.. 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 14-29

.. code-block:: Python


    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,
    )
    from biogeme.native_draws import RandomNumberGeneratorTuple
    from biogeme.parameters import Parameters








.. GENERATED FROM PYTHON SOURCE LINES 30-31

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

.. GENERATED FROM PYTHON SOURCE LINES 31-49

.. code-block:: Python

    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 50-51

Function generating the draws.

.. GENERATED FROM PYTHON SOURCE LINES 51-59

.. code-block:: Python

    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 60-61

Associate the function with a name.

.. GENERATED FROM PYTHON SOURCE LINES 61-68

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 69-70

Submit the generator to the database.

.. GENERATED FROM PYTHON SOURCE LINES 70-72

.. code-block:: Python

    database.set_random_number_generators(myRandomNumberGenerators)








.. GENERATED FROM PYTHON SOURCE LINES 73-74

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 74-76

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 77-79

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

.. GENERATED FROM PYTHON SOURCE LINES 81-82

Mean of the distribution.

.. GENERATED FROM PYTHON SOURCE LINES 82-84

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 85-87

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

.. GENERATED FROM PYTHON SOURCE LINES 87-90

.. code-block:: Python

    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 91-92

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

.. GENERATED FROM PYTHON SOURCE LINES 92-104

.. code-block:: Python

    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 105-106

Definition of the utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 106-110

.. code-block:: Python

    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 111-112

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 112-114

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 115-116

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 116-118

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 119-121

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

.. GENERATED FROM PYTHON SOURCE LINES 121-123

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 124-127

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 127-129

.. code-block:: Python

    condprobIndiv = PanelLikelihoodTrajectory(obsprob)








.. GENERATED FROM PYTHON SOURCE LINES 130-131

We integrate over the random parameters using Monte-Carlo

.. GENERATED FROM PYTHON SOURCE LINES 131-133

.. code-block:: Python

    logprob = log(MonteCarlo(condprobIndiv))








.. GENERATED FROM PYTHON SOURCE LINES 134-137

As the objective is to illustrate the
syntax, we calculate the Monte-Carlo approximation with a small
number of draws.

.. GENERATED FROM PYTHON SOURCE LINES 137-140

.. code-block:: Python

    the_biogeme = bio.BIOGEME(database, logprob, number_of_draws=100, seed=1223)
    the_biogeme.modelName = 'b26triangular_panel_mixture'





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

 .. code-block:: none

    Biogeme parameters read from biogeme.toml. 




.. GENERATED FROM PYTHON SOURCE LINES 141-142

Estimate the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 142-144

.. code-block:: Python

    results = the_biogeme.estimate()





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

 .. code-block:: none

    As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds" 
    *** Initial values of the parameters are obtained from the file __b26triangular_panel_mixture.iter 
    Cannot read file __b26triangular_panel_mixture.iter. Statement is ignored. 
    The number of draws (100) is low. The results may not be meaningful. 
    As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds" 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: BFGS 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               1               2               2              -1               2              -1              -1               2      4.5e+03      0.069        1      0.4    + 
        1         1.1e-16               3               3               0               3               0              -2               3      4.1e+03      0.044        1     0.26    + 
        2            0.26             3.3             3.1           -0.43             3.1              -1            -2.5               3      3.9e+03       0.04       10      1.2   ++ 
        3            0.26             3.3             3.1           -0.43             3.1              -1            -2.5               3      3.9e+03       0.04        5     -6.5    - 
        4            0.26             3.3             3.1           -0.43             3.1              -1            -2.5               3      3.9e+03       0.04      2.5       -4    - 
        5            0.26             3.3             3.1           -0.43             3.1              -1            -2.5               3      3.9e+03       0.04      1.2       -2    - 
        6            0.26             3.3             3.1           -0.43             3.1              -1            -2.5               3      3.9e+03       0.04     0.62     -0.5    - 
        7            0.42             3.9             3.4            -1.1             3.5            -1.6            -3.1             2.9      3.9e+03      0.052     0.62     0.53    + 
        8            0.23             4.1             3.6           -0.69             3.9              -2            -2.7             3.6      3.8e+03      0.027     0.62     0.64    + 
        9            0.36             4.4             3.7              -1             4.1            -1.9            -3.1             4.2      3.8e+03      0.014     0.62     0.88    + 
       10          -0.063             4.8             3.7           -0.65             4.4            -1.9            -3.7             4.5      3.7e+03      0.022     0.62     0.78    + 
       11          -0.063             4.8             3.7           -0.65             4.4            -1.9            -3.7             4.5      3.7e+03      0.022     0.31     -0.9    - 
       12          -0.063             4.8             3.7           -0.65             4.4            -1.9            -3.7             4.5      3.7e+03      0.022     0.16    -0.23    - 
       13           0.093             4.9             3.9           -0.71             4.6            -2.1            -3.9             4.3      3.7e+03      0.044     0.16     0.32    + 
       14            0.14               5             3.9           -0.69             4.6            -2.1            -3.7             4.5      3.7e+03      0.029     0.16     0.68    + 
       15             0.2             5.1             3.9           -0.66             4.7            -2.1            -3.9             4.5      3.7e+03       0.02      1.6     0.91   ++ 
       16            0.82             6.6             4.1           -0.19             5.6            -2.4            -4.8             5.8      3.7e+03      0.039      1.6     0.55    + 
       17            0.82             6.6             4.1           -0.19             5.6            -2.4            -4.8             5.8      3.7e+03      0.039     0.78     -1.1    - 
       18           0.036             6.9             4.1           -0.25             5.6            -2.3              -5               6      3.7e+03      0.014     0.78     0.15    + 
       19           0.036             6.9             4.1           -0.25             5.6            -2.3              -5               6      3.7e+03      0.014     0.39    -0.49    - 
       20            0.43               7             3.9           -0.48             5.6            -2.6            -5.1               6      3.7e+03       0.01     0.39      0.7    + 
       21            0.48             7.4             3.8           -0.26             5.7            -2.4            -5.1             6.1      3.7e+03      0.007     0.39      0.5    + 
       22            0.25             7.8             3.5           -0.19             5.8            -2.8            -5.3             6.3      3.7e+03      0.015     0.39     0.47    + 
       23            0.38             8.1             3.3           -0.58             5.7            -2.7            -5.3             6.4      3.7e+03     0.0069     0.39     0.18    + 
       24            0.41             8.5             3.1           -0.26               6            -2.5            -5.4             6.5      3.7e+03     0.0076     0.39     0.46    + 
       25            0.29             8.8             2.7           -0.24             6.1            -2.8            -5.4             6.5      3.7e+03     0.0057     0.39     0.57    + 
       26            0.29             8.8             2.7           -0.24             6.1            -2.8            -5.4             6.5      3.7e+03     0.0057      0.2    -0.89    - 
       27            0.12             8.8             2.7           -0.43             6.1            -2.8            -5.5             6.6      3.7e+03     0.0038      0.2     0.22    + 
       28            0.32             8.9             2.8           -0.35             6.1            -2.8            -5.5             6.6      3.7e+03     0.0029      0.2     0.74    + 
       29            0.32             8.9             2.8           -0.35             6.1            -2.8            -5.5             6.6      3.7e+03     0.0029    0.098    -0.85    - 
       30            0.32             8.9             2.8           -0.35             6.1            -2.8            -5.5             6.6      3.7e+03     0.0029    0.049    -0.44    - 
       31            0.27             8.9             2.8           -0.33             6.1            -2.8            -5.5             6.6      3.7e+03     0.0031    0.049     0.47    + 
       32            0.28             8.9             2.8           -0.37             6.2            -2.8            -5.6             6.7      3.7e+03      0.001    0.049     0.54    + 
       33            0.29             8.9             2.8           -0.33             6.2            -2.8            -5.6             6.7      3.7e+03     0.0022    0.049     0.76    + 
       34            0.27               9             2.8           -0.34             6.2            -2.8            -5.6             6.7      3.7e+03    0.00035     0.49     0.96   ++ 
       35            0.27               9             2.8           -0.34             6.2            -2.8            -5.6             6.7      3.7e+03    0.00035    0.066    -0.48    - 
       36            0.28             9.1             2.8           -0.34             6.2            -2.8            -5.6             6.7      3.7e+03    0.00018    0.066     0.79    + 
       37            0.28             9.1             2.8           -0.34             6.2            -2.8            -5.6             6.7      3.7e+03    0.00018    0.018       -2    - 
       38            0.28             9.1             2.8           -0.34             6.2            -2.8            -5.6             6.7      3.7e+03    0.00018   0.0091   0.0077    - 
       39            0.28             9.1             2.8           -0.34             6.2            -2.8            -5.6             6.7      3.7e+03      6e-05   0.0091     0.62    - 
    Results saved in file b26triangular_panel_mixture.html 
    Results saved in file b26triangular_panel_mixture.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 145-147

.. code-block:: Python

    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:           -3656.133
    Akaike Information Criterion:   7328.266
    Bayesian Information Criterion: 7365.248





.. GENERATED FROM PYTHON SOURCE LINES 148-150

.. code-block:: Python

    pandas_results = results.get_estimated_parameters()
    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>0.272879</td>
          <td>0.260035</td>
          <td>1.049395</td>
          <td>2.939962e-01</td>
        </tr>
        <tr>
          <th>ASC_CAR_S</th>
          <td>9.060495</td>
          <td>0.918376</td>
          <td>9.865782</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>ASC_SM_S</th>
          <td>2.845355</td>
          <td>0.545474</td>
          <td>5.216297</td>
          <td>1.825359e-07</td>
        </tr>
        <tr>
          <th>ASC_TRAIN</th>
          <td>-0.337910</td>
          <td>0.227348</td>
          <td>-1.486311</td>
          <td>1.371970e-01</td>
        </tr>
        <tr>
          <th>ASC_TRAIN_S</th>
          <td>6.197271</td>
          <td>0.764653</td>
          <td>8.104689</td>
          <td>4.440892e-16</td>
        </tr>
        <tr>
          <th>B_COST</th>
          <td>-2.840325</td>
          <td>0.360247</td>
          <td>-7.884375</td>
          <td>3.108624e-15</td>
        </tr>
        <tr>
          <th>B_TIME</th>
          <td>-5.625062</td>
          <td>0.339386</td>
          <td>-16.574249</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME_S</th>
          <td>6.751839</td>
          <td>0.399455</td>
          <td>16.902640</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 21.121 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-jupyter

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

    .. 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-zip

      :download:`Download zipped: plot_b26triangular_panel_mixture.zip <plot_b26triangular_panel_mixture.zip>`


.. only:: html

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

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