.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b12panel_flat.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_b12panel_flat.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_swissmetro_plot_b12panel_flat.py:


Mixture of logit with panel data
================================

Example of a mixture of logit models, using Monte-Carlo integration.
 The datafile is organized as panel data, but a flat version is
 generated.  It means that each row corresponds to one individuals,
 and contains all observations associated with this individual.


:author: Michel Bierlaire, EPFL
:date: Sun Apr  9 18:14:16 2023

.. GENERATED FROM PYTHON SOURCE LINES 16-31

.. code-block:: default


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








.. GENERATED FROM PYTHON SOURCE LINES 32-33

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

.. GENERATED FROM PYTHON SOURCE LINES 33-43

.. code-block:: default

    from swissmetro_panel import (
        flat_database,
        SM_AV,
        CAR_AV_SP,
        TRAIN_AV_SP,
    )

    logger = blog.get_screen_logger(level=blog.INFO)
    logger.info('Example b12panel_flat.py')





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

 .. code-block:: none

    Example b12panel_flat.py 




.. GENERATED FROM PYTHON SOURCE LINES 44-45

We set the seed so that the results are reproducible. This is not necessary in general.

.. GENERATED FROM PYTHON SOURCE LINES 45-47

.. code-block:: default

    np.random.seed(seed=90267)








.. GENERATED FROM PYTHON SOURCE LINES 48-51

The Pandas data structure is available as database.data. Use all the
Pandas functions to invesigate the database
print(database.data.describe())

.. GENERATED FROM PYTHON SOURCE LINES 53-54

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 54-56

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 57-59

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

.. GENERATED FROM PYTHON SOURCE LINES 59-61

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 62-63

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

.. GENERATED FROM PYTHON SOURCE LINES 63-66

.. 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_ANTI')








.. GENERATED FROM PYTHON SOURCE LINES 67-68

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

.. GENERATED FROM PYTHON SOURCE LINES 68-80

.. 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', 'NORMAL_ANTI')

    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', 'NORMAL_ANTI')

    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', 'NORMAL_ANTI')








.. GENERATED FROM PYTHON SOURCE LINES 81-83

In a flatten database, the names of the variables include the time
or, here, the number of the question, as a prefix

.. GENERATED FROM PYTHON SOURCE LINES 85-86

Definition of the utility functions

.. GENERATED FROM PYTHON SOURCE LINES 86-107

.. code-block:: default

    V1 = [
        ASC_TRAIN_RND
        + B_TIME_RND * Variable(f'{t}_TRAIN_TT_SCALED')
        + B_COST * Variable(f'{t}_TRAIN_COST_SCALED')
        for t in range(1, 10)
    ]

    V2 = [
        ASC_SM_RND
        + B_TIME_RND * Variable(f'{t}_SM_TT_SCALED')
        + B_COST * Variable(f'{t}_SM_COST_SCALED')
        for t in range(1, 10)
    ]

    V3 = [
        ASC_CAR_RND
        + B_TIME_RND * Variable(f'{t}_CAR_TT_SCALED')
        + B_COST * Variable(f'{t}_CAR_CO_SCALED')
        for t in range(1, 10)
    ]








.. 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[t], 2: V2[t], 3: V3[t]} for t in range(9)]








.. 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 116-120

Conditional on the random parameters, the likelihood of one observation is
given by the logit model (called the kernel). The likelihood of all observations for
one individual (the trajectory) is the product of the likelihood of
each observation.

.. GENERATED FROM PYTHON SOURCE LINES 120-123

.. code-block:: default

    obsprob = [models.loglogit(V[t], av, Variable(f'{t+1}_CHOICE')) for t in range(9)]
    condprobIndiv = exp(bioMultSum(obsprob))








.. GENERATED FROM PYTHON SOURCE LINES 124-125

We integrate over the random parameters using Monte-Carlo.

.. GENERATED FROM PYTHON SOURCE LINES 125-127

.. code-block:: default

    logprob = log(MonteCarlo(condprobIndiv))








.. GENERATED FROM PYTHON SOURCE LINES 128-132

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: `<few_draws.toml>`_

.. GENERATED FROM PYTHON SOURCE LINES 132-135

.. code-block:: default

    the_biogeme = bio.BIOGEME(flat_database, logprob, parameter_file='few_draws.toml')
    the_biogeme.modelName = 'b12panel_flat'





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

 .. code-block:: none

    File few_draws.toml has been parsed. 




.. GENERATED FROM PYTHON SOURCE LINES 136-137

Estimate the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 137-139

.. 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 __b12panel_flat.iter 
    Cannot read file __b12panel_flat.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             0.2             1.4            0.91           -0.79            0.97           -0.98              -1             1.3      4.1e+03      0.047       10      1.2   ++ 
        1             0.2             1.4            0.91           -0.79            0.97           -0.98              -1             1.3      4.1e+03      0.047        5     -0.4    - 
        2           -0.33             2.6              -3            -1.6               6           -0.78            -2.9            0.87        4e+03      0.041        5     0.26    + 
        3           -0.33             2.6              -3            -1.6               6           -0.78            -2.9            0.87        4e+03      0.041      2.5     -1.2    - 
        4            0.88             2.4            -1.5            -3.6             3.5            -3.3            -3.3             3.4      3.9e+03      0.061      2.5     0.23    + 
        5            0.49             1.9            -2.7            -1.1             3.9            -2.4            -3.3             3.9      3.8e+03      0.024      2.5     0.47    + 
        6            0.49             1.9            -2.7            -1.1             3.9            -2.4            -3.3             3.9      3.8e+03      0.024      1.2     -2.6    - 
        7            0.49             2.8            -1.8            -2.3             2.9            -2.8            -4.5             3.5      3.7e+03       0.03      1.2     0.72    + 
        8          -0.035             3.2            -2.1            -1.1             3.3            -2.7            -4.4             3.4      3.7e+03      0.015      1.2     0.83    + 
        9           -0.29             3.9            -0.8           -0.73             2.4            -2.6              -5               4      3.7e+03      0.014      1.2     0.48    + 
       10           -0.17             3.9            0.45          -0.037               2            -2.9            -5.4             4.3      3.6e+03       0.03       12     0.92   ++ 
       11           -0.17             3.9            0.45          -0.037               2            -2.9            -5.4             4.3      3.6e+03       0.03      6.2      -10    - 
       12           -0.17             3.9            0.45          -0.037               2            -2.9            -5.4             4.3      3.6e+03       0.03      3.1     -3.8    - 
       13           -0.17             3.9            0.45          -0.037               2            -2.9            -5.4             4.3      3.6e+03       0.03      1.6     -1.7    - 
       14           -0.17             3.9            0.45          -0.037               2            -2.9            -5.4             4.3      3.6e+03       0.03     0.78    -0.58    - 
       15           0.069             3.8             1.2           -0.67             2.4            -3.1            -5.6             4.1      3.6e+03      0.022     0.78     0.37    + 
       16           0.069             3.8             1.2           -0.67             2.4            -3.1            -5.6             4.1      3.6e+03      0.022     0.39   -0.038    - 
       17           0.069             3.8             1.2           -0.67             2.4            -3.1            -5.6             4.1      3.6e+03      0.022      0.2    0.018    - 
       18           0.096             3.6               1           -0.47             2.2            -3.3            -5.8             3.9      3.6e+03     0.0095      0.2     0.16    + 
       19            0.23             3.7            0.84           -0.32             2.2            -3.1            -5.8             3.9      3.6e+03     0.0028        2     0.97   ++ 
       20            0.25             3.7            0.85           -0.27             2.2            -3.2            -5.9               4      3.6e+03    4.9e-05       20        1   ++ 
       21            0.25             3.7            0.85           -0.27             2.2            -3.2            -5.9               4      3.6e+03      2e-08       20        1   ++ 
    Results saved in file b12panel_flat.html 
    Results saved in file b12panel_flat.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 140-142

.. code-block:: default

    print(results.short_summary())





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

 .. code-block:: none

    Results for model b12panel_flat
    Nbr of parameters:              8
    Sample size:                    752
    Excluded data:                  0
    Final log likelihood:           -3618.834
    Akaike Information Criterion:   7253.667
    Bayesian Information Criterion: 7290.649





.. GENERATED FROM PYTHON SOURCE LINES 143-145

.. 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>0.251362</td>
          <td>0.226183</td>
          <td>1.111322</td>
          <td>2.664298e-01</td>
        </tr>
        <tr>
          <th>ASC_CAR_S</th>
          <td>3.729035</td>
          <td>0.228817</td>
          <td>16.297028</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>ASC_SM_S</th>
          <td>0.851459</td>
          <td>0.246782</td>
          <td>3.450242</td>
          <td>5.600843e-04</td>
        </tr>
        <tr>
          <th>ASC_TRAIN</th>
          <td>-0.264982</td>
          <td>0.220243</td>
          <td>-1.203138</td>
          <td>2.289229e-01</td>
        </tr>
        <tr>
          <th>ASC_TRAIN_S</th>
          <td>2.197599</td>
          <td>0.217478</td>
          <td>10.104926</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_COST</th>
          <td>-3.154317</td>
          <td>0.446267</td>
          <td>-7.068228</td>
          <td>1.569189e-12</td>
        </tr>
        <tr>
          <th>B_TIME</th>
          <td>-5.888321</td>
          <td>0.309687</td>
          <td>-19.013777</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME_S</th>
          <td>4.019026</td>
          <td>0.205731</td>
          <td>19.535323</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 21.573 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b12panel_flat.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_b12panel_flat.py <plot_b12panel_flat.py>`

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

      :download:`Download Jupyter notebook: plot_b12panel_flat.ipynb <plot_b12panel_flat.ipynb>`


.. only:: html

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

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