.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/montecarlo/plot_b06estimation_integral.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_montecarlo_plot_b06estimation_integral.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_montecarlo_plot_b06estimation_integral.py:


Estimation of mixtures of logit
===============================

Estimation of a mixtures of logit models where the integral is
calculated using numerical integration.

Michel Bierlaire, EPFL
Sat Jun 28 2025, 21:12:42

.. GENERATED FROM PYTHON SOURCE LINES 12-36

.. code-block:: Python


    from IPython.core.display_functions import display
    from swissmetro 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,
    )

    from biogeme.biogeme import BIOGEME
    from biogeme.expressions import Beta, IntegrateNormal, RandomVariable, log
    from biogeme.models import logit
    from biogeme.results_processing import (
        EstimationResults,
        get_pandas_estimated_parameters,
    )








.. GENERATED FROM PYTHON SOURCE LINES 37-44

.. 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, None, 0)
    b_time_s = Beta('b_time_s', 1, None, None, 0)
    b_cost = Beta('b_cost', 0, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 45-47

Define a random parameter, normally distributed, designed to be used
for Monte-Carlo simulation

.. GENERATED FROM PYTHON SOURCE LINES 47-50

.. code-block:: Python

    omega = RandomVariable('omega')
    b_time_rnd = b_time + b_time_s * omega








.. GENERATED FROM PYTHON SOURCE LINES 51-52

Definition of the utility functions

.. GENERATED FROM PYTHON SOURCE LINES 52-56

.. code-block:: Python

    v_train = asc_train + b_time_rnd * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED
    v_swissmetro = asc_sm + b_time_rnd * SM_TT_SCALED + b_cost * SM_COST_SCALED
    v_car = asc_car + b_time_rnd * CAR_TT_SCALED + b_cost * CAR_CO_SCALED








.. GENERATED FROM PYTHON SOURCE LINES 57-58

Associate utility functions with the numbering of alternatives

.. GENERATED FROM PYTHON SOURCE LINES 58-60

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 61-62

Associate the availability conditions with the alternatives

.. GENERATED FROM PYTHON SOURCE LINES 62-64

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 65-66

The choice model is a logit, with availability conditions

.. GENERATED FROM PYTHON SOURCE LINES 66-70

.. code-block:: Python

    cond_prob = logit(util, av, CHOICE)
    prob = IntegrateNormal(cond_prob, 'omega')
    log_prob = log(prob)








.. GENERATED FROM PYTHON SOURCE LINES 71-76

.. code-block:: Python

    the_biogeme = BIOGEME(database, log_prob)
    the_biogeme.model_name = '06estimation_integral'
    results_file = f'saved_results/{the_biogeme.model_name}.yaml'









.. GENERATED FROM PYTHON SOURCE LINES 77-82

.. code-block:: Python

    try:
        results = EstimationResults.from_yaml_file(filename=results_file)
    except FileNotFoundError:
        results = the_biogeme.estimate()








.. GENERATED FROM PYTHON SOURCE LINES 83-85

.. code-block:: Python

    print(results.short_summary())





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

 .. code-block:: none

    Results for model 06estimation_integral
    Nbr of parameters:              5
    Sample size:                    6768
    Excluded data:                  3960
    Final log likelihood:           -5213.725
    Akaike Information Criterion:   10437.45
    Bayesian Information Criterion: 10471.55





.. GENERATED FROM PYTHON SOURCE LINES 86-87

Get the results in a pandas table

.. GENERATED FROM PYTHON SOURCE LINES 87-91

.. 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  asc_train -0.395901         0.063674       -6.217619    5.047569e-10
    1     b_time -2.278361         0.117234      -19.434326    0.000000e+00
    2   b_time_s  1.675032         0.102317       16.370945    0.000000e+00
    3     b_cost -1.288167         0.086419      -14.906055    0.000000e+00
    4    asc_car  0.142821         0.051744        2.760128    5.777867e-03





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

   **Total running time of the script:** (0 minutes 0.110 seconds)


.. _sphx_glr_download_auto_examples_montecarlo_plot_b06estimation_integral.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_b06estimation_integral.ipynb <plot_b06estimation_integral.ipynb>`

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

      :download:`Download Python source code: plot_b06estimation_integral.py <plot_b06estimation_integral.py>`

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

      :download:`Download zipped: plot_b06estimation_integral.zip <plot_b06estimation_integral.zip>`


.. only:: html

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

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