.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b23binary_probit.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_b23binary_probit.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_swissmetro_plot_b23binary_probit.py:


Binary probit model
===================

Example of a binary probit model.
Two alternatives: Train and Car.

:author: Michel Bierlaire, EPFL
:date: Wed Apr 12 17:58:18 2023

.. GENERATED FROM PYTHON SOURCE LINES 13-17

.. code-block:: default


    import biogeme.biogeme as bio
    from biogeme.expressions import Beta, bioNormalCdf, Elem, log








.. GENERATED FROM PYTHON SOURCE LINES 18-19

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

.. GENERATED FROM PYTHON SOURCE LINES 19-30

.. code-block:: default

    from swissmetro_binary import (
        database,
        CHOICE,
        TRAIN_AV_SP,
        CAR_AV_SP,
        TRAIN_TT_SCALED,
        TRAIN_COST_SCALED,
        CAR_TT_SCALED,
        CAR_CO_SCALED,
    )








.. GENERATED FROM PYTHON SOURCE LINES 31-32

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 32-38

.. code-block:: default

    ASC_CAR = Beta('ASC_CAR', 0, None, None, 0)
    B_TIME_CAR = Beta('B_TIME_CAR', 0, None, None, 0)
    B_TIME_TRAIN = Beta('B_TIME_TRAIN', 0, None, None, 0)
    B_COST_CAR = Beta('B_COST_CAR', 0, None, None, 0)
    B_COST_TRAIN = Beta('B_COST_TRAIN', 0, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 39-41

Definition of the utility functions.
We estimate a binary probit model. There are only two alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 41-44

.. code-block:: default

    V1 = B_TIME_TRAIN * TRAIN_TT_SCALED + B_COST_TRAIN * TRAIN_COST_SCALED
    V3 = ASC_CAR + B_TIME_CAR * CAR_TT_SCALED + B_COST_CAR * CAR_CO_SCALED








.. GENERATED FROM PYTHON SOURCE LINES 45-47

Associate choice probability with the numbering of alternatives.
If one alternative is not available, the choice probability of the other one is 1.

.. GENERATED FROM PYTHON SOURCE LINES 47-52

.. code-block:: default

    logP = {
        1: TRAIN_AV_SP * (CAR_AV_SP * log(bioNormalCdf(V1 - V3) + 1 - CAR_AV_SP)),
        3: CAR_AV_SP * (TRAIN_AV_SP * log(bioNormalCdf(V3 - V1) + 1 - TRAIN_AV_SP)),
    }








.. GENERATED FROM PYTHON SOURCE LINES 53-55

Definition of the model. This is the contribution of each
observation to the log likelihood function.

.. GENERATED FROM PYTHON SOURCE LINES 55-57

.. code-block:: default

    logprob = Elem(logP, CHOICE)








.. GENERATED FROM PYTHON SOURCE LINES 58-59

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 59-62

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, logprob)
    the_biogeme.modelName = 'b23probit'








.. GENERATED FROM PYTHON SOURCE LINES 63-64

Estimate the parameters

.. GENERATED FROM PYTHON SOURCE LINES 64-66

.. code-block:: default

    results = the_biogeme.estimate()








.. GENERATED FROM PYTHON SOURCE LINES 67-69

.. code-block:: default

    print(results.short_summary())





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

 .. code-block:: none

    Results for model b23probit
    Nbr of parameters:              5
    Sample size:                    2678
    Excluded data:                  8050
    Final log likelihood:           -906.9459
    Akaike Information Criterion:   1823.892
    Bayesian Information Criterion: 1853.356





.. GENERATED FROM PYTHON SOURCE LINES 70-72

.. 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>-0.353276</td>
          <td>0.107955</td>
          <td>-3.272442</td>
          <td>1.066228e-03</td>
        </tr>
        <tr>
          <th>B_COST_CAR</th>
          <td>-0.530672</td>
          <td>0.136053</td>
          <td>-3.900477</td>
          <td>9.600346e-05</td>
        </tr>
        <tr>
          <th>B_COST_TRAIN</th>
          <td>-0.980475</td>
          <td>0.147040</td>
          <td>-6.668105</td>
          <td>2.591283e-11</td>
        </tr>
        <tr>
          <th>B_TIME_CAR</th>
          <td>-0.184152</td>
          <td>0.075674</td>
          <td>-2.433501</td>
          <td>1.495360e-02</td>
        </tr>
        <tr>
          <th>B_TIME_TRAIN</th>
          <td>-0.649749</td>
          <td>0.095329</td>
          <td>-6.815839</td>
          <td>9.371393e-12</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** (0 minutes 0.052 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b23binary_probit.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_b23binary_probit.py <plot_b23binary_probit.py>`

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

      :download:`Download Jupyter notebook: plot_b23binary_probit.ipynb <plot_b23binary_probit.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_