
.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/indicators/plot_b02estimation.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_indicators_plot_b02estimation.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_indicators_plot_b02estimation.py:


Estimation and simulation of a nested logit model
=================================================

 We estimate a nested logit model, and we perform simulation using the
 estimated model.

Michel Bierlaire, EPFL
Sat Jun 28 2025, 16:08:07

.. GENERATED FROM PYTHON SOURCE LINES 12-26

.. code-block:: Python


    from IPython.core.display_functions import display

    import biogeme.biogeme_logging as blog
    from biogeme.biogeme import BIOGEME
    from biogeme.calculator import get_value_c
    from biogeme.data.optima import read_data
    from biogeme.models import lognested
    from biogeme.results_processing import get_pandas_estimated_parameters
    from scenarios import scenario

    logger = blog.get_screen_logger(level=blog.INFO)
    logger.info('Example plot_b02estimation')


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

 .. code-block:: none

    Example plot_b02estimation 


.. GENERATED FROM PYTHON SOURCE LINES 27-29

Obtain the specification for the default scenario.
The definition of the scenarios is available in :ref:`scenarios`.

.. GENERATED FROM PYTHON SOURCE LINES 29-31

.. code-block:: Python

    V, nests, choice, _ = scenario()


.. GENERATED FROM PYTHON SOURCE LINES 32-34

The choice model is a nested logit, with availability conditions
For estimation, we need the log of the probability.

.. GENERATED FROM PYTHON SOURCE LINES 34-36

.. code-block:: Python

    log_probability = lognested(util=V, availability=None, nests=nests, choice=choice)


.. GENERATED FROM PYTHON SOURCE LINES 37-38

Get the database

.. GENERATED FROM PYTHON SOURCE LINES 38-39

.. code-block:: Python

    database = read_data()


.. GENERATED FROM PYTHON SOURCE LINES 40-41

Create the Biogeme object for estimation.

.. GENERATED FROM PYTHON SOURCE LINES 41-44

.. code-block:: Python

    the_biogeme = BIOGEME(database, log_probability)
    the_biogeme.model_name = 'b02estimation'


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

 .. code-block:: none

    Biogeme parameters read from biogeme.toml. 


.. GENERATED FROM PYTHON SOURCE LINES 45-46

Estimate the parameters. Perform bootstrapping.

.. GENERATED FROM PYTHON SOURCE LINES 46-48

.. code-block:: Python

    results = the_biogeme.estimate(run_bootstrap=True)


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

 .. code-block:: none

    *** Initial values of the parameters are obtained from the file __b02estimation.iter 
    Parameter values restored from __b02estimation.iter 
    Starting values for the algorithm: {'beta_time_fulltime': -1.5964670520847424, 'beta_time_other': -0.5526862214775381, 'beta_cost': -0.719072321557382, 'mu_no_car': 1.5237160520807354, 'asc_sm': 0.06300034044143561, 'beta_dist_male': -0.6876768914763282, 'beta_dist_female': -0.8321525469977931, 'beta_dist_unreported': -0.7047372090923671, 'asc_car': 0.2586072914689233} 
    As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: BFGS with trust region for simple bounds 
    Optimization algorithm has converged. 
    Relative gradient: 4.478787282617695e-06 
    Cause of termination: Relative gradient = 4.5e-06 <= 6.1e-06 
    Number of function evaluations: 1 
    Number of gradient evaluations: 1 
    Number of hessian evaluations: 0 
    Algorithm: BFGS with trust region for simple bound constraints 
    Number of iterations: 0 
    Optimization time: 0:00:00.466837 
    Calculate second derivatives and BHHH 
    Re-estimate the model 100 times for bootstrapping 
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      warnings.warn(

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    File b02estimation~00.html has been generated. 
    File b02estimation~00.yaml has been generated. 


.. GENERATED FROM PYTHON SOURCE LINES 49-50

Get the results in a pandas table

.. GENERATED FROM PYTHON SOURCE LINES 50-54

.. 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  ...  Bootstrap t-stat.  Bootstrap p-value
    0    beta_time_fulltime -1.596467  ...          -5.445201       5.174692e-08
    1       beta_time_other -0.552686  ...          -2.037927       4.155725e-02
    2             beta_cost -0.719072  ...          -5.167539       2.371969e-07
    3             mu_no_car  1.523716  ...           5.342280       9.178487e-08
    4                asc_sm  0.063000  ...           0.284539       7.759970e-01
    5        beta_dist_male -0.687677  ...          -3.925931       8.639485e-05
    6      beta_dist_female -0.832153  ...          -3.929043       8.528455e-05
    7  beta_dist_unreported -0.704737  ...          -2.987710       2.810762e-03
    8               asc_car  0.258607  ...           2.881082       3.963129e-03

    [9 rows x 5 columns]


.. GENERATED FROM PYTHON SOURCE LINES 55-56

Simulation

.. GENERATED FROM PYTHON SOURCE LINES 56-65

.. code-block:: Python

    simulated_choices = get_value_c(
        expression=log_probability,
        betas=results.get_beta_values(),
        database=database,
        numerically_safe=False,
        use_jit=True,
    )
    display(simulated_choices)


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

 .. code-block:: none

    Bootstraps:   0%|          | 0/100 [16:49<?, ?it/s]
    [-0.65553681 -1.42271161 -0.13348367 ... -0.37368096 -0.29814134
     -0.27030377]


.. GENERATED FROM PYTHON SOURCE LINES 66-76

.. code-block:: Python

    loglikelihood = get_value_c(
        expression=log_probability,
        betas=results.get_beta_values(),
        database=database,
        aggregation=True,
        numerically_safe=False,
        use_jit=True,
    )
    print(f'Final log likelihood:     {results.final_log_likelihood}')
    print(f'Simulated log likelihood: {loglikelihood}')


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

 .. code-block:: none

    Final log likelihood:     -1295.1202531057634
    Simulated log likelihood: -1295.1202531057634


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

   **Total running time of the script:** (16 minutes 53.085 seconds)


.. _sphx_glr_download_auto_examples_indicators_plot_b02estimation.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_b02estimation.ipynb <plot_b02estimation.ipynb>`

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

      :download:`Download Python source code: plot_b02estimation.py <plot_b02estimation.py>`

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

      :download:`Download zipped: plot_b02estimation.zip <plot_b02estimation.zip>`


.. only:: html

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

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