <td>0.123889</td>\n",
       "      <td>0.193056</td>\n",
       "      <td>0.129722</td>\n",
       "      <td>0.163889</td>\n",
       "      <td>0.129722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dur_pt_rail</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.183333</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.183333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dur_pt_bus</th>\n",
       "      <td>0.208056</td>\n",
       "      <td>0.016667</td>\n",
       "      <td>0.228333</td>\n",
       "      <td>0.366667</td>\n",
       "      <td>0.228333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dur_pt_int_total</th>\n",
       "      <td>0.091667</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dur_pt_int_waiting</th>\n",
       "      <td>0.091667</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.083889</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.083889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dur_pt_int_walking</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.016111</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.016111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pt_n_interchanges</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dur_driving</th>\n",
       "      <td>0.115556</td>\n",
       "      <td>0.056111</td>\n",
       "      <td>0.374167</td>\n",
       "      <td>0.283333</td>\n",
       "      <td>0.374167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cost_transit</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.5</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cost_driving_total</th>\n",
       "      <td>0.33</td>\n",
       "      <td>0.19</td>\n",
       "      <td>1.27</td>\n",
       "      <td>1.13</td>\n",
       "      <td>1.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cost_driving_fuel</th>\n",
       "      <td>0.33</td>\n",
       "      <td>0.19</td>\n",
       "      <td>1.27</td>\n",
       "      <td>1.13</td>\n",
       "      <td>1.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cost_driving_con_charge</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>driving_traffic_percent</th>\n",
       "      <td>0.033654</td>\n",
       "      <td>0.049505</td>\n",
       "      <td>0.357832</td>\n",
       "      <td>0.302941</td>\n",
       "      <td>0.357832</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>travel_mode_nb</th>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>walk_av</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cycle_av</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pt_av</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive_av</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                   0           1           2           3  \\\n",
       "trip_id                           17         125         139         140   \n",
       "household_id                       3          26          29          29   \n",
       "person_n                           1           0           0           0   \n",
       "trip_n                             1           6           0           1   \n",
       "travel_mode                       pt       drive          pt          pt   \n",
       "purpose                          HBW         HBW         HBW         HBW   \n",
       "fueltype                 Average_Car  Petrol_Car  Petrol_Car  Petrol_Car   \n",
       "faretype                        full        free        full        full   \n",
       "bus_scale                        1.0         0.0         1.0         1.0   \n",
       "survey_year                        1           1           1           1   \n",
       "travel_year                     2012        2012        2012        2012   \n",
       "travel_month                       4           4           4           4   \n",
       "travel_date                        1           2           2           2   \n",
       "day_of_week                        7           1           1           1   \n",
       "start_time_linear               21.5         0.0        13.0        22.0   \n",
       "age                               32          61          62          62   \n",
       "female                             1           0           0           0   \n",
       "driving_license                    0           1           0           0   \n",
       "car_ownership                      0           2           1           1   \n",
       "distance                        1901         961        6161        6161   \n",
       "dur_walking                 0.512222    0.241667    2.361111    2.369167   \n",
       "dur_cycling                 0.141667       0.055    0.601667    0.561667   \n",
       "dur_pt_total                  0.4325    0.208333    0.638056    0.537222   \n",
       "dur_pt_access               0.123889    0.193056    0.129722    0.163889   \n",
       "dur_pt_rail                      0.0         0.0    0.183333         0.0   \n",
       "dur_pt_bus                  0.208056    0.016667    0.228333    0.366667   \n",
       "dur_pt_int_total            0.091667         0.0         0.1         0.0   \n",
       "dur_pt_int_waiting          0.091667         0.0    0.083889         0.0   \n",
       "dur_pt_int_walking               0.0         0.0    0.016111         0.0   \n",
       "pt_n_interchanges                  1           0           1           0   \n",
       "dur_driving                 0.115556    0.056111    0.374167    0.283333   \n",
       "cost_transit                     3.0         0.0         3.0         1.5   \n",
       "cost_driving_total              0.33        0.19        1.27        1.13   \n",
       "cost_driving_fuel               0.33        0.19        1.27        1.13   \n",
       "cost_driving_con_charge          0.0         0.0         0.0         0.0   \n",
       "driving_traffic_percent     0.033654    0.049505    0.357832    0.302941   \n",
       "travel_mode_nb                     3           4           3           3   \n",
       "walk_av                            1           1           1           1   \n",
       "cycle_av                           1           1           1           1   \n",
       "pt_av                              1           1           1           1   \n",
       "drive_av                           1           1           1           1   \n",
       "\n",
       "                                  4  \n",
       "trip_id                         141  \n",
       "household_id                     29  \n",
       "person_n                          1  \n",
       "trip_n                            0  \n",
       "travel_mode                      pt  \n",
       "purpose                         HBW  \n",
       "fueltype                 Petrol_Car  \n",
       "faretype                       full  \n",
       "bus_scale                       1.0  \n",
       "survey_year                       1  \n",
       "travel_year                    2012  \n",
       "travel_month                      4  \n",
       "travel_date                       2  \n",
       "day_of_week                       1  \n",
       "start_time_linear              13.0  \n",
       "age                              54  \n",
       "female                            1  \n",
       "driving_license                   0  \n",
       "car_ownership                     1  \n",
       "distance                       6161  \n",
       "dur_walking                2.361111  \n",
       "dur_cycling                0.601667  \n",
       "dur_pt_total               0.638056  \n",
       "dur_pt_access              0.129722  \n",
       "dur_pt_rail                0.183333  \n",
       "dur_pt_bus                 0.228333  \n",
       "dur_pt_int_total                0.1  \n",
       "dur_pt_int_waiting         0.083889  \n",
       "dur_pt_int_walking         0.016111  \n",
       "pt_n_interchanges                 1  \n",
       "dur_driving                0.374167  \n",
       "cost_transit                    3.0  \n",
       "cost_driving_total             1.27  \n",
       "cost_driving_fuel              1.27  \n",
       "cost_driving_con_charge         0.0  \n",
       "driving_traffic_percent    0.357832  \n",
       "travel_mode_nb                    3  \n",
       "walk_av                           1  \n",
       "cycle_av                          1  \n",
       "pt_av                             1  \n",
       "drive_av                          1  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# look at the first 5 rows of the data\n",
    "wide_london.head(5).T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3: Convert the data from wide to long format\n",
    "In this section, we will use the pylogit package, which is designed for estimating various discrete choice models, including multinomial logit, mixed logit, and nested logit https://pypi.org/project/pylogit/. Additionally, the package can be used to transform data from wide to long format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['trip_id', 'household_id', 'person_n', 'trip_n', 'travel_mode',\n",
       "       'purpose', 'fueltype', 'faretype', 'bus_scale', 'survey_year',\n",
       "       'travel_year', 'travel_month', 'travel_date', 'day_of_week',\n",
       "       'start_time_linear', 'age', 'female', 'driving_license',\n",
       "       'car_ownership', 'distance', 'dur_walking', 'dur_cycling',\n",
       "       'dur_pt_total', 'dur_pt_access', 'dur_pt_rail', 'dur_pt_bus',\n",
       "       'dur_pt_int_total', 'dur_pt_int_waiting', 'dur_pt_int_walking',\n",
       "       'pt_n_interchanges', 'dur_driving', 'cost_transit',\n",
       "       'cost_driving_total', 'cost_driving_fuel', 'cost_driving_con_charge',\n",
       "       'driving_traffic_percent', 'travel_mode_nb', 'walk_av', 'cycle_av',\n",
       "       'pt_av', 'drive_av'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# look at the columns of the london dataset\n",
    "wide_london.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/m2/kskgzsyn6t9b8xsjgl711fv00000gp/T/ipykernel_4673/2968110328.py:36: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  wide_london[obs_id_column] = np.arange(wide_london.shape[0],\n"
     ]
    }
   ],
   "source": [
    "# Create the list of individual specific variables (variables that are specific to an individual \n",
    "# and do not vary across alternatives)\n",
    "ind_variables = wide_london.columns.tolist()[:20]\n",
    "\n",
    "\n",
    "# Specify the variables that vary across individuals and some or all alternatives\n",
    "# The keys are the column names that will be used in the long format dataframe\n",
    "# The values are dictionaries whose key-value pairs are the alternative id and\n",
    "# the column name of the corresponding column that encodes that variable for\n",
    "# the given alternative. Examples below.\n",
    "alt_varying_variables = {u'travel_time': dict([(1, 'dur_walking'),\n",
    "                                               (2, 'dur_cycling'),\n",
    "                                               (3, 'dur_pt_total'),\n",
    "                                               (4, 'dur_driving')]),\n",
    "                        u'travel_cost': dict([(3, 'cost_transit'),\n",
    "                                              (4, 'cost_driving_total')])}\n",
    "\n",
    "# Specify the availability variables\n",
    "# Note that the keys of the dictionary are the alternative id's.\n",
    "# The values are the columns denoting the availability for the\n",
    "# given mode in the dataset.\n",
    "availability_variables = {1: 'walk_av',\n",
    "                          2: 'cycle_av',\n",
    "                          3: 'pt_av',\n",
    "                          4: 'drive_av'}\n",
    "\n",
    "\n",
    "# Determine the columns for: alternative ids, the observation ids and the choice\n",
    "# The 'custom_alt_id' is the name of a column to be created in the long-format data\n",
    "# It will identify the alternative associated with each row.\n",
    "custom_alt_id = \"mode_id\"\n",
    "\n",
    "# Create a custom id column that ignores the fact that this is a \n",
    "# panel/repeated-observations dataset. Note the +1 ensures the id's start at one.\n",
    "obs_id_column = \"custom_id\"\n",
    "wide_london[obs_id_column] = np.arange(wide_london.shape[0],\n",
    "                                            dtype=int) + 1\n",
    "\n",
    "\n",
    "# Create a variable recording the choice column\n",
    "choice_column = \"travel_mode_nb\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/GEOSAF/Desktop/BiogemeEnv/lib/python3.12/site-packages/pylogit/choice_tools.py:454: UserWarning: Note, there are 42 variables in wide_data but the inputs ind_vars, alt_specific_vars, and subset_specific_vars only account for 32 variables.\n",
      "  warnings.warn(msg.format(num_dataframe_vars, data_title) +\n"
     ]
    },
    {
     "data": {
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       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
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       "      <th>9</th>\n",
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       "      <th>custom_id</th>\n",
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       "      <td>1</td>\n",
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       "      <td>2</td>\n",
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       "      <td>3</td>\n",
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       "      <th>mode_id</th>\n",
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       "      <td>2</td>\n",
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       "    <tr>\n",
       "      <th>travel_mode_nb</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>17</td>\n",
       "      <td>17</td>\n",
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       "      <td>17</td>\n",
       "      <td>125</td>\n",
       "      <td>125</td>\n",
       "      <td>125</td>\n",
       "      <td>125</td>\n",
       "      <td>139</td>\n",
       "      <td>139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>household_id</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>26</td>\n",
       "      <td>26</td>\n",
       "      <td>26</td>\n",
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       "      <td>29</td>\n",
       "      <td>29</td>\n",
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       "    <tr>\n",
       "      <th>person_n</th>\n",
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       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>travel_mode</th>\n",
       "      <td>pt</td>\n",
       "      <td>pt</td>\n",
       "      <td>pt</td>\n",
       "      <td>pt</td>\n",
       "      <td>drive</td>\n",
       "      <td>drive</td>\n",
       "      <td>drive</td>\n",
       "      <td>drive</td>\n",
       "      <td>pt</td>\n",
       "      <td>pt</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>purpose</th>\n",
       "      <td>HBW</td>\n",
       "      <td>HBW</td>\n",
       "      <td>HBW</td>\n",
       "      <td>HBW</td>\n",
       "      <td>HBW</td>\n",
       "      <td>HBW</td>\n",
       "      <td>HBW</td>\n",
       "      <td>HBW</td>\n",
       "      <td>HBW</td>\n",
       "      <td>HBW</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fueltype</th>\n",
       "      <td>Average_Car</td>\n",
       "      <td>Average_Car</td>\n",
       "      <td>Average_Car</td>\n",
       "      <td>Average_Car</td>\n",
       "      <td>Petrol_Car</td>\n",
       "      <td>Petrol_Car</td>\n",
       "      <td>Petrol_Car</td>\n",
       "      <td>Petrol_Car</td>\n",
       "      <td>Petrol_Car</td>\n",
       "      <td>Petrol_Car</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>faretype</th>\n",
       "      <td>full</td>\n",
       "      <td>full</td>\n",
       "      <td>full</td>\n",
       "      <td>full</td>\n",
       "      <td>free</td>\n",
       "      <td>free</td>\n",
       "      <td>free</td>\n",
       "      <td>free</td>\n",
       "      <td>full</td>\n",
       "      <td>full</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bus_scale</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>survey_year</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>travel_year</th>\n",
       "      <td>2012</td>\n",
       "      <td>2012</td>\n",
       "      <td>2012</td>\n",
       "      <td>2012</td>\n",
       "      <td>2012</td>\n",
       "      <td>2012</td>\n",
       "      <td>2012</td>\n",
       "      <td>2012</td>\n",
       "      <td>2012</td>\n",
       "      <td>2012</td>\n",
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       "    <tr>\n",
       "      <th>travel_month</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
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       "    <tr>\n",
       "      <th>travel_date</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>day_of_week</th>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>start_time_linear</th>\n",
       "      <td>21.5</td>\n",
       "      <td>21.5</td>\n",
       "      <td>21.5</td>\n",
       "      <td>21.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>13.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>32</td>\n",
       "      <td>32</td>\n",
       "      <td>32</td>\n",
       "      <td>32</td>\n",
       "      <td>61</td>\n",
       "      <td>61</td>\n",
       "      <td>61</td>\n",
       "      <td>61</td>\n",
       "      <td>62</td>\n",
       "      <td>62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>female</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>driving_license</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>car_ownership</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>distance</th>\n",
       "      <td>1901</td>\n",
       "      <td>1901</td>\n",
       "      <td>1901</td>\n",
       "      <td>1901</td>\n",
       "      <td>961</td>\n",
       "      <td>961</td>\n",
       "      <td>961</td>\n",
       "      <td>961</td>\n",
       "      <td>6161</td>\n",
       "      <td>6161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>travel_time</th>\n",
       "      <td>0.512222</td>\n",
       "      <td>0.141667</td>\n",
       "      <td>0.4325</td>\n",
       "      <td>0.115556</td>\n",
       "      <td>0.241667</td>\n",
       "      <td>0.055</td>\n",
       "      <td>0.208333</td>\n",
       "      <td>0.056111</td>\n",
       "      <td>2.361111</td>\n",
       "      <td>0.601667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>travel_cost</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.33</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.19</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             0            1            2            3  \\\n",
       "custom_id                    1            1            1            1   \n",
       "mode_id                      1            2            3            4   \n",
       "travel_mode_nb               0            0            1            0   \n",
       "trip_id                     17           17           17           17   \n",
       "household_id                 3            3            3            3   \n",
       "person_n                     1            1            1            1   \n",
       "trip_n                       1            1            1            1   \n",
       "travel_mode                 pt           pt           pt           pt   \n",
       "purpose                    HBW          HBW          HBW          HBW   \n",
       "fueltype           Average_Car  Average_Car  Average_Car  Average_Car   \n",
       "faretype                  full         full         full         full   \n",
       "bus_scale                  1.0          1.0          1.0          1.0   \n",
       "survey_year                  1            1            1            1   \n",
       "travel_year               2012         2012         2012         2012   \n",
       "travel_month                 4            4            4            4   \n",
       "travel_date                  1            1            1            1   \n",
       "day_of_week                  7            7            7            7   \n",
       "start_time_linear         21.5         21.5         21.5         21.5   \n",
       "age                         32           32           32           32   \n",
       "female                       1            1            1            1   \n",
       "driving_license              0            0            0            0   \n",
       "car_ownership                0            0            0            0   \n",
       "distance                  1901         1901         1901         1901   \n",
       "travel_time           0.512222     0.141667       0.4325     0.115556   \n",
       "travel_cost                0.0          0.0          3.0         0.33   \n",
       "\n",
       "                            4           5           6           7           8  \\\n",
       "custom_id                   2           2           2           2           3   \n",
       "mode_id                     1           2           3           4           1   \n",
       "travel_mode_nb              0           0           0           1           0   \n",
       "trip_id                   125         125         125         125         139   \n",
       "household_id               26          26          26          26          29   \n",
       "person_n                    0           0           0           0           0   \n",
       "trip_n                      6           6           6           6           0   \n",
       "travel_mode             drive       drive       drive       drive          pt   \n",
       "purpose                   HBW         HBW         HBW         HBW         HBW   \n",
       "fueltype           Petrol_Car  Petrol_Car  Petrol_Car  Petrol_Car  Petrol_Car   \n",
       "faretype                 free        free        free        free        full   \n",
       "bus_scale                 0.0         0.0         0.0         0.0         1.0   \n",
       "survey_year                 1           1           1           1           1   \n",
       "travel_year              2012        2012        2012        2012        2012   \n",
       "travel_month                4           4           4           4           4   \n",
       "travel_date                 2           2           2           2           2   \n",
       "day_of_week                 1           1           1           1           1   \n",
       "start_time_linear         0.0         0.0         0.0         0.0        13.0   \n",
       "age                        61          61          61          61          62   \n",
       "female                      0           0           0           0           0   \n",
       "driving_license             1           1           1           1           0   \n",
       "car_ownership               2           2           2           2           1   \n",
       "distance                  961         961         961         961        6161   \n",
       "travel_time          0.241667       0.055    0.208333    0.056111    2.361111   \n",
       "travel_cost               0.0         0.0         0.0        0.19         0.0   \n",
       "\n",
       "                            9  \n",
       "custom_id                   3  \n",
       "mode_id                     2  \n",
       "travel_mode_nb              0  \n",
       "trip_id                   139  \n",
       "household_id               29  \n",
       "person_n                    0  \n",
       "trip_n                      0  \n",
       "travel_mode                pt  \n",
       "purpose                   HBW  \n",
       "fueltype           Petrol_Car  \n",
       "faretype                 full  \n",
       "bus_scale                 1.0  \n",
       "survey_year                 1  \n",
       "travel_year              2012  \n",
       "travel_month                4  \n",
       "travel_date                 2  \n",
       "day_of_week                 1  \n",
       "start_time_linear        13.0  \n",
       "age                        62  \n",
       "female                      0  \n",
       "driving_license             0  \n",
       "car_ownership               1  \n",
       "distance                 6161  \n",
       "travel_time          0.601667  \n",
       "travel_cost               0.0  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Perform the conversion to long-format\n",
    "long_london = pl.convert_wide_to_long(wide_london, \n",
    "                                           ind_variables, \n",
    "                                           alt_varying_variables, \n",
    "                                           availability_variables, \n",
    "                                           obs_id_column, \n",
    "                                           choice_column,\n",
    "                                           new_alt_id_name=custom_alt_id)\n",
    "# Look at the resulting long-format dataframe\n",
    "long_london.head(10).T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 4: Model Specification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Step 4.1: Class Membership Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set the number of clusters (latent classes) to 2\n",
    "n_classes = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/m2/kskgzsyn6t9b8xsjgl711fv00000gp/T/ipykernel_4673/1612562048.py:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  wide_london['car_ownership0'] = (wide_london['car_ownership'] == 0).astype(int)\n",
      "/var/folders/m2/kskgzsyn6t9b8xsjgl711fv00000gp/T/ipykernel_4673/1612562048.py:3: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  wide_london['car_ownership1'] = (wide_london['car_ownership'] == 1).astype(int)\n",
      "/var/folders/m2/kskgzsyn6t9b8xsjgl711fv00000gp/T/ipykernel_4673/1612562048.py:4: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  wide_london['car_ownership2'] = (wide_london['car_ownership'] == 2).astype(int)\n"
     ]
    }
   ],
   "source": [
    "# create dummy variables for car ownership\n",
    "wide_london['car_ownership0'] = (wide_london['car_ownership'] == 0).astype(int)\n",
    "wide_london['car_ownership1'] = (wide_london['car_ownership'] == 1).astype(int)\n",
    "wide_london['car_ownership2'] = (wide_london['car_ownership'] == 2).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the class membership model is defined as a Gaussian Bernoulli Mixture Model\n",
    "# Gaussian Mixture Model is used for continuous variables while Bernoulli Mixture Model for discrete variables\n",
    "\n",
    "# select the continuous variables for the class membership model\n",
    "X_Mem_C = wide_london[['age']]\n",
    "# it is a good practice to standardize the continuous variables for the Gaussian Mixture Model\n",
    "Standardized_X_Mem_C = preprocessing.scale(X_Mem_C)\n",
    "\n",
    "# select the discrete variables for the class membership model\n",
    "X_Mem_D = wide_london[['female','driving_license','car_ownership1','car_ownership2']]\n",
    "X_Mem_D = X_Mem_D.values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Step 4.2: Class-Specific Choice Model\n",
    "This section is based on the latent class choice model (lccm) package. For more details on how to specify the class-specific choice model, you can check the lccm package on the following link: https://github.com/ferasz/LCCM\n",
    "\n",
    "You can use alternative specific or generic speficifation for the parameters. \n",
    "We will use in this example both types to demonstrate how each one can be used:\n",
    "\n",
    "- intercept: alternative specific constants included in all the utilities except the one related to walk, hence the one braket with the numbers of the corresponding alternatives [2,3,4] (walk is used as a base)\n",
    "- travel time parameters for both classes are specified as alternative specific and included in the utilities of all modes, hence the one braket with the numbers of the corresponding alternatives [1,2,3,4]\n",
    "- travel cost parameters for both classes are specified as generic and included only in the utilities of drive and pt, hence the two brakets and the numbers of the alternatives [[3,4]]\n",
    "\n",
    "\n",
    "The specification of the two classes is as follows:\n",
    "##### Latent Class 1:\n",
    "\n",
    "$V_{walk} =        \\beta_{tt, class1} * TravelTime_{walk}  $  \n",
    "\n",
    "$V_{cycle} = ASC-cycle_{class1} + \\beta_{tt, class1} * TravelTime_{cycle}$\n",
    "\n",
    "$V_{pt} = ASC-pt_{class1} + \\beta_{tt, class1} * TravelTime_{pt} + \\beta_{cost, class1} * TravelCost_{pt} $\n",
    "\n",
    "$V_{drive} = ASC-drive_{class1} + \\beta_{tt, class1} * TravelTime_{drive} + \\beta_{cost, class1} * TravelCost_{drive} $\n",
    "\n",
    "##### Latent Class 2:\n",
    "\n",
    "$V_{walk} =        \\beta_{tt, class2} * TravelTime_{walk}  $  \n",
    "\n",
    "$V_{cycle} = ASC-cycle_{class2} + \\beta_{tt, class2} * TravelTime_{cycle}$\n",
    "\n",
    "$V_{pt} = ASC-pt_{class2} + \\beta_{tt, class2} * TravelTime_{pt} + \\beta_{cost, class2} * TravelCost_{pt} $\n",
    "\n",
    "$V_{drive} = ASC-drive_{class2} + \\beta_{tt, class2} * TravelTime_{drive} + \\beta_{cost, class2} * TravelCost_{drive} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# scale travel time from hours to minutes\n",
    "long_london['travel_time'] = long_london['travel_time'] * 60\n",
    "\n",
    "# add a column of ones named'intercept'. This will be used later to define the Alternative-Specific Constants (ASCs).\n",
    "long_london['intercept']=np.ones(long_london.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# NOTE: Specification and variable names must be in lists of ordered dictionaries.\n",
    "# class_specific_specs defines the variables names to be used in the specification of the \n",
    "# class specific choice model of each class.\n",
    "# class_specific_labels defines the names associated with each of the variables which\n",
    "# will be displayed in the output tables after estimation.\n",
    "\n",
    "\n",
    "class_specific_specs = [OrderedDict([('intercept',[2,3,4]),\n",
    "                                     ('travel_time',[1,2,3,4]),\n",
    "                                     ('travel_cost',[[3,4]])]),\n",
    "                        OrderedDict([('intercept',[2,3,4]),\n",
    "                                     ('travel_time',[1,2,3,4]),\n",
    "                                     ('travel_cost',[[3,4]])])]\n",
    "                       \n",
    "class_specific_labels = [OrderedDict([('ASC',['ASC(cycle)',\n",
    "                                             'ASC(pt)',\n",
    "                                             'ASC(drive)',]),\n",
    "                                      ('travel_time',['Travel Time(walk)',\n",
    "                                                      'Travel Time(cycle)',\n",
    "                                                      'Travel Time(pt)',\n",
    "                                                      'Travel Time(drive)']),\n",
    "                                      ('travel_cost',['Travel Cost'])]),\n",
    "                         OrderedDict([('ASC',['ASC(cycle)',\n",
    "                                             'ASC(pt)',\n",
    "                                             'ASC(drive)',]),\n",
    "                                      ('travel_time',['Travel Time(walk)',\n",
    "                                                      'Travel Time(cycle)',\n",
    "                                                      'Travel Time(pt)',\n",
    "                                                      'Travel Time(drive)']),\n",
    "                                      ('travel_cost',['Travel Cost'])])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Starting Values for the Class-Specific Choice Model paramerters\n",
    "paramClassSpec = []\n",
    "paramClassSpec.append(np.array([0,0,0,0,0,0,0,0])) # for the first class\n",
    "paramClassSpec.append(np.array([0,0,0,0,0,0,0,0])) # for the second class"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 5: Model Estimation and Results\n",
    "\n",
    "To train/estimate the model, the following must be included in the GBM_LCCM.lccm_fit function:\n",
    "- data: data used for the class-speficic choice model in long format\n",
    "- X: continuous variables used for the class membership model in wide format\n",
    "- X_Dummy: discrete variables used for the class membership model in wide format\n",
    "\n",
    "For prediction/test, the following must be included in the GBM_LCCM.lccm_fit function:\n",
    "- dataTest = data for the class-speficic choice model in long format\n",
    "- XTest = continuous variables used for the class membership model in wide format\n",
    "- XTest_Dummy = discrete variables used for the class membership model in wide format\n",
    "\n",
    "Note that after training your model you can test it on a different dataset (test dataset). For this example, we use the same one that was used in training. However, you can split the data into train and test datasets(e.g. 80%-20%), estimate the model on the train dataset (data, X, X_Dummy) and test the model on the test dataset (dataTest, XTest, XTest_Dummy). The model will generate the prediction accuracy in terms of LL at the end of the notebook (Predicted Log-Likelihood).\n",
    "\n",
    "The remaining variables that must be included in the GBM_LCCM.lccm_fit function are:\n",
    "- prediction_test: 'Yes' if you would like to test the model on a test dataset and 'No' otherwise\n",
    "- GMM_Initialization: 'random' to initialize the clusters of the Gaussian Bernoulli Mixture models randomly \n",
    "or 'kmeans' to initinalize the clusters using the k-means clustering algorithms\n",
    "- covariance_type: the covariance structure of Gaussian Mixture Models can have four different types:\n",
    "    - full, tied, diagonal and spherical. For more details about each type, you can refer to the following link: \n",
    "    - https://scikit-learn.org/stable/modules/generated/sklearn.mixture.GaussianMixture.html\n",
    "- ind_id_col: name of column identifying the individual for each row of data \n",
    "- obs_id_col: name of column identifying the observation (choice scenario)\n",
    "- choice_col: name of column identifying whether the alternative corresponding by a row was chosen or not\n",
    "- n_classes: number of latent classes (clusters)\n",
    "- paramClassSpec: starting values for the class-specific choice models. If paramClassSpec is None, the model will generate the starting values randomly\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing data\n",
      "Initializing EM Algorithm...\n",
      "\n",
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      "\n",
      "Enumerating choices for the sample\n",
      "\n",
      "\n",
      "Number of Parameters:                                 29\n",
      "Number of Observations:                            13505\n",
      "Null Log-Likelihood:                            -71287.6\n",
      "Joint Log-Likelihood:                          -60915.69\n",
      "AIC-Joint:                                     121889.37\n",
      "BIC-Joint:                                        122107\n",
      "Estimation time (minutes):                          0.28\n",
      "\n",
      "\n",
      "Marginal Log-Likelihood:                        -9401.79\n",
      "AIC:                                            18861.59\n",
      "BIC:                                               19079\n",
      "\n",
      "\n",
      "\n",
      "Class-Specific Choice Model:\n",
      "-----------------------------------------------------------------------------------------\n",
      "Number of Parameters:                        \n",
      "Class 1 Model: \n",
      "-----------------------------------------------------------------------------------------\n",
      "Variables                                     parameters    std_err     t_stat    p_value\n",
      "-----------------------------------------------------------------------------------------\n",
      "ASC(cycle)                                       -2.4209     0.1175   -20.6067     0.0000\n",
      "ASC(pt)                                          -1.2004     0.1012   -11.8659     0.0000\n",
      "ASC(drive)                                        0.1686     0.0643     2.6204     0.0088\n",
      "Travel Time(walk)                                -0.0939     0.0017   -54.6869     0.0000\n",
      "Travel Time(cycle)                               -0.1081     0.0034   -32.0725     0.0000\n",
      "Travel Time(pt)                                  -0.0774     0.0022   -35.0799     0.0000\n",
      "Travel Time(drive)                               -0.1309     0.0022   -60.4121     0.0000\n",
      "Travel Cost                                      -0.1739     0.0092   -18.9638     0.0000\n",
      "-----------------------------------------------------------------------------------------\n",
      "Class 2 Model: \n",
      "-----------------------------------------------------------------------------------------\n",
      "Variables                                     parameters    std_err     t_stat    p_value\n",
      "-----------------------------------------------------------------------------------------\n",
      "ASC(cycle)                                       -4.3077     0.1176   -36.6397     0.0000\n",
      "ASC(pt)                                          -2.5560     0.0957   -26.7039     0.0000\n",
      "ASC(drive)                                       -3.2492     0.1306   -24.8875     0.0000\n",
      "Travel Time(walk)                                -0.1295     0.0018   -73.2160     0.0000\n",
      "Travel Time(cycle)                               -0.0979     0.0045   -21.7199     0.0000\n",
      "Travel Time(pt)                                  -0.0418     0.0032   -13.2671     0.0000\n",
      "Travel Time(drive)                               -0.1571     0.0083   -18.8625     0.0000\n",
      "Travel Cost                                      -0.1772     0.0361    -4.9104     0.0000\n",
      "-----------------------------------------------------------------------------------------\n",
      "\n",
      "\n",
      "Class Membership Model:\n",
      "-----------------------------------------------------------------------------------------\n",
      "Number of Parameters:                                 13\n",
      "\n",
      "-----------------------------------------------------------------------------------------\n",
      "Mixing Coefficients\n",
      "-----------------------------------------------------------------------------------------\n",
      "Class 1                                           0.5064\n",
      "Class 2                                           0.4936\n",
      "\n",
      "-----------------------------------------------------------------------------------------\n",
      "Means (Continuous)        X 1      \n",
      "-----------------------------------------------------------------------------------------\n",
      "Class 1                0.3002 \n",
      "Class 2               -0.3080 \n",
      "\n",
      "-----------------------------------------------------------------------------------------\n",
      "Means (Dummy)             X 1      X 2      X 3      X 4      \n",
      "-----------------------------------------------------------------------------------------\n",
      "Class 1                0.3857   0.9868   0.4826   0.4060 \n",
      "Class 2                0.5176   0.4830   0.4716   0.0150 \n",
      "\n",
      "-----------------------------------------------------------------------------------------\n",
      "Covariances               X 1      \n",
      "-----------------------------------------------------------------------------------------\n",
      "Class 1, X1            0.9749 \n",
      "\n",
      "Class 2, X1            0.8385 \n",
      "\n",
      "\n",
      "-----------------------------------------------------------------------------------------\n",
      "Predicted Log-Likelihood:                       -9401.79\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Define a location to store the resutls \n",
    "outputFilePath = '.../GBM_LCCM_Example/'\n",
    "\n",
    "# In this example we will assume that eahc trip was done by different individual\n",
    "# So, that is why ind_id_col is equal to 'trip_id'\n",
    "\n",
    "\n",
    "# Train/Estimate the model\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter('ignore')\n",
    "    \n",
    "    \n",
    "    GBM_LCCM.lccm_fit(data = long_london,\n",
    "                      X = Standardized_X_Mem_C,\n",
    "                      X_Dummy = X_Mem_D,\n",
    "                      dataTest = long_london,\n",
    "                      XTest = Standardized_X_Mem_C,\n",
    "                      XTest_Dummy = X_Mem_D,\n",
    "                      prediction_test = 'Yes',\n",
    "                      GMM_Initialization = 'random',\n",
    "                      ind_id_col = 'trip_id', \n",
    "                      obs_id_col = 'custom_id',\n",
    "                      alt_id_col = 'mode_id',\n",
    "                      choice_col = 'travel_mode_nb', \n",
    "                      n_classes = n_classes,\n",
    "                      covariance_type = 'full',\n",
    "                      reg_covar = 1e-6,\n",
    "                      tol = 1e-3,\n",
    "                      max_iter = 100,\n",
    "                      class_specific_specs = class_specific_specs,\n",
    "                      class_specific_labels = class_specific_labels,\n",
    "                      #paramClassSpec = paramClassSpec,\n",
    "                      outputFilePath = outputFilePath,\n",
    "                      outputFileName = 'ModelResults')"
   ]
  }
 ],
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