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        "#%%\n",
        "\"\"\"File 05normalMixtureIntegral.py\n",
        "\n",
        ":author: Michel Bierlaire, EPFL\n",
        ":date: Sat Sep  7 18:23:01 2019\n",
        "\n",
        " Example of a mixture of logit models, using numerical integration.\n",
        " Three alternatives: Train, Car and Swissmetro\n",
        " SP data\n",
        "\"\"\"\n",
        "\n",
        "import pandas as pd\n",
        "import biogeme.database as db\n",
        "import biogeme.biogeme as bio\n",
        "import biogeme.distributions as dist\n",
        "from biogeme import models\n",
        "import biogeme.messaging as msg\n",
        "from biogeme.expressions import (\n",
        "    Beta,\n",
        "    DefineVariable,\n",
        "    RandomVariable,\n",
        "    log,\n",
        "    Integrate,\n",
        ")\n",
        "\n",
        "# Read the data\n",
        "df = pd.read_csv('swissmetro.dat', sep='\\t')\n",
        "database = db.Database('swissmetro', df)\n",
        "\n",
        "# The Pandas data structure is available as database.data. Use all the\n",
        "# Pandas functions to investigate the database. For example:\n",
        "# print(database.data.describe())\n",
        "\n",
        "# The following statement allows you to use the names of the variable\n",
        "# as Python variable.\n",
        "globals().update(database.variables)\n",
        "\n",
        "# Removing some observations can be done directly using pandas.\n",
        "# remove = (((database.data.PURPOSE != 1) &\n",
        "#           (database.data.PURPOSE != 3)) |\n",
        "#          (database.data.CHOICE == 0))\n",
        "# database.data.drop(database.data[remove].index,inplace=True)\n",
        "\n",
        "# Here we use the \"biogeme\" way for backward compatibility\n",
        "exclude = ((PURPOSE != 1) * (PURPOSE != 3) + (CHOICE == 0)) > 0\n",
        "database.remove(exclude)\n",
        "\n",
        "# Parameters to be estimated\n",
        "ASC_CAR = Beta('ASC_CAR', 0, None, None, 0)\n",
        "ASC_TRAIN = Beta('ASC_TRAIN', 0, None, None, 0)\n",
        "ASC_SM = Beta('ASC_SM', 0, None, None, 1)\n",
        "B_COST = Beta('B_COST', 0, None, None, 0)\n",
        "\n",
        "# Define a random parameter, normally distributed, designed to be used\n",
        "# for numerical integration\n",
        "B_TIME = Beta('B_TIME', 0, None, None, 0)\n",
        "# It is advised not to use 0 as starting value for the following parameter.\n",
        "B_TIME_S = Beta('B_TIME_S', 1, None, None, 0)\n",
        "omega = RandomVariable('omega')\n",
        "density = dist.normalpdf(omega)\n",
        "B_TIME_RND = B_TIME + B_TIME_S * omega\n",
        "\n",
        "# Definition of new variables\n",
        "SM_COST = SM_CO * (GA == 0)\n",
        "TRAIN_COST = TRAIN_CO * (GA == 0)\n",
        "\n",
        "# Definition of new variables: adding columns to the database\n",
        "CAR_AV_SP = DefineVariable('CAR_AV_SP', CAR_AV * (SP != 0), database)\n",
        "TRAIN_AV_SP = DefineVariable('TRAIN_AV_SP', TRAIN_AV * (SP != 0), database)\n",
        "TRAIN_TT_SCALED = DefineVariable('TRAIN_TT_SCALED', TRAIN_TT / 100.0, database)\n",
        "TRAIN_COST_SCALED = DefineVariable(\n",
        "    'TRAIN_COST_SCALED', TRAIN_COST / 100, database\n",
        ")\n",
        "SM_TT_SCALED = DefineVariable('SM_TT_SCALED', SM_TT / 100.0, database)\n",
        "SM_COST_SCALED = DefineVariable('SM_COST_SCALED', SM_COST / 100, database)\n",
        "CAR_TT_SCALED = DefineVariable('CAR_TT_SCALED', CAR_TT / 100, database)\n",
        "CAR_CO_SCALED = DefineVariable('CAR_CO_SCALED', CAR_CO / 100, database)\n",
        "\n",
        "# Definition of the utility functions\n",
        "V1 = ASC_TRAIN + B_TIME_RND * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED\n",
        "V2 = ASC_SM + B_TIME_RND * SM_TT_SCALED + B_COST * SM_COST_SCALED\n",
        "V3 = ASC_CAR + B_TIME_RND * CAR_TT_SCALED + B_COST * CAR_CO_SCALED\n",
        "\n",
        "# Associate utility functions with the numbering of alternatives\n",
        "V = {1: V1, 2: V2, 3: V3}\n",
        "\n",
        "# Associate the availability conditions with the alternatives\n",
        "av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP}\n",
        "\n",
        "# Conditional to omega, we have a logit model (called the kernel)\n",
        "condprob = models.logit(V, av, CHOICE)\n",
        "# We integrate over omega using numerical integration\n",
        "logprob = log(Integrate(condprob * density, 'omega'))\n",
        "\n",
        "# Define level of verbosity\n",
        "logger = msg.bioMessage()\n",
        "# logger.setSilent()\n",
        "# logger.setWarning()\n",
        "logger.setGeneral()\n",
        "# logger.setDetailed()\n",
        "\n",
        "# Create the Biogeme object\n",
        "biogeme = bio.BIOGEME(database, logprob)\n",
        "biogeme.modelName = '05normalMixtureIntegral'\n",
        "\n",
        "# Estimate the parameters\n",
        "results = biogeme.estimate()\n",
        "pandasResults = results.getEstimatedParameters()\n",
        "print(pandasResults)\n"
      ],
      "outputs": [],
      "execution_count": null
    }
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