.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b26triangular_panel_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_b26triangular_panel_mixture.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_swissmetro_plot_b26triangular_panel_mixture.py:


Triangular mixture with panel data
==================================

 Example of a mixture of logit models, using Monte-Carlo integration.
 The mixing distribution is user-defined (triangular, here).
 The datafile is organized as panel data.

:author: Michel Bierlaire, EPFL
:date: Tue Dec  6 18:30:44 2022

.. GENERATED FROM PYTHON SOURCE LINES 14-26

.. code-block:: default

    import numpy as np
    import biogeme.biogeme as bio
    from biogeme import models
    import biogeme.biogeme_logging as blog
    from biogeme.expressions import (
        Beta,
        bioDraws,
        MonteCarlo,
        PanelLikelihoodTrajectory,
        log,
    )








.. GENERATED FROM PYTHON SOURCE LINES 27-28

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

.. GENERATED FROM PYTHON SOURCE LINES 28-46

.. code-block:: default

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

    logger = blog.get_screen_logger(level=blog.INFO)
    logger.info('Example b26triangular_panel_mixture.py')






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

 .. code-block:: none

    Example b26triangular_panel_mixture.py 




.. GENERATED FROM PYTHON SOURCE LINES 47-48

Function generating the draws.

.. GENERATED FROM PYTHON SOURCE LINES 48-56

.. code-block:: default

    def the_triangular_generator(sample_size: int, number_of_draws: int) -> np.ndarray:
        """
        Provide my own random number generator to the database.
        See the numpy.random documentation to obtain a list of other distributions.
        """
        return np.random.triangular(-1, 0, 1, (sample_size, number_of_draws))









.. GENERATED FROM PYTHON SOURCE LINES 57-58

Associate the function with a name.

.. GENERATED FROM PYTHON SOURCE LINES 58-65

.. code-block:: default

    myRandomNumberGenerators = {
        'TRIANGULAR': (
            the_triangular_generator,
            'Draws from a triangular distribution',
        )
    }








.. GENERATED FROM PYTHON SOURCE LINES 66-67

Submit the generator to the database.

.. GENERATED FROM PYTHON SOURCE LINES 67-69

.. code-block:: default

    database.setRandomNumberGenerators(myRandomNumberGenerators)








.. GENERATED FROM PYTHON SOURCE LINES 70-71

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 71-73

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 74-76

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

.. GENERATED FROM PYTHON SOURCE LINES 78-79

Mean of the distribution.

.. GENERATED FROM PYTHON SOURCE LINES 79-81

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 82-84

Scale of the distribution. It is advised not to use 0 as starting
value for the following parameter.

.. GENERATED FROM PYTHON SOURCE LINES 84-87

.. 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', 'TRIANGULAR')








.. GENERATED FROM PYTHON SOURCE LINES 88-89

We do the same for the constants, to address serial correlation.

.. GENERATED FROM PYTHON SOURCE LINES 89-101

.. code-block:: default

    ASC_CAR = Beta('ASC_CAR', 0, None, None, 0)
    ASC_CAR_S = Beta('ASC_CAR_S', 1, None, None, 0)
    ASC_CAR_RND = ASC_CAR + ASC_CAR_S * bioDraws('ASC_CAR_RND', 'TRIANGULAR')

    ASC_TRAIN = Beta('ASC_TRAIN', 0, None, None, 0)
    ASC_TRAIN_S = Beta('ASC_TRAIN_S', 1, None, None, 0)
    ASC_TRAIN_RND = ASC_TRAIN + ASC_TRAIN_S * bioDraws('ASC_TRAIN_RND', 'TRIANGULAR')

    ASC_SM = Beta('ASC_SM', 0, None, None, 1)
    ASC_SM_S = Beta('ASC_SM_S', 1, None, None, 0)
    ASC_SM_RND = ASC_SM + ASC_SM_S * bioDraws('ASC_SM_RND', 'TRIANGULAR')








.. GENERATED FROM PYTHON SOURCE LINES 102-103

Definition of the utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 103-107

.. code-block:: default

    V1 = ASC_TRAIN_RND + B_TIME_RND * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
    V2 = ASC_SM_RND + B_TIME_RND * SM_TT_SCALED + B_COST * SM_COST_SCALED
    V3 = ASC_CAR_RND + B_TIME_RND * CAR_TT_SCALED + B_COST * CAR_CO_SCALED








.. GENERATED FROM PYTHON SOURCE LINES 108-109

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 109-111

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 112-113

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 113-115

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 116-118

Conditional to the random parameters, the likelihood of one observation is
given by the logit model (called the kernel).

.. GENERATED FROM PYTHON SOURCE LINES 118-120

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 121-124

Conditional on the random parameters, the likelihood of all observations for
one individual (the trajectory) is the product of the likelihood of
each observation.

.. GENERATED FROM PYTHON SOURCE LINES 124-126

.. code-block:: default

    condprobIndiv = PanelLikelihoodTrajectory(obsprob)








.. GENERATED FROM PYTHON SOURCE LINES 127-128

We integrate over the random parameters using Monte-Carlo

.. GENERATED FROM PYTHON SOURCE LINES 128-130

.. code-block:: default

    logprob = log(MonteCarlo(condprobIndiv))








.. GENERATED FROM PYTHON SOURCE LINES 131-135

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 135-138

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, logprob, parameter_file='few_draws.toml')
    the_biogeme.modelName = 'b26triangular_panel_mixture'





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

 .. code-block:: none

    File few_draws.toml has been parsed. 




.. GENERATED FROM PYTHON SOURCE LINES 139-140

Estimate the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 140-142

.. 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 __b26triangular_panel_mixture.iter 
    Cannot read file __b26triangular_panel_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_CAR_S        ASC_SM_S       ASC_TRAIN     ASC_TRAIN_S          B_COST          B_TIME        B_TIME_S     Function    Relgrad   Radius      Rho      
        0           -0.11             1.4             1.4           -0.55             1.1           -0.79              -1             1.1      4.6e+03      0.047       10      1.2   ++ 
        1           -0.11             1.4             1.4           -0.55             1.1           -0.79              -1             1.1      4.6e+03      0.047        5    -0.15    - 
        2            0.65             3.6          -0.046            0.22             6.1            0.56            -2.3               4      4.2e+03      0.056        5     0.42    + 
        3            0.65             3.6          -0.046            0.22             6.1            0.56            -2.3               4      4.2e+03      0.056      2.5    -0.79    - 
        4            0.65             3.6          -0.046            0.22             6.1            0.56            -2.3               4      4.2e+03      0.056      1.2    -0.13    - 
        5            0.41             4.6          -0.046              -1               6           -0.69            -3.6             3.9      3.8e+03      0.059      1.2     0.71    + 
        6           0.098             4.8            0.06           -0.99             6.2            -1.9            -3.4             4.5      3.7e+03      0.027      1.2     0.84    + 
        7           0.098             4.8            0.06           -0.99             6.2            -1.9            -3.4             4.5      3.7e+03      0.027     0.62     -0.2    - 
        8           0.098             4.8            0.06           -0.99             6.2            -1.9            -3.4             4.5      3.7e+03      0.027     0.31     -0.2    - 
        9           0.098             4.8            0.06           -0.99             6.2            -1.9            -3.4             4.5      3.7e+03      0.027     0.16   -0.097    - 
       10           0.098             4.8            0.06           -0.99             6.2            -1.9            -3.4             4.5      3.7e+03      0.027    0.078    0.093    - 
       11            0.02             4.8          -0.018              -1             6.2            -1.9            -3.5             4.5      3.7e+03      0.026    0.078     0.45    + 
       12           0.098             4.9          -0.096           -0.94             6.3            -1.8            -3.5             4.5      3.7e+03      0.023     0.78        1   ++ 
       13            0.14             5.7           -0.16           -0.94             6.5            -1.9            -3.8             4.9      3.7e+03      0.021      7.8        1   ++ 
       14            0.14             5.7           -0.16           -0.94             6.5            -1.9            -3.8             4.9      3.7e+03      0.021      3.9    0.054    - 
       15            0.37             7.9             3.7           0.089             4.9            -2.6            -5.9               8      3.7e+03      0.039      3.9     0.69    + 
       16            0.37             7.9             3.7           0.089             4.9            -2.6            -5.9               8      3.7e+03      0.039        2    -0.15    - 
       17            0.37             7.9             3.7           0.089             4.9            -2.6            -5.9               8      3.7e+03      0.039     0.98    -0.15    - 
       18            0.37             7.9             3.7           0.089             4.9            -2.6            -5.9               8      3.7e+03      0.039     0.49    -0.15    - 
       19            0.37             7.9             3.7           0.089             4.9            -2.6            -5.9               8      3.7e+03      0.039     0.24   -0.029    - 
       20            0.37             7.9             3.7           0.089             4.9            -2.6            -5.9               8      3.7e+03      0.039     0.12    0.018    - 
       21            0.48               8             3.7          -0.029             4.9            -2.7            -6.1             7.9      3.7e+03      0.012     0.12     0.37    + 
       22            0.58             8.1             3.8           0.017             4.8            -2.7              -6             7.8      3.7e+03      0.012      1.2     0.99   ++ 
       23            0.47             9.3             4.2          -0.016             3.9            -2.9            -5.5             7.3      3.7e+03     0.0087      1.2     0.74    + 
       24             0.9             9.1             5.3             0.4             2.7            -2.7            -6.2             8.1      3.7e+03     0.0068      1.2     0.56    + 
       25            0.46             9.5             4.7            0.34             1.5            -2.9            -5.9             7.7      3.6e+03     0.0027      1.2     0.83    + 
       26            0.65             9.4             5.1            0.42            0.71              -3            -6.1               8      3.6e+03    0.00054       12     0.95   ++ 
       27            0.65             9.5             5.1            0.42            0.69              -3            -6.1             8.1      3.6e+03    8.5e-06  1.2e+02        1   ++ 
       28            0.65             9.5             5.1            0.42            0.69              -3            -6.1             8.1      3.6e+03    2.6e-09  1.2e+02        1   ++ 
    Results saved in file b26triangular_panel_mixture.html 
    Results saved in file b26triangular_panel_mixture.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 143-145

.. code-block:: default

    print(results.short_summary())





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

 .. code-block:: none

    Results for model b26triangular_panel_mixture
    Nbr of parameters:              8
    Sample size:                    752
    Observations:                   6768
    Excluded data:                  3960
    Final log likelihood:           -3645.824
    Akaike Information Criterion:   7307.648
    Bayesian Information Criterion: 7344.63





.. GENERATED FROM PYTHON SOURCE LINES 146-148

.. 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>0.646809</td>
          <td>0.271284</td>
          <td>2.384250</td>
          <td>1.711398e-02</td>
        </tr>
        <tr>
          <th>ASC_CAR_S</th>
          <td>9.474742</td>
          <td>0.846701</td>
          <td>11.190188</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>ASC_SM_S</th>
          <td>5.066061</td>
          <td>0.426483</td>
          <td>11.878705</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>ASC_TRAIN</th>
          <td>0.421241</td>
          <td>0.234063</td>
          <td>1.799693</td>
          <td>7.190920e-02</td>
        </tr>
        <tr>
          <th>ASC_TRAIN_S</th>
          <td>0.688281</td>
          <td>1.558410</td>
          <td>0.441656</td>
          <td>6.587382e-01</td>
        </tr>
        <tr>
          <th>B_COST</th>
          <td>-2.964488</td>
          <td>0.517913</td>
          <td>-5.723913</td>
          <td>1.040981e-08</td>
        </tr>
        <tr>
          <th>B_TIME</th>
          <td>-6.143703</td>
          <td>0.345251</td>
          <td>-17.794911</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME_S</th>
          <td>8.055966</td>
          <td>0.437295</td>
          <td>18.422268</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 34.863 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b26triangular_panel_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_b26triangular_panel_mixture.py <plot_b26triangular_panel_mixture.py>`

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

      :download:`Download Jupyter notebook: plot_b26triangular_panel_mixture.ipynb <plot_b26triangular_panel_mixture.ipynb>`


.. only:: html

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

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