.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b07discrete_mixture.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_swissmetro_plot_b07discrete_mixture.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_swissmetro_plot_b07discrete_mixture.py:


Latent class model
==================

Example of a discrete mixture of logit (or latent class model).

:author: Michel Bierlaire, EPFL
:date: Sun Apr  9 17:57:07 2023

.. GENERATED FROM PYTHON SOURCE LINES 12-17

.. code-block:: default


    import biogeme.biogeme as bio
    from biogeme import models
    from biogeme.expressions import Beta, log








.. GENERATED FROM PYTHON SOURCE LINES 18-19

See the data processing script: :ref:`swissmetro_data`.

.. GENERATED FROM PYTHON SOURCE LINES 19-33

.. code-block:: default

    from swissmetro_data import (
        database,
        CHOICE,
        SM_AV,
        CAR_AV_SP,
        TRAIN_AV_SP,
        TRAIN_TT_SCALED,
        TRAIN_COST_SCALED,
        SM_TT_SCALED,
        SM_COST_SCALED,
        CAR_TT_SCALED,
        CAR_CO_SCALED,
    )








.. GENERATED FROM PYTHON SOURCE LINES 34-35

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 35-41

.. code-block:: default

    ASC_CAR = Beta('ASC_CAR', 0, None, None, 0)
    ASC_TRAIN = Beta('ASC_TRAIN', 0, None, None, 0)
    ASC_SM = Beta('ASC_SM', 0, None, None, 1)
    B_TIME = Beta('B_TIME', 0, None, None, 0)
    B_COST = Beta('B_COST', 0, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 42-43

Class membership probability.

.. GENERATED FROM PYTHON SOURCE LINES 43-46

.. code-block:: default

    PROB_CLASS1 = Beta('PROB_CLASS1', 0.5, 0, 1, 0)
    PROB_CLASS2 = 1 - PROB_CLASS1








.. GENERATED FROM PYTHON SOURCE LINES 47-49

Definition of the utility functions for latent class 1, where the
time coefficient is zero.

.. GENERATED FROM PYTHON SOURCE LINES 49-53

.. code-block:: default

    V11 = ASC_TRAIN + B_COST * TRAIN_COST_SCALED
    V12 = ASC_SM + B_COST * SM_COST_SCALED
    V13 = ASC_CAR + B_COST * CAR_CO_SCALED








.. GENERATED FROM PYTHON SOURCE LINES 54-55

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 55-57

.. code-block:: default

    V1 = {1: V11, 2: V12, 3: V13}








.. GENERATED FROM PYTHON SOURCE LINES 58-60

Definition of the utility functions for latent class 2, whete the
time coefficient is estimated.

.. GENERATED FROM PYTHON SOURCE LINES 60-64

.. code-block:: default

    V21 = ASC_TRAIN + B_TIME * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
    V22 = ASC_SM + B_TIME * SM_TT_SCALED + B_COST * SM_COST_SCALED
    V23 = ASC_CAR + B_TIME * CAR_TT_SCALED + B_COST * CAR_CO_SCALED








.. GENERATED FROM PYTHON SOURCE LINES 65-66

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 66-68

.. code-block:: default

    V2 = {1: V21, 2: V22, 3: V23}








.. GENERATED FROM PYTHON SOURCE LINES 69-70

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 70-72

.. code-block:: default

    av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP}








.. GENERATED FROM PYTHON SOURCE LINES 73-74

The choice model is a discrete mixture of logit, with availability conditions

.. GENERATED FROM PYTHON SOURCE LINES 74-79

.. code-block:: default

    prob1 = models.logit(V1, av, CHOICE)
    prob2 = models.logit(V2, av, CHOICE)
    prob = PROB_CLASS1 * prob1 + PROB_CLASS2 * prob2
    logprob = log(prob)








.. GENERATED FROM PYTHON SOURCE LINES 80-81

Create the Biogeme object

.. GENERATED FROM PYTHON SOURCE LINES 81-84

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, logprob)
    the_biogeme.modelName = 'b07discrete_mixture'








.. GENERATED FROM PYTHON SOURCE LINES 85-86

Estimate the parameters

.. GENERATED FROM PYTHON SOURCE LINES 86-88

.. code-block:: default

    results = the_biogeme.estimate()








.. GENERATED FROM PYTHON SOURCE LINES 89-91

.. code-block:: default

    print(results.short_summary())





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Results for model b07discrete_mixture
    Nbr of parameters:              5
    Sample size:                    6768
    Excluded data:                  3960
    Final log likelihood:           -5208.498
    Akaike Information Criterion:   10427
    Bayesian Information Criterion: 10461.1





.. GENERATED FROM PYTHON SOURCE LINES 92-94

.. code-block:: default

    pandas_results = results.getEstimatedParameters()
    pandas_results





.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>Value</th>
          <th>Rob. Std err</th>
          <th>Rob. t-test</th>
          <th>Rob. p-value</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>ASC_CAR</th>
          <td>0.124605</td>
          <td>0.050735</td>
          <td>2.455992</td>
          <td>1.404963e-02</td>
        </tr>
        <tr>
          <th>ASC_TRAIN</th>
          <td>-0.397586</td>
          <td>0.062033</td>
          <td>-6.409280</td>
          <td>1.462082e-10</td>
        </tr>
        <tr>
          <th>B_COST</th>
          <td>-1.264065</td>
          <td>0.085606</td>
          <td>-14.766051</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME</th>
          <td>-2.797932</td>
          <td>0.171663</td>
          <td>-16.298946</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>PROB_CLASS1</th>
          <td>0.250792</td>
          <td>0.021741</td>
          <td>11.535649</td>
          <td>0.000000e+00</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.836 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b07discrete_mixture.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example




    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_b07discrete_mixture.py <plot_b07discrete_mixture.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_b07discrete_mixture.ipynb <plot_b07discrete_mixture.ipynb>`


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