.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b05normal_mixture.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_swissmetro_plot_b05normal_mixture.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_swissmetro_plot_b05normal_mixture.py:


.. _plot_b05normal_mixture:

Mixture of logit models
=======================

Example of a normal mixture of logit models, using Monte-Carlo integration.

:author: Michel Bierlaire, EPFL
:date: Sun Apr  9 17:30:14 2023

.. GENERATED FROM PYTHON SOURCE LINES 12-18

.. code-block:: default


    import biogeme.biogeme_logging as blog
    import biogeme.biogeme as bio
    from biogeme import models
    from biogeme.expressions import Beta, bioDraws, log, MonteCarlo








.. GENERATED FROM PYTHON SOURCE LINES 19-20

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

.. GENERATED FROM PYTHON SOURCE LINES 20-37

.. code-block:: default

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

    logger = blog.get_screen_logger(level=blog.INFO)
    logger.info('Example b05normal_mixtures.py')





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

 .. code-block:: none

    Example b05normal_mixtures.py 




.. GENERATED FROM PYTHON SOURCE LINES 38-39

Parameters to be estimated

.. GENERATED FROM PYTHON SOURCE LINES 39-44

.. 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_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 47-49

.. code-block:: default

    B_TIME = Beta('B_TIME', 0, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 50-51

It is advised *not* to use 0 as starting value for the following parameter.

.. GENERATED FROM PYTHON SOURCE LINES 51-54

.. code-block:: default

    B_TIME_S = Beta('B_TIME_S', 1, None, None, 0)
    B_TIME_RND = B_TIME + B_TIME_S * bioDraws('B_TIME_RND', 'NORMAL')








.. GENERATED FROM PYTHON SOURCE LINES 55-56

Definition of the utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 56-60

.. 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 61-62

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 62-64

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 65-66

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 66-68

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 69-70

Conditional to B_TIME_RND, we have a logit model (called the kernel).

.. GENERATED FROM PYTHON SOURCE LINES 70-72

.. code-block:: default

    prob = models.logit(V, av, CHOICE)








.. GENERATED FROM PYTHON SOURCE LINES 73-74

We integrate over B_TIME_RND using Monte-Carlo.

.. GENERATED FROM PYTHON SOURCE LINES 74-76

.. code-block:: default

    logprob = log(MonteCarlo(prob))








.. GENERATED FROM PYTHON SOURCE LINES 77-78

These notes will be included as such in the report file.

.. GENERATED FROM PYTHON SOURCE LINES 78-83

.. code-block:: default

    USER_NOTES = (
        'Example of a mixture of logit models with three alternatives, '
        'approximated using Monte-Carlo integration.'
    )








.. GENERATED FROM PYTHON SOURCE LINES 84-88

Create the Biogeme object. As the objective is to illustrate the
syntax, we calculate the Monte-Carlo approximation with a small
number of draws. To achieve that, we provide a parameter file
different from the default one.

.. GENERATED FROM PYTHON SOURCE LINES 88-93

.. code-block:: default

    the_biogeme = bio.BIOGEME(
        database, logprob, userNotes=USER_NOTES, parameter_file='few_draws.toml'
    )
    the_biogeme.modelName = 'b05normal_mixture'





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

 .. code-block:: none

    File few_draws.toml has been parsed. 




.. GENERATED FROM PYTHON SOURCE LINES 94-96

.. code-block:: default

    print(f'Number of draws: {the_biogeme.number_of_draws}')





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

 .. code-block:: none

    Number of draws: 100




.. GENERATED FROM PYTHON SOURCE LINES 97-98

Estimate the parameters

.. GENERATED FROM PYTHON SOURCE LINES 98-99

.. code-block:: default

    results = the_biogeme.estimate()




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

 .. code-block:: none

    *** Initial values of the parameters are obtained from the file __b05normal_mixture.iter 
    Cannot read file __b05normal_mixture.iter. Statement is ignored. 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Iter.         ASC_CAR       ASC_TRAIN          B_COST          B_TIME        B_TIME_S     Function    Relgrad   Radius      Rho      
        0          -0.083            -0.8           -0.32              -1            0.87      5.4e+03      0.046       10        1   ++ 
        1           0.013           -0.57              -1            -1.6            0.92      5.2e+03     0.0082    1e+02      1.1   ++ 
        2           0.096           -0.43            -1.2              -2             1.4      5.2e+03     0.0041    1e+03      1.1   ++ 
        3            0.12           -0.41            -1.3            -2.2             1.6      5.2e+03    0.00069    1e+04      1.1   ++ 
        4            0.13           -0.41            -1.3            -2.2             1.6      5.2e+03    9.3e-06    1e+05        1   ++ 
        5            0.13           -0.41            -1.3            -2.2             1.6      5.2e+03    2.2e-09    1e+05        1   ++ 
    Results saved in file b05normal_mixture.html 
    Results saved in file b05normal_mixture.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 100-101

.. code-block:: default

    print(results.short_summary())




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

 .. code-block:: none

    Results for model b05normal_mixture
    Nbr of parameters:              5
    Sample size:                    6768
    Excluded data:                  3960
    Final log likelihood:           -5216.34
    Akaike Information Criterion:   10442.68
    Bayesian Information Criterion: 10476.78





.. GENERATED FROM PYTHON SOURCE LINES 102-104

.. 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>0.126639</td>
          <td>0.051638</td>
          <td>2.452445</td>
          <td>1.418890e-02</td>
        </tr>
        <tr>
          <th>ASC_TRAIN</th>
          <td>-0.408591</td>
          <td>0.065910</td>
          <td>-6.199183</td>
          <td>5.675691e-10</td>
        </tr>
        <tr>
          <th>B_COST</th>
          <td>-1.280129</td>
          <td>0.085585</td>
          <td>-14.957358</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME</th>
          <td>-2.224435</td>
          <td>0.115421</td>
          <td>-19.272284</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME_S</th>
          <td>1.606218</td>
          <td>0.122634</td>
          <td>13.097709</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 8.466 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b05normal_mixture.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_b05normal_mixture.py <plot_b05normal_mixture.py>`

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

      :download:`Download Jupyter notebook: plot_b05normal_mixture.ipynb <plot_b05normal_mixture.ipynb>`


.. only:: html

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

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