.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b24halton_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_b24halton_mixture.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_swissmetro_plot_b24halton_mixture.py:


Mixture of logit with Halton draws
==================================

Example of a mixture of logit models, using quasi Monte-Carlo integration with
Halton draws (base 5). The mixing distribution is normal.

:author: Michel Bierlaire, EPFL
:date: Wed Apr 12 18:21:13 2023

.. GENERATED FROM PYTHON SOURCE LINES 14-22

.. code-block:: Python


    import biogeme.biogeme_logging as blog
    import biogeme.biogeme as bio
    from biogeme import models

    from biogeme.expressions import Beta, bioDraws, MonteCarlo, log
    from biogeme.parameters import Parameters








.. GENERATED FROM PYTHON SOURCE LINES 23-24

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

.. GENERATED FROM PYTHON SOURCE LINES 24-41

.. code-block:: Python

    from swissmetro_data 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 b24halton_mixture.py')





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

 .. code-block:: none

    Example b24halton_mixture.py 




.. GENERATED FROM PYTHON SOURCE LINES 42-43

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 43-48

.. code-block:: Python

    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 49-51

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

.. GENERATED FROM PYTHON SOURCE LINES 51-53

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 54-55

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

.. GENERATED FROM PYTHON SOURCE LINES 55-56

.. code-block:: Python

    B_TIME_S = Beta('B_TIME_S', 1, None, None, 0)







.. GENERATED FROM PYTHON SOURCE LINES 57-59

Define a random parameter with a normal distribution, designed to be used
for quasi Monte-Carlo simulation with Halton draws (base 5).

.. GENERATED FROM PYTHON SOURCE LINES 59-61

.. code-block:: Python

    B_TIME_RND = B_TIME + B_TIME_S * bioDraws('b_time_rnd', 'NORMAL_HALTON5')








.. GENERATED FROM PYTHON SOURCE LINES 62-63

Definition of the utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 63-67

.. code-block:: Python

    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 68-69

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 69-71

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 72-73

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 73-75

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 76-77

Conditional on b_time_rnd, we have a logit model (called the kernel)

.. GENERATED FROM PYTHON SOURCE LINES 77-79

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 80-81

We integrate over b_time_rnd using Monte-Carlo.

.. GENERATED FROM PYTHON SOURCE LINES 81-83

.. code-block:: Python

    logprob = log(MonteCarlo(prob))








.. GENERATED FROM PYTHON SOURCE LINES 84-85

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

.. GENERATED FROM PYTHON SOURCE LINES 85-90

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 91-94

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 94-99

.. code-block:: Python

    the_biogeme = bio.BIOGEME(
        database, logprob, user_notes=USER_NOTES, number_of_draws=100, seed=1223
    )
    the_biogeme.modelName = 'b24halton_mixture'





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

 .. code-block:: none

    Biogeme parameters read from biogeme.toml. 




.. GENERATED FROM PYTHON SOURCE LINES 100-101

Estimate the parameters

.. GENERATED FROM PYTHON SOURCE LINES 101-103

.. 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 __b24halton_mixture.iter 
    Cannot read file __b24halton_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_TRAIN          B_COST          B_TIME        B_TIME_S     Function    Relgrad   Radius      Rho      
        0               1              -1              -1              -1               2      6.1e+03       0.16        1     0.25    + 
        1               0           -0.73            -0.4              -2               3      5.5e+03      0.049        1     0.36    + 
        2            0.51           -0.94            -1.4            -2.3             2.6      5.4e+03      0.054        1     0.39    + 
        3            0.51           -0.94            -1.4            -2.3             2.6      5.4e+03      0.054      0.5    -0.15    - 
        4          0.0062           -0.44            -1.1            -2.8             2.6      5.3e+03       0.03      0.5      0.5    + 
        5            0.33          -0.089            -1.6            -2.6             2.5      5.3e+03      0.046      0.5     0.13    + 
        6            0.33          -0.089            -1.6            -2.6             2.5      5.3e+03      0.046     0.25    -0.18    - 
        7            0.26           -0.34            -1.4            -2.9             2.3      5.2e+03      0.022     0.25     0.65    + 
        8            0.23            -0.3            -1.2            -2.6             2.2      5.2e+03     0.0087     0.25     0.52    + 
        9            0.23            -0.3            -1.2            -2.6             2.2      5.2e+03     0.0087     0.12     -2.2    - 
       10            0.23            -0.3            -1.2            -2.6             2.2      5.2e+03     0.0087    0.062    -0.13    - 
       11            0.29           -0.36            -1.3            -2.6             2.1      5.2e+03     0.0072    0.062     0.31    + 
       12            0.23            -0.3            -1.4            -2.6             2.1      5.2e+03     0.0065    0.062     0.58    + 
       13            0.21           -0.36            -1.3            -2.6               2      5.2e+03      0.011    0.062     0.32    + 
       14            0.22           -0.33            -1.3            -2.5               2      5.2e+03     0.0034     0.62     0.94   ++ 
       15            0.22           -0.33            -1.3            -2.5               2      5.2e+03     0.0034     0.31   -0.026    - 
       16            0.13           -0.39            -1.3            -2.3             1.7      5.2e+03     0.0039     0.31     0.58    + 
       17            0.13           -0.39            -1.3            -2.3             1.7      5.2e+03     0.0039     0.16     -6.3    - 
       18            0.13           -0.39            -1.3            -2.3             1.7      5.2e+03     0.0039    0.078     -4.7    - 
       19            0.13           -0.39            -1.3            -2.3             1.7      5.2e+03     0.0039    0.039     -2.2    - 
       20            0.13           -0.39            -1.3            -2.3             1.7      5.2e+03     0.0039     0.02    -0.15    - 
       21            0.15           -0.41            -1.3            -2.3             1.7      5.2e+03    0.00097     0.02     0.41    + 
       22            0.14           -0.39            -1.3            -2.3             1.7      5.2e+03    0.00075     0.02     0.29    + 
       23            0.15            -0.4            -1.3            -2.3             1.7      5.2e+03    0.00083     0.02     0.41    + 
       24            0.15            -0.4            -1.3            -2.3             1.7      5.2e+03    0.00083   0.0098   -0.089    - 
       25            0.14            -0.4            -1.3            -2.3             1.7      5.2e+03    0.00036   0.0098     0.46    + 
       26            0.14           -0.41            -1.3            -2.3             1.7      5.2e+03    0.00064   0.0098     0.28    + 
       27            0.14            -0.4            -1.3            -2.3             1.7      5.2e+03    0.00031   0.0098     0.28    + 
       28            0.14            -0.4            -1.3            -2.3             1.7      5.2e+03    0.00031   0.0049    -0.24    - 
       29            0.14            -0.4            -1.3            -2.3             1.7      5.2e+03    0.00031   0.0024    -0.83    - 
       30            0.14            -0.4            -1.3            -2.3             1.7      5.2e+03    0.00047   0.0024      0.1    + 
       31            0.14            -0.4            -1.3            -2.3             1.7      5.2e+03    0.00023    0.024     0.94   ++ 
       32            0.14            -0.4            -1.3            -2.3             1.7      5.2e+03    0.00023    0.012     -8.4    - 
       33            0.14            -0.4            -1.3            -2.3             1.7      5.2e+03    0.00023   0.0061     -2.8    - 
       34            0.14            -0.4            -1.3            -2.3             1.7      5.2e+03    0.00023   0.0031    -0.17    - 
       35            0.14            -0.4            -1.3            -2.3             1.7      5.2e+03    2.8e-05   0.0031     0.79    - 
    Results saved in file b24halton_mixture.html 
    Results saved in file b24halton_mixture.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 104-106

.. code-block:: Python

    print(results.short_summary())





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

 .. code-block:: none

    Results for model b24halton_mixture
    Nbr of parameters:              5
    Sample size:                    6768
    Excluded data:                  3960
    Final log likelihood:           -5215.687
    Akaike Information Criterion:   10441.37
    Bayesian Information Criterion: 10475.47





.. GENERATED FROM PYTHON SOURCE LINES 107-109

.. 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>0.136579</td>
          <td>0.051823</td>
          <td>2.635494</td>
          <td>8.401497e-03</td>
        </tr>
        <tr>
          <th>ASC_TRAIN</th>
          <td>-0.403435</td>
          <td>0.065704</td>
          <td>-6.140162</td>
          <td>8.243723e-10</td>
        </tr>
        <tr>
          <th>B_COST</th>
          <td>-1.284767</td>
          <td>0.086275</td>
          <td>-14.891565</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME</th>
          <td>-2.258401</td>
          <td>0.117811</td>
          <td>-19.169680</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME_S</th>
          <td>1.660487</td>
          <td>0.133546</td>
          <td>12.433865</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 12.833 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b24halton_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_b24halton_mixture.ipynb <plot_b24halton_mixture.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_b24halton_mixture.py <plot_b24halton_mixture.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_b24halton_mixture.zip <plot_b24halton_mixture.zip>`


.. only:: html

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

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