.. 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.

:author: Michel Bierlaire, EPFL
:date: Thu Apr 13 21:03:03 2023

.. GENERATED FROM PYTHON SOURCE LINES 12-32

.. code-block:: default


    import biogeme.biogeme as bio
    import biogeme.distributions as dist
    from biogeme import models
    from biogeme.expressions import Beta, RandomVariable, Integrate, log

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








.. GENERATED FROM PYTHON SOURCE LINES 33-40

.. code-block:: default

    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 41-43

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

.. GENERATED FROM PYTHON SOURCE LINES 43-47

.. code-block:: default

    omega = RandomVariable('omega')
    density = dist.normalpdf(omega)
    B_TIME_RND = B_TIME + B_TIME_S * omega








.. GENERATED FROM PYTHON SOURCE LINES 48-49

Definition of the utility functions

.. GENERATED FROM PYTHON SOURCE LINES 49-53

.. code-block:: default

    V1 = ASC_TRAIN + B_TIME_RND * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
    V2 = ASC_SM + B_TIME_RND * SM_TT_SCALED + B_COST * SM_COST_SCALED
    V3 = ASC_CAR + B_TIME_RND * CAR_TT_SCALED + B_COST * CAR_CO_SCALED








.. GENERATED FROM PYTHON SOURCE LINES 54-55

Associate utility functions with the numbering of alternatives

.. GENERATED FROM PYTHON SOURCE LINES 55-57

.. code-block:: default

    V = {1: V1, 2: V2, 3: V3}








.. GENERATED FROM PYTHON SOURCE LINES 58-59

Associate the availability conditions with the alternatives

.. GENERATED FROM PYTHON SOURCE LINES 59-61

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 62-63

The choice model is a logit, with availability conditions

.. GENERATED FROM PYTHON SOURCE LINES 63-67

.. code-block:: default

    condprob = models.logit(V, av, CHOICE)
    prob = Integrate(condprob * density, 'omega')
    logprob = log(prob)








.. GENERATED FROM PYTHON SOURCE LINES 68-71

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, logprob)
    the_biogeme.modelName = '06estimationIntegral'








.. GENERATED FROM PYTHON SOURCE LINES 72-74

.. code-block:: default

    results = the_biogeme.estimate()








.. GENERATED FROM PYTHON SOURCE LINES 75-77

.. code-block:: default

    print(results.short_summary())





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

 .. code-block:: none

    Results for model 06estimationIntegral
    Nbr of parameters:              5
    Sample size:                    6768
    Excluded data:                  3960
    Final log likelihood:           -5214.879
    Akaike Information Criterion:   10439.76
    Bayesian Information Criterion: 10473.86





.. GENERATED FROM PYTHON SOURCE LINES 78-80

.. code-block:: default

    pandas_results = results.getEstimatedParameters()
    pandas_results





.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>Value</th>
          <th>Rob. Std err</th>
          <th>Rob. t-test</th>
          <th>Rob. p-value</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>ASC_CAR</th>
          <td>0.137075</td>
          <td>0.051715</td>
          <td>2.650599</td>
          <td>8.034925e-03</td>
        </tr>
        <tr>
          <th>ASC_TRAIN</th>
          <td>-0.401234</td>
          <td>0.065607</td>
          <td>-6.115756</td>
          <td>9.610024e-10</td>
        </tr>
        <tr>
          <th>B_COST</th>
          <td>-1.285301</td>
          <td>0.086258</td>
          <td>-14.900638</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME</th>
          <td>-2.259140</td>
          <td>0.116548</td>
          <td>-19.383794</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME_S</th>
          <td>1.654096</td>
          <td>0.124704</td>
          <td>13.264163</td>
          <td>0.000000e+00</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** (0 minutes 11.212 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-python

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

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

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


.. only:: html

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

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