
.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/bayesian_swissmetro/plot_b09_nested.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_b09_nested.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_bayesian_swissmetro_plot_b09_nested.py:


9. Nested logit model
=====================

Bayesian estimation of a nested logit model.

Michel Bierlaire, EPFL
Mon Nov 03 2025, 20:02:56

.. GENERATED FROM PYTHON SOURCE LINES 11-21

.. code-block:: Python


    from IPython.core.display_functions import display

    from biogeme import 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 lognested
    from biogeme.nests import NestsForNestedLogit, OneNestForNestedLogit


.. GENERATED FROM PYTHON SOURCE LINES 22-23

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

.. GENERATED FROM PYTHON SOURCE LINES 23-40

.. 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,
    )

    logger = blog.get_screen_logger(level=blog.INFO)
    logger.info('Example b09_nested')


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

 .. code-block:: none

    Example b09_nested 


.. GENERATED FROM PYTHON SOURCE LINES 41-42

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 42-49

.. code-block:: Python

    asc_car = Beta('asc_car', 0, None, None, 0)
    asc_train = Beta('asc_train', 0, None, None, 0)
    asc_sm = Beta('asc_sm', 0, None, None, 1)
    b_time = Beta('b_time', 0, None, 0, 0)
    b_cost = Beta('b_cost', 0, None, 0, 0)
    nest_parameter = Beta('nest_parameter', 1, 1, 3, 0)


.. GENERATED FROM PYTHON SOURCE LINES 50-51

Definition of the utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 51-55

.. code-block:: Python

    v_train = asc_train + b_time * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED
    v_swissmetro = 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 56-57

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 57-59

.. code-block:: Python

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


.. GENERATED FROM PYTHON SOURCE LINES 60-61

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 61-63

.. code-block:: Python

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


.. GENERATED FROM PYTHON SOURCE LINES 64-68

Definition of nests. Only the non-trivial nests must be defined. A
trivial nest is a nest containing exactly one alternative.  In this
example, we create a nest for the existing modes, that is train (1)
and car (3).

.. GENERATED FROM PYTHON SOURCE LINES 68-75

.. code-block:: Python


    existing = OneNestForNestedLogit(
        nest_param=nest_parameter, list_of_alternatives=[1, 3], name='existing'
    )

    nests = NestsForNestedLogit(choice_set=list(v), tuple_of_nests=(existing,))


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

 .. code-block:: none

    The following elements do not appear in any nest and are assumed each to be alone in a separate nest: {2}. If it is not the intention, check the assignment of alternatives to nests. 


.. GENERATED FROM PYTHON SOURCE LINES 76-79

Definition of the model. This is the contribution of each
observation to the log likelihood function.
The choice model is a nested logit, with availability conditions.

.. GENERATED FROM PYTHON SOURCE LINES 79-81

.. code-block:: Python

    log_probability = lognested(v, av, nests, CHOICE)


.. GENERATED FROM PYTHON SOURCE LINES 82-83

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 83-89

.. code-block:: Python

    the_biogeme = BIOGEME(
        database,
        log_probability,
    )
    the_biogeme.model_name = 'b09_nested'


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

 .. code-block:: none

    Biogeme parameters read from biogeme.toml. 


.. GENERATED FROM PYTHON SOURCE LINES 90-91

Estimate the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 91-98

.. 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

    *** Initial values of the parameters are obtained from the file __b09_nested.iter 
    Cannot read file __b09_nested.iter. Statement is ignored. 
    Starting values for the algorithm: {} 
    /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()
    Detected CPU devices: 1 | System logical cores: 12
    Current XLA_FLAGS: --xla_force_host_platform_device_count=100
    Platform: Darwin 24.6.0 | Python: 3.13.1
 
    Auto sampling: JAX available (devices=1, platforms=cpu) → numpyro/vectorized 
    /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 261 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 631 ms
    waic finished in 631 ms
    loo_res finished in 7351 ms (7.35 s)
    loo finished in 7351 ms (7.35 s)
    Diagnostics computation took 22.7 seconds (cached). 
    File b09_nested.html has been generated. 
    Save simulation results on b09_nested.nc 
    Saved Bayesian results (posterior + metadata) to b09_nested.nc 


.. GENERATED FROM PYTHON SOURCE LINES 99-101

.. 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                                                 0:01:03.929416
    Posterior predictive log-likelihood (sum of log mean p)  -5234.07
    Expected log-likelihood E[log L(Y|θ)]                    -5239.44
    Best-draw log-likelihood (posterior upper bound)         -5236.91
    WAIC (Widely Applicable Information Criterion)           -5244.89
    WAIC Standard Error                                      62.46
    Effective number of parameters (p_WAIC)                  10.82
    LOO (Leave-One-Out Cross-Validation)                     -5244.88
    LOO Standard Error                                       62.46
    Effective number of parameters (p_LOO)                   10.81


.. GENERATED FROM PYTHON SOURCE LINES 102-105

.. 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_train     -0.511596  ...  3719.532913  4154.509847
    1         asc_car     -0.166489  ...  3469.142538  4263.760221
    2          b_time     -0.899984  ...  3220.978491  4222.676227
    3          b_cost     -0.856607  ...  4598.688723  4570.329257
    4  nest_parameter      2.057677  ...  4077.007373  4295.689611

    [5 rows x 12 columns]


.. GENERATED FROM PYTHON SOURCE LINES 106-108

We calculate the correlation between the error terms of the
alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 108-113

.. code-block:: Python

    corr = nests.correlation(
        parameters=results.get_beta_values(),
        alternatives_names={1: 'Train', 2: 'Swissmetro', 3: 'Car'},
    )
    print(corr)


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

 .. code-block:: none

                   Train  Swissmetro       Car
    Train       1.000000         0.0  0.763819
    Swissmetro  0.000000         1.0  0.000000
    Car         0.763819         0.0  1.000000


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

   **Total running time of the script:** (2 minutes 0.825 seconds)


.. _sphx_glr_download_auto_examples_bayesian_swissmetro_plot_b09_nested.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

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

      :download:`Download Jupyter notebook: plot_b09_nested.ipynb <plot_b09_nested.ipynb>`

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

      :download:`Download Python source code: plot_b09_nested.py <plot_b09_nested.py>`

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

      :download:`Download zipped: plot_b09_nested.zip <plot_b09_nested.zip>`


.. only:: html

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

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