
.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/bayesian_swissmetro/plot_b23a_binary_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_bayesian_swissmetro_plot_b23a_binary_logit.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_bayesian_swissmetro_plot_b23a_binary_logit.py:


23a. Binary logit model
=======================

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

Michel Bierlaire, EPFL
Tue Nov 18 2025, 18:42:42

.. GENERATED FROM PYTHON SOURCE LINES 13-20

.. code-block:: Python


    from IPython.core.display_functions import display

    from biogeme.bayesian_estimation import BayesianResults, get_pandas_estimated_parameters
    from biogeme.biogeme import BIOGEME
    from biogeme.expressions import Beta
    from biogeme.models import loglogit


.. 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, 0, 0)
    b_time_train = Beta('b_time_train', 0, None, 0, 0)
    b_cost_car = Beta('b_cost_car', 0, None, 0, 0)
    b_cost_train = Beta('b_cost_train', 0, None, 0, 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 = 'b23a_binary_logit'


.. GENERATED FROM PYTHON SOURCE LINES 66-67

Estimate the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 67-73

.. code-block:: Python

    try:
        results = BayesianResults.from_netcdf(
            filename=f'saved_results/{the_biogeme.model_name}.nc'
        )
    except FileNotFoundError:
        results = the_biogeme.bayesian_estimation()


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

 .. code-block:: none

    /Users/bierlair/MyFiles/github/biogeme/src/biogeme/biogeme.py:832: UserWarning: Note: JAX currently sees 1 CPU device. To parallelize across CPU devices, set XLA_FLAGS as above and restart Python/Jupyter.
    macOS / Linux (bash/zsh):
      export XLA_FLAGS="--xla_force_host_platform_device_count=<number_of_cores>"

    Jupyter (new cell, before `import jax`):
      %env XLA_FLAGS="--xla_force_host_platform_device_count=<number_of_cores>"

      warning_cpu_devices()
    /Users/bierlair/MyFiles/github/biogeme/src/biogeme/biogeme.py:859: UserWarning: The effect of Potentials on other parameters is ignored during prior predictive sampling. This is likely to lead to invalid or biased predictive samples.
      pm.sample_prior_predictive(
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    posterior_predictive_loglike finished in 87 ms
    /Users/bierlair/python_envs/venv313/lib/python3.13/site-packages/arviz/stats/stats.py:1667: UserWarning: For one or more samples the posterior variance of the log predictive densities exceeds 0.4. This could be indication of WAIC starting to fail. 
    See http://arxiv.org/abs/1507.04544 for details
      warnings.warn(
    waic_res finished in 232 ms
    waic finished in 232 ms
    loo_res finished in 2711 ms (2.71 s)
    loo finished in 2711 ms (2.71 s)


.. GENERATED FROM PYTHON SOURCE LINES 74-76

.. code-block:: Python

    print(results.short_summary())


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

 .. code-block:: none

    Sample size                                              2232
    Sampler                                                  NUTS
    Number of chains                                         4
    Number of draws per chain                                2000
    Total number of draws                                    8000
    Acceptance rate target                                   0.9
    Run time                                                 0:00:34.328287
    Posterior predictive log-likelihood (sum of log mean p)  -869.73
    Expected log-likelihood E[log L(Y|θ)]                    -875.39
    Best-draw log-likelihood (posterior upper bound)         -872.92
    WAIC (Widely Applicable Information Criterion)           -882.42
    WAIC Standard Error                                      34.81
    Effective number of parameters (p_WAIC)                  12.69
    LOO (Leave-One-Out Cross-Validation)                     -882.37
    LOO Standard Error                                       34.80
    Effective number of parameters (p_LOO)                   12.64


.. GENERATED FROM PYTHON SOURCE LINES 77-78

Get the results in a pandas table

.. GENERATED FROM PYTHON SOURCE LINES 78-82

.. 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 (mean)  ...   ESS (bulk)   ESS (tail)
    0       asc_car     -0.901620  ...  5561.528458  4851.382236
    1  b_time_train     -1.158381  ...  4435.671075  4494.601164
    2  b_cost_train     -2.402039  ...  6019.122471  4842.254908
    3    b_time_car     -0.417747  ...  5025.790890  3121.605048
    4    b_cost_car     -1.078325  ...  5699.909181  4401.614672

    [5 rows x 12 columns]


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

   **Total running time of the script:** (0 minutes 56.023 seconds)


.. _sphx_glr_download_auto_examples_bayesian_swissmetro_plot_b23a_binary_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_b23a_binary_logit.ipynb <plot_b23a_binary_logit.ipynb>`

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

      :download:`Download Python source code: plot_b23a_binary_logit.py <plot_b23a_binary_logit.py>`

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

      :download:`Download zipped: plot_b23a_binary_logit.zip <plot_b23a_binary_logit.zip>`


.. only:: html

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

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