.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b23binary_logit.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_logit.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_swissmetro_plot_b23binary_logit.py:


Binary logit model
==================

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

Michel Bierlaire, EPFL
Sat Jun 28 2025, 12:42:27

.. GENERATED FROM PYTHON SOURCE LINES 13-20

.. code-block:: Python


    from IPython.core.display_functions import display
    from biogeme.biogeme import BIOGEME
    from biogeme.expressions import Beta
    from biogeme.models import loglogit
    from biogeme.results_processing import get_pandas_estimated_parameters








.. GENERATED FROM PYTHON SOURCE LINES 21-22

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

.. GENERATED FROM PYTHON SOURCE LINES 22-33

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 34-35

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 35-41

.. 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 42-44

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

.. GENERATED FROM PYTHON SOURCE LINES 44-47

.. 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 48-49

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 49-51

.. code-block:: Python

    v = {1: v_train, 3: v_car}








.. GENERATED FROM PYTHON SOURCE LINES 52-53

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 53-55

.. code-block:: Python

    av = {1: TRAIN_AV_SP, 3: CAR_AV_SP}








.. GENERATED FROM PYTHON SOURCE LINES 56-58

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

.. GENERATED FROM PYTHON SOURCE LINES 58-60

.. code-block:: Python

    log_probability = loglogit(v, av, CHOICE)








.. GENERATED FROM PYTHON SOURCE LINES 61-62

Create the Biogeme object

.. GENERATED FROM PYTHON SOURCE LINES 62-65

.. code-block:: Python

    the_biogeme = BIOGEME(database, log_probability)
    the_biogeme.model_name = 'b23logit'








.. GENERATED FROM PYTHON SOURCE LINES 66-67

Estimate the parameters

.. GENERATED FROM PYTHON SOURCE LINES 67-69

.. code-block:: Python

    results = the_biogeme.estimate()








.. GENERATED FROM PYTHON SOURCE LINES 70-72

.. code-block:: Python

    print(results.short_summary())





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

 .. code-block:: none

    Results for model b23logit
    Nbr of parameters:              5
    Sample size:                    2232
    Excluded data:                  8496
    Final log likelihood:           -872.9052
    Akaike Information Criterion:   1755.81
    Bayesian Information Criterion: 1784.364





.. GENERATED FROM PYTHON SOURCE LINES 73-75

.. 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 -1.134867         0.210637       -5.387777    7.133434e-08
    1  b_cost_train -2.393364         0.272021       -8.798468    0.000000e+00
    2       asc_car -0.896101         0.178268       -5.026696    4.990013e-07
    3    b_time_car -0.383847         0.310672       -1.235537    2.166306e-01
    4    b_cost_car -1.088054         0.295942       -3.676576    2.363851e-04





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

   **Total running time of the script:** (0 minutes 1.716 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b23binary_logit.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_logit.ipynb <plot_b23binary_logit.ipynb>`

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

      :download:`Download Python source code: plot_b23binary_logit.py <plot_b23binary_logit.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_b23binary_logit.zip <plot_b23binary_logit.zip>`


.. only:: html

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

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