.. 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.

Michel Bierlaire, EPFL
Sat Jun 28 2025, 12:43:40

.. GENERATED FROM PYTHON SOURCE LINES 13-19

.. code-block:: Python


    from IPython.core.display_functions import display
    from biogeme.biogeme import BIOGEME
    from biogeme.expressions import Beta, Elem, NormalCdf, log
    from biogeme.results_processing import get_pandas_estimated_parameters








.. GENERATED FROM PYTHON SOURCE LINES 20-21

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

.. GENERATED FROM PYTHON SOURCE LINES 21-30

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 31-32

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 32-38

.. code-block:: Python

    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:: Python

    v_train = b_time_train * TRAIN_TT_SCALED + b_cost_train * TRAIN_COST_SCALED
    v_car = asc_car + b_time_car * CAR_TT_SCALED + b_cost_car * CAR_CO_SCALED








.. GENERATED FROM PYTHON SOURCE LINES 45-46

Associate choice probability with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 46-51

.. code-block:: Python

    log_probability_dict = {
        1: log(NormalCdf(v_train - v_car)),
        3: log(NormalCdf(v_car - v_train)),
    }








.. GENERATED FROM PYTHON SOURCE LINES 52-54

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

.. GENERATED FROM PYTHON SOURCE LINES 54-56

.. code-block:: Python

    log_probability = Elem(log_probability_dict, CHOICE)








.. GENERATED FROM PYTHON SOURCE LINES 57-58

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 58-61

.. code-block:: Python

    the_biogeme = BIOGEME(database, log_probability, save_iterations=False)
    the_biogeme.model_name = 'b23probit'








.. GENERATED FROM PYTHON SOURCE LINES 62-63

Estimate the parameters

.. GENERATED FROM PYTHON SOURCE LINES 63-65

.. code-block:: Python

    results = the_biogeme.estimate()








.. GENERATED FROM PYTHON SOURCE LINES 66-68

.. code-block:: Python

    print(results.short_summary())





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

 .. code-block:: none

    Results for model b23probit
    Nbr of parameters:              5
    Sample size:                    2232
    Excluded data:                  8496
    Final log likelihood:           -906.9459
    Akaike Information Criterion:   1823.892
    Bayesian Information Criterion: 1852.445





.. GENERATED FROM PYTHON SOURCE LINES 69-71

.. code-block:: Python

    pandas_results = get_pandas_estimated_parameters(estimation_results=results)
    display(pandas_results)




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

 .. code-block:: none

               Name     Value  Robust std err.  Robust t-stat.  Robust p-value
    0  b_time_train -0.649749         0.095329       -6.815839    9.371393e-12
    1  b_cost_train -0.980475         0.147040       -6.668105    2.591283e-11
    2       asc_car -0.353276         0.107955       -3.272442    1.066228e-03
    3    b_time_car -0.184152         0.075674       -2.433501    1.495360e-02
    4    b_cost_car -0.530672         0.136053       -3.900477    9.600346e-05





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

   **Total running time of the script:** (0 minutes 0.879 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-jupyter

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

    .. 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-zip

      :download:`Download zipped: plot_b23binary_probit.zip <plot_b23binary_probit.zip>`


.. only:: html

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

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