
.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/bayesian_swissmetro/plot_b01a_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_b01a_logit.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_bayesian_swissmetro_plot_b01a_logit.py:


1a. Estimation of a logit model (Bayesian)
==========================================

 Three alternatives:

   - train,
   - car and,
   - Swissmetro.

 Stated preferences data.

Michel Bierlaire, EPFL
Thu Oct 30 2025, 10:15:52

.. GENERATED FROM PYTHON SOURCE LINES 17-29

.. code-block:: Python


    from IPython.core.display_functions import display

    import biogeme.biogeme_logging as blog
    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 30-31

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

.. GENERATED FROM PYTHON SOURCE LINES 31-45

.. code-block:: Python

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


.. GENERATED FROM PYTHON SOURCE LINES 46-48

The logger sets the verbosity of Biogeme. By default, Biogeme is quite silent and generates only warnings.
To have more information about what it happening behind the scene, the level should be set to `blog.INFO`.

.. GENERATED FROM PYTHON SOURCE LINES 48-52

.. code-block:: Python

    logger = blog.get_screen_logger(level=blog.DEBUG)
    logger.info('Example b01a_logit.py')


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

 .. code-block:: none

    [INFO] 2025-12-25 14:43:15,419 Example b01a_logit.py <plot_b01a_logit.py:49>


.. GENERATED FROM PYTHON SOURCE LINES 53-56

Parameters to be estimated: alternative specific constants.
By default, the prior distribution is normal, possibly truncated if bounds are defined, with the mean
defined by the user, and scale parameter 10.

.. GENERATED FROM PYTHON SOURCE LINES 56-59

.. code-block:: Python

    asc_car = Beta('asc_car', 0, None, None, 0)
    asc_train = Beta('asc_train', 0, None, None, 0)


.. GENERATED FROM PYTHON SOURCE LINES 60-63

The constant associated with Swissmetro is normalized to zero. It does not need to be defined at all.
Here, we illustrate the fact that setting the last argument of the `Beta` function to 1 fixes the parameter
to its default value (here, 0).

.. GENERATED FROM PYTHON SOURCE LINES 63-65

.. code-block:: Python

    asc_sm = Beta('asc_sm', 0, None, None, 1)


.. GENERATED FROM PYTHON SOURCE LINES 66-68

Coefficients of the attributes. It is useful to set the upper bound to 0 to reflect the prior assumption about
the sign of those parameters.

.. GENERATED FROM PYTHON SOURCE LINES 68-72

.. code-block:: Python

    b_time = Beta('b_time', 0, None, 0, 0)
    b_cost = Beta('b_cost', 0, None, 0, 0)


.. GENERATED FROM PYTHON SOURCE LINES 73-74

Definition of the utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 74-78

.. code-block:: Python

    v_train = asc_train + b_time * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED
    v_sm = asc_sm + b_time * SM_TT_SCALED + b_cost * SM_COST_SCALED
    v_car = asc_car + b_time * CAR_TT_SCALED + b_cost * CAR_CO_SCALED


.. GENERATED FROM PYTHON SOURCE LINES 79-80

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 80-82

.. code-block:: Python

    v = {1: v_train, 2: v_sm, 3: v_car}


.. GENERATED FROM PYTHON SOURCE LINES 83-84

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 84-86

.. code-block:: Python

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


.. GENERATED FROM PYTHON SOURCE LINES 87-89

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

.. GENERATED FROM PYTHON SOURCE LINES 89-91

.. code-block:: Python

    log_probability = loglogit(v, av, CHOICE)


.. GENERATED FROM PYTHON SOURCE LINES 92-93

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 93-96

.. code-block:: Python

    the_biogeme = BIOGEME(database, log_probability)
    the_biogeme.model_name = 'b01a_logit'


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

 .. code-block:: none

    [DEBUG] 2025-12-25 14:43:15,421 READ FILE biogeme.toml : automatic <parameters.py:184>
    [INFO] 2025-12-25 14:43:15,421 Default values of the Biogeme parameters are used. <parameters.py:222>
    [WARNING] 2025-12-25 14:43:15,423 File biogeme.toml has been created <parameters.py:259>


.. GENERATED FROM PYTHON SOURCE LINES 97-98

Estimate the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 98-100

.. code-block:: Python

    results: BayesianResults = the_biogeme.bayesian_estimation()


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

 .. code-block:: none

    [INFO] 2025-12-25 14:43:15,423 *** Initial values of the parameters are obtained from the file __b01a_logit.iter <biogeme.py:813>
    [INFO] 2025-12-25 14:43:15,424 Cannot read file __b01a_logit.iter. Statement is ignored. <biogeme.py:700>
    [INFO] 2025-12-25 14:43:15,424 Starting values for the algorithm: {} <biogeme.py:824>
    /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()
    [INFO] 2025-12-25 14:43:15,425 Detected CPU devices: 1 | System logical cores: 12
    Current XLA_FLAGS: (none set)
    Platform: Darwin 24.6.0 | Python: 3.13.1
     <biogeme.py:833>
    [INFO] 2025-12-25 14:43:15,474 Auto sampling: JAX available (devices=1, platforms=cpu) → numpyro/vectorized <sampling_strategy.py:130>
    /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 294 ms
    expected_log_likelihood finished in 11 ms
    best_draw_log_likelihood finished in 10 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 639 ms
    waic finished in 639 ms
    loo_res finished in 7580 ms (7.58 s)
    loo finished in 7580 ms (7.58 s)
    [INFO] 2025-12-25 14:44:28,380 Diagnostics computation took 22.9 seconds (cached). <bayesian_results.py:235>
    [INFO] 2025-12-25 14:44:29,340 File b01a_logit.html has been generated. <html_output.py:943>
    [INFO] 2025-12-25 14:44:29,340 Save simulation results on b01a_logit.nc <raw_bayesian_results.py:155>
    [INFO] 2025-12-25 14:44:54,756 Saved Bayesian results (posterior + metadata) to b01a_logit.nc <raw_bayesian_results.py:207>


.. GENERATED FROM PYTHON SOURCE LINES 101-103

.. code-block:: Python

    print(results.short_summary())


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

 .. code-block:: none

    Sample size                                              6768
    Sampler                                                  NUTS
    Number of chains                                         4
    Number of draws per chain                                2000
    Total number of draws                                    8000
    Acceptance rate target                                   0.9
    Run time                                                 0:00:41.437931
    Posterior predictive log-likelihood (sum of log mean p)  -5329.78
    Expected log-likelihood E[log L(Y|θ)]                    -5333.27
    Best-draw log-likelihood (posterior upper bound)         -5331.27
    WAIC (Widely Applicable Information Criterion)           -5336.78
    WAIC Standard Error                                      59.63
    Effective number of parameters (p_WAIC)                  7.00
    LOO (Leave-One-Out Cross-Validation)                     -5336.79
    LOO Standard Error                                       59.63
    Effective number of parameters (p_LOO)                   7.01


.. GENERATED FROM PYTHON SOURCE LINES 104-105

Get the results in a pandas table

.. GENERATED FROM PYTHON SOURCE LINES 105-110

.. 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)  Value (median)  ...     R hat   ESS (bulk)   ESS (tail)
    0  asc_train     -0.700918       -0.700670  ...  1.000130  3402.152245  4601.166818
    1    asc_car     -0.154128       -0.153721  ...  1.000899  3564.651200  4448.207029
    2     b_time     -1.278959       -1.278735  ...  0.999974  3360.898307  4439.786854
    3     b_cost     -1.084059       -1.083901  ...  1.000379  4775.294477  4711.471226

    [4 rows x 12 columns]


.. GENERATED FROM PYTHON SOURCE LINES 111-112

Describe the draws stored in the PyMC report.

.. GENERATED FROM PYTHON SOURCE LINES 112-113

.. code-block:: Python

    display(results.report_stored_variables())


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

 .. code-block:: none

                 group           variable                dims            shape
    0    constant_data          CAR_AV_SP              (obs,)          (6768,)
    1    constant_data      CAR_CO_SCALED              (obs,)          (6768,)
    2    constant_data      CAR_TT_SCALED              (obs,)          (6768,)
    3    constant_data             CHOICE              (obs,)          (6768,)
    4    constant_data              SM_AV              (obs,)          (6768,)
    5    constant_data     SM_COST_SCALED              (obs,)          (6768,)
    6    constant_data       SM_TT_SCALED              (obs,)          (6768,)
    7    constant_data        TRAIN_AV_SP              (obs,)          (6768,)
    8    constant_data  TRAIN_COST_SCALED              (obs,)          (6768,)
    9    constant_data    TRAIN_TT_SCALED              (obs,)          (6768,)
    10  log_likelihood            _choice  (chain, draw, obs)  (4, 2000, 6768)
    11       posterior            asc_car       (chain, draw)        (4, 2000)
    12       posterior          asc_train       (chain, draw)        (4, 2000)
    13       posterior             b_cost       (chain, draw)        (4, 2000)
    14       posterior             b_time       (chain, draw)        (4, 2000)
    15       posterior           log_like  (chain, draw, obs)  (4, 2000, 6768)
    16           prior            asc_car       (chain, draw)        (1, 2000)
    17           prior          asc_train       (chain, draw)        (1, 2000)
    18           prior             b_cost       (chain, draw)        (1, 2000)
    19           prior             b_time       (chain, draw)        (1, 2000)
    20           prior           log_like  (chain, draw, obs)  (1, 2000, 6768)
    21    sample_stats    acceptance_rate       (chain, draw)        (4, 2000)
    22    sample_stats          diverging       (chain, draw)        (4, 2000)
    23    sample_stats             energy       (chain, draw)        (4, 2000)
    24    sample_stats                 lp       (chain, draw)        (4, 2000)
    25    sample_stats            n_steps       (chain, draw)        (4, 2000)
    26    sample_stats          step_size       (chain, draw)        (4, 2000)
    27    sample_stats         tree_depth       (chain, draw)        (4, 2000)


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

   **Total running time of the script:** (1 minutes 39.642 seconds)


.. _sphx_glr_download_auto_examples_bayesian_swissmetro_plot_b01a_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_b01a_logit.ipynb <plot_b01a_logit.ipynb>`

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

      :download:`Download Python source code: plot_b01a_logit.py <plot_b01a_logit.py>`

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

      :download:`Download zipped: plot_b01a_logit.zip <plot_b01a_logit.zip>`


.. only:: html

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

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