.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b03scale.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_b03scale.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_swissmetro_plot_b03scale.py:


Heteroscedastic specification
=============================

 Illustrates a heteroscedastic specification. A different scale is
 associated with different segments of the sample.

:author: Michel Bierlaire, EPFL
:date: Sun Apr  9 17:23:03 2023

.. GENERATED FROM PYTHON SOURCE LINES 14-19

.. code-block:: default


    import biogeme.biogeme as bio
    from biogeme import models
    from biogeme.expressions import Beta








.. GENERATED FROM PYTHON SOURCE LINES 20-21

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

.. GENERATED FROM PYTHON SOURCE LINES 21-37

.. 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,
        GROUP,
    )









.. GENERATED FROM PYTHON SOURCE LINES 38-39

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 39-46

.. 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_TIME = Beta('B_TIME', 0, None, None, 0)
    B_COST = Beta('B_COST', 0, None, None, 0)
    Scale_group3 = Beta('Scale_group3', 1, 0.001, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 47-48

Definition of the utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 48-52

.. code-block:: default

    V1 = ASC_TRAIN + B_TIME * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
    V2 = ASC_SM + B_TIME * SM_TT_SCALED + B_COST * SM_COST_SCALED
    V3 = ASC_CAR + B_TIME * CAR_TT_SCALED + B_COST * CAR_CO_SCALED








.. GENERATED FROM PYTHON SOURCE LINES 53-54

Scale associated with group 3 is estimated.

.. GENERATED FROM PYTHON SOURCE LINES 54-56

.. code-block:: default

    scale = (GROUP != 3) + (GROUP == 3) * Scale_group3








.. GENERATED FROM PYTHON SOURCE LINES 57-59

Scale the utility functions, and associate them with the numbering
of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 59-61

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 62-63

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 63-65

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 66-68

Definition of the model. This is the contribution of each
observation to the log likelihood function.

.. GENERATED FROM PYTHON SOURCE LINES 68-70

.. code-block:: default

    logprob = models.loglogit(V, av, CHOICE)








.. GENERATED FROM PYTHON SOURCE LINES 71-72

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

.. GENERATED FROM PYTHON SOURCE LINES 72-77

.. code-block:: default

    USER_NOTES = (
        'Illustrates heteroscedastic specification. A different scale is'
        ' associated with different segments of the sample.'
    )








.. GENERATED FROM PYTHON SOURCE LINES 78-79

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 79-82

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, logprob, user_notes=USER_NOTES)
    the_biogeme.modelName = 'b03scale'








.. GENERATED FROM PYTHON SOURCE LINES 83-84

Estimate the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 84-86

.. code-block:: default

    results = the_biogeme.estimate()








.. GENERATED FROM PYTHON SOURCE LINES 87-89

.. code-block:: default

    print(results.short_summary())





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

 .. code-block:: none

    Results for model b03scale
    Nbr of parameters:              5
    Sample size:                    6768
    Excluded data:                  3960
    Final log likelihood:           -4976.691
    Akaike Information Criterion:   9963.381
    Bayesian Information Criterion: 9997.481





.. GENERATED FROM PYTHON SOURCE LINES 90-91

Get the results in a pandas table

.. GENERATED FROM PYTHON SOURCE LINES 91-93

.. 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>-0.015332</td>
          <td>0.018508</td>
          <td>-0.828415</td>
          <td>0.407435</td>
        </tr>
        <tr>
          <th>ASC_TRAIN</th>
          <td>-0.447096</td>
          <td>0.041146</td>
          <td>-10.866099</td>
          <td>0.000000</td>
        </tr>
        <tr>
          <th>B_COST</th>
          <td>-0.357349</td>
          <td>0.038418</td>
          <td>-9.301647</td>
          <td>0.000000</td>
        </tr>
        <tr>
          <th>B_TIME</th>
          <td>-0.374455</td>
          <td>0.044514</td>
          <td>-8.412151</td>
          <td>0.000000</td>
        </tr>
        <tr>
          <th>Scale_group3</th>
          <td>4.177737</td>
          <td>0.370552</td>
          <td>11.274371</td>
          <td>0.000000</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.310 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b03scale.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_b03scale.py <plot_b03scale.py>`

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

      :download:`Download Jupyter notebook: plot_b03scale.ipynb <plot_b03scale.ipynb>`


.. only:: html

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

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