.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/assisted/plot_b04segmentation.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_assisted_plot_b04segmentation.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_assisted_plot_b04segmentation.py:


Catalog for segmented parameters
================================

Investigate the segmentations of parameters.

We consider 4 specifications for the constants:

    - Not segmented
    - Segmented by GA (yearly subscription to public transport)
    - Segmented by luggage
    - Segmented both by GA and luggage

We consider 3 specifications for the time coefficients:

    - Not Segmented
    - Segmented with first class
    - Segmented with trip purpose

We obtain a total of 12 specifications.
See `Bierlaire and Ortelli (2023)
<https://transp-or.epfl.ch/documents/technicalReports/BierOrte23.pdf>`_.

:author: Michel Bierlaire, EPFL
:date: Thu Jul 13 16:18:10 2023

.. GENERATED FROM PYTHON SOURCE LINES 29-37

.. code-block:: default

    import numpy as np
    import biogeme.biogeme as bio
    from biogeme import models
    from biogeme.expressions import Beta
    from biogeme.catalog import segmentation_catalogs
    from biogeme.results import compile_estimation_results, pareto_optimal









.. GENERATED FROM PYTHON SOURCE LINES 38-39

See :ref:`swissmetro_data`.

.. GENERATED FROM PYTHON SOURCE LINES 39-53

.. 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,
    )








.. GENERATED FROM PYTHON SOURCE LINES 54-55

Definition of the segmentations.

.. GENERATED FROM PYTHON SOURCE LINES 55-67

.. code-block:: default

    segmentation_ga = database.generate_segmentation(
        variable='GA', mapping={0: 'noGA', 1: 'GA'}
    )

    segmentation_luggage = database.generate_segmentation(
        variable='LUGGAGE', mapping={0: 'no_lugg', 1: 'one_lugg', 3: 'several_lugg'}
    )

    segmentation_first = database.generate_segmentation(
        variable='FIRST', mapping={0: '2nd_class', 1: '1st_class'}
    )








.. GENERATED FROM PYTHON SOURCE LINES 68-70

We consider two trip purposes: 'commuters' and anything else. We
need to define a binary variable first.

.. GENERATED FROM PYTHON SOURCE LINES 70-76

.. code-block:: default

    database.data['COMMUTERS'] = np.where(database.data['PURPOSE'] == 1, 1, 0)

    segmentation_purpose = database.generate_segmentation(
        variable='COMMUTERS', mapping={0: 'non_commuters', 1: 'commuters'}
    )








.. GENERATED FROM PYTHON SOURCE LINES 77-78

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 78-83

.. code-block:: default

    ASC_CAR = Beta('ASC_CAR', 0, None, None, 0)
    ASC_TRAIN = Beta('ASC_TRAIN', 0, None, None, 0)
    B_TIME = Beta('B_TIME', 0, None, None, 0)
    B_COST = Beta('B_COST', 0, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 84-85

Catalogs for the alternative specific constants.

.. GENERATED FROM PYTHON SOURCE LINES 85-95

.. code-block:: default

    ASC_TRAIN_catalog, ASC_CAR_catalog = segmentation_catalogs(
        generic_name='ASC',
        beta_parameters=[ASC_TRAIN, ASC_CAR],
        potential_segmentations=(
            segmentation_ga,
            segmentation_luggage,
        ),
        maximum_number=2,
    )








.. GENERATED FROM PYTHON SOURCE LINES 96-100

Catalog for the travel time coefficient.
Note that the function returns a list of catalogs. Here, the list
contains only one of them.  This is why there is a comma after
"B_TIME_catalog".

.. GENERATED FROM PYTHON SOURCE LINES 100-110

.. code-block:: default

    (B_TIME_catalog,) = segmentation_catalogs(
        generic_name='B_TIME',
        beta_parameters=[B_TIME],
        potential_segmentations=(
            segmentation_first,
            segmentation_purpose,
        ),
        maximum_number=1,
    )








.. GENERATED FROM PYTHON SOURCE LINES 111-112

Definition of the utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 112-116

.. code-block:: default

    V1 = ASC_TRAIN_catalog + B_TIME_catalog * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
    V2 = B_TIME_catalog * SM_TT_SCALED + B_COST * SM_COST_SCALED
    V3 = ASC_CAR_catalog + B_TIME_catalog * CAR_TT_SCALED + B_COST * CAR_CO_SCALED








.. GENERATED FROM PYTHON SOURCE LINES 117-118

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 118-120

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 121-122

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 122-124

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 125-127

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

.. GENERATED FROM PYTHON SOURCE LINES 127-129

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 130-131

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 131-136

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, logprob)
    the_biogeme.modelName = 'b04segmentation'
    the_biogeme.generate_html = False
    the_biogeme.generate_pickle = False








.. GENERATED FROM PYTHON SOURCE LINES 137-138

Estimate the parameters

.. GENERATED FROM PYTHON SOURCE LINES 138-140

.. code-block:: default

    dict_of_results = the_biogeme.estimate_catalog()








.. GENERATED FROM PYTHON SOURCE LINES 141-142

Number of estimated models.

.. GENERATED FROM PYTHON SOURCE LINES 142-144

.. code-block:: default

    print(f'A total of {len(dict_of_results)} models have been estimated')





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

 .. code-block:: none

    A total of 12 models have been estimated




.. GENERATED FROM PYTHON SOURCE LINES 145-146

All estimation results

.. GENERATED FROM PYTHON SOURCE LINES 146-150

.. code-block:: default

    compiled_results, specs = compile_estimation_results(
        dict_of_results, use_short_names=True
    )








.. GENERATED FROM PYTHON SOURCE LINES 151-153

.. code-block:: default

    compiled_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>Model_000000</th>
          <th>Model_000001</th>
          <th>Model_000002</th>
          <th>Model_000003</th>
          <th>Model_000004</th>
          <th>Model_000005</th>
          <th>Model_000006</th>
          <th>Model_000007</th>
          <th>Model_000008</th>
          <th>Model_000009</th>
          <th>Model_000010</th>
          <th>Model_000011</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>Number of estimated parameters</th>
          <td>7</td>
          <td>7</td>
          <td>5</td>
          <td>10</td>
          <td>4</td>
          <td>5</td>
          <td>6</td>
          <td>11</td>
          <td>9</td>
          <td>11</td>
          <td>9</td>
          <td>8</td>
        </tr>
        <tr>
          <th>Sample size</th>
          <td>6768</td>
          <td>6768</td>
          <td>6768</td>
          <td>6768</td>
          <td>6768</td>
          <td>6768</td>
          <td>6768</td>
          <td>6768</td>
          <td>6768</td>
          <td>6768</td>
          <td>6768</td>
          <td>6768</td>
        </tr>
        <tr>
          <th>Final log likelihood</th>
          <td>-4976.118642</td>
          <td>-5048.818199</td>
          <td>-5331.250708</td>
          <td>-5022.276564</td>
          <td>-5331.252007</td>
          <td>-5234.708233</td>
          <td>-5050.677696</td>
          <td>-5020.027091</td>
          <td>-5160.079285</td>
          <td>-4952.546476</td>
          <td>-5240.921463</td>
          <td>-5241.011928</td>
        </tr>
        <tr>
          <th>Akaike Information Criterion</th>
          <td>9966.237283</td>
          <td>10111.636399</td>
          <td>10672.501415</td>
          <td>10064.553128</td>
          <td>10670.504014</td>
          <td>10479.416466</td>
          <td>10113.355392</td>
          <td>10062.054183</td>
          <td>10338.158569</td>
          <td>9927.092951</td>
          <td>10499.842927</td>
          <td>10498.023855</td>
        </tr>
        <tr>
          <th>Bayesian Information Criterion</th>
          <td>10013.97701</td>
          <td>10159.376125</td>
          <td>10706.60122</td>
          <td>10132.752737</td>
          <td>10697.783857</td>
          <td>10513.51627</td>
          <td>10154.275157</td>
          <td>10137.073753</td>
          <td>10399.538218</td>
          <td>10002.112521</td>
          <td>10561.222575</td>
          <td>10552.583543</td>
        </tr>
        <tr>
          <th>ASC_CAR (t-test)</th>
          <td>-0.281  (-4.53)</td>
          <td>-0.246  (-3.77)</td>
          <td>-0.155  (-2.53)</td>
          <td>-0.293  (-3.93)</td>
          <td>-0.155  (-2.66)</td>
          <td>-0.187  (-3.23)</td>
          <td>-0.249  (-3.97)</td>
          <td>-0.29  (-3.77)</td>
          <td>-0.24  (-3.36)</td>
          <td>-0.298  (-4.12)</td>
          <td>-0.237  (-3.13)</td>
          <td>-0.238  (-3.26)</td>
        </tr>
        <tr>
          <th>ASC_CAR_GA (t-test)</th>
          <td>-0.231  (-1.19)</td>
          <td>-0.298  (-1.55)</td>
          <td></td>
          <td>-0.291  (-1.49)</td>
          <td></td>
          <td></td>
          <td>-0.301  (-1.56)</td>
          <td>-0.287  (-1.48)</td>
          <td></td>
          <td>-0.206  (-1.05)</td>
          <td></td>
          <td></td>
        </tr>
        <tr>
          <th>ASC_TRAIN (t-test)</th>
          <td>-1.37  (-14.7)</td>
          <td>-1.28  (-13)</td>
          <td>-0.701  (-7.69)</td>
          <td>-1.75  (-15.1)</td>
          <td>-0.701  (-8.49)</td>
          <td>-0.814  (-9.45)</td>
          <td>-1.28  (-14)</td>
          <td>-1.74  (-14.6)</td>
          <td>-1.58  (-13.8)</td>
          <td>-1.79  (-15.4)</td>
          <td>-1.54  (-12.8)</td>
          <td>-1.54  (-13.5)</td>
        </tr>
        <tr>
          <th>ASC_TRAIN_GA (t-test)</th>
          <td>1.91  (21.5)</td>
          <td>1.99  (22.6)</td>
          <td></td>
          <td>1.78  (19.4)</td>
          <td></td>
          <td></td>
          <td>1.97  (22.3)</td>
          <td>1.8  (19.6)</td>
          <td></td>
          <td>1.75  (19.1)</td>
          <td></td>
          <td></td>
        </tr>
        <tr>
          <th>B_COST (t-test)</th>
          <td>-1.26  (-15.3)</td>
          <td>-1.1  (-14.9)</td>
          <td>-1.08  (-16)</td>
          <td>-1.1  (-14.8)</td>
          <td>-1.08  (-15.9)</td>
          <td>-1.23  (-16.6)</td>
          <td>-1.1  (-14.8)</td>
          <td>-1.1  (-14.8)</td>
          <td>-1.22  (-16.3)</td>
          <td>-1.25  (-15.3)</td>
          <td>-1.09  (-15.8)</td>
          <td>-1.09  (-15.7)</td>
        </tr>
        <tr>
          <th>B_TIME (t-test)</th>
          <td>-0.621  (-4.46)</td>
          <td>-1.16  (-13.6)</td>
          <td>-1.28  (-15.1)</td>
          <td>-1.17  (-11.2)</td>
          <td>-1.28  (-12.3)</td>
          <td>-0.647  (-4.69)</td>
          <td>-1.18  (-11.3)</td>
          <td>-1.14  (-13.5)</td>
          <td>-0.656  (-4.64)</td>
          <td>-0.622  (-4.42)</td>
          <td>-1.24  (-14.6)</td>
          <td>-1.24  (-11.9)</td>
        </tr>
        <tr>
          <th>B_TIME_1st_class (t-test)</th>
          <td>-0.914  (-8.6)</td>
          <td></td>
          <td></td>
          <td></td>
          <td></td>
          <td>-1.02  (-9.87)</td>
          <td></td>
          <td></td>
          <td>-0.943  (-8.88)</td>
          <td>-0.891  (-8.26)</td>
          <td></td>
          <td></td>
        </tr>
        <tr>
          <th>B_TIME_commuters (t-test)</th>
          <td></td>
          <td>-0.183  (-0.799)</td>
          <td>-0.00469  (-0.0222)</td>
          <td></td>
          <td></td>
          <td></td>
          <td></td>
          <td>-0.202  (-0.874)</td>
          <td></td>
          <td></td>
          <td>-0.0396  (-0.184)</td>
          <td></td>
        </tr>
        <tr>
          <th>ASC_CAR_one_lugg (t-test)</th>
          <td></td>
          <td></td>
          <td></td>
          <td>0.0744  (1.13)</td>
          <td></td>
          <td></td>
          <td></td>
          <td>0.0749  (1.14)</td>
          <td>0.0616  (0.923)</td>
          <td>0.0324  (0.486)</td>
          <td>0.104  (1.57)</td>
          <td>0.103  (1.56)</td>
        </tr>
        <tr>
          <th>ASC_CAR_several_lugg (t-test)</th>
          <td></td>
          <td></td>
          <td></td>
          <td>-0.252  (-1.06)</td>
          <td></td>
          <td></td>
          <td></td>
          <td>-0.261  (-1.1)</td>
          <td>-0.432  (-1.83)</td>
          <td>-0.437  (-1.82)</td>
          <td>-0.252  (-1.07)</td>
          <td>-0.25  (-1.06)</td>
        </tr>
        <tr>
          <th>ASC_TRAIN_one_lugg (t-test)</th>
          <td></td>
          <td></td>
          <td></td>
          <td>0.712  (7.23)</td>
          <td></td>
          <td></td>
          <td></td>
          <td>0.717  (7.3)</td>
          <td>1.05  (11.1)</td>
          <td>0.635  (6.4)</td>
          <td>1.15  (12.3)</td>
          <td>1.15  (12.3)</td>
        </tr>
        <tr>
          <th>ASC_TRAIN_several_lugg (t-test)</th>
          <td></td>
          <td></td>
          <td></td>
          <td>0.593  (2.67)</td>
          <td></td>
          <td></td>
          <td></td>
          <td>0.584  (2.65)</td>
          <td>0.799  (3.74)</td>
          <td>0.431  (2)</td>
          <td>0.976  (4.43)</td>
          <td>0.978  (4.47)</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 154-155

Glossary

.. GENERATED FROM PYTHON SOURCE LINES 155-158

.. code-block:: default

    for short_name, spec in specs.items():
        print(f'{short_name}\t{spec}')





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

 .. code-block:: none

    Model_000000    ASC:GA;B_TIME:FIRST
    Model_000001    ASC:GA;B_TIME:COMMUTERS
    Model_000002    ASC:no_seg;B_TIME:COMMUTERS
    Model_000003    ASC:GA-LUGGAGE;B_TIME:no_seg
    Model_000004    ASC:no_seg;B_TIME:no_seg
    Model_000005    ASC:no_seg;B_TIME:FIRST
    Model_000006    ASC:GA;B_TIME:no_seg
    Model_000007    ASC:GA-LUGGAGE;B_TIME:COMMUTERS
    Model_000008    ASC:LUGGAGE;B_TIME:FIRST
    Model_000009    ASC:GA-LUGGAGE;B_TIME:FIRST
    Model_000010    ASC:LUGGAGE;B_TIME:COMMUTERS
    Model_000011    ASC:LUGGAGE;B_TIME:no_seg




.. GENERATED FROM PYTHON SOURCE LINES 159-160

Estimation results of the Pareto optimal models.

.. GENERATED FROM PYTHON SOURCE LINES 160-165

.. code-block:: default

    pareto_results = pareto_optimal(dict_of_results)
    compiled_pareto_results, pareto_specs = compile_estimation_results(
        pareto_results, use_short_names=True
    )








.. GENERATED FROM PYTHON SOURCE LINES 166-168

.. code-block:: default

    compiled_pareto_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>Model_000000</th>
          <th>Model_000001</th>
          <th>Model_000002</th>
          <th>Model_000003</th>
          <th>Model_000004</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>Number of estimated parameters</th>
          <td>11</td>
          <td>4</td>
          <td>5</td>
          <td>6</td>
          <td>7</td>
        </tr>
        <tr>
          <th>Sample size</th>
          <td>6768</td>
          <td>6768</td>
          <td>6768</td>
          <td>6768</td>
          <td>6768</td>
        </tr>
        <tr>
          <th>Final log likelihood</th>
          <td>-4952.546476</td>
          <td>-5331.252007</td>
          <td>-5234.708233</td>
          <td>-5050.677696</td>
          <td>-4976.118642</td>
        </tr>
        <tr>
          <th>Akaike Information Criterion</th>
          <td>9927.092951</td>
          <td>10670.504014</td>
          <td>10479.416466</td>
          <td>10113.355392</td>
          <td>9966.237283</td>
        </tr>
        <tr>
          <th>Bayesian Information Criterion</th>
          <td>10002.112521</td>
          <td>10697.783857</td>
          <td>10513.51627</td>
          <td>10154.275157</td>
          <td>10013.97701</td>
        </tr>
        <tr>
          <th>ASC_CAR (t-test)</th>
          <td>-0.298  (-4.12)</td>
          <td>-0.155  (-2.66)</td>
          <td>-0.187  (-3.23)</td>
          <td>-0.249  (-3.97)</td>
          <td>-0.281  (-4.53)</td>
        </tr>
        <tr>
          <th>ASC_CAR_GA (t-test)</th>
          <td>-0.206  (-1.05)</td>
          <td></td>
          <td></td>
          <td>-0.301  (-1.56)</td>
          <td>-0.231  (-1.19)</td>
        </tr>
        <tr>
          <th>ASC_CAR_one_lugg (t-test)</th>
          <td>0.0324  (0.486)</td>
          <td></td>
          <td></td>
          <td></td>
          <td></td>
        </tr>
        <tr>
          <th>ASC_CAR_several_lugg (t-test)</th>
          <td>-0.437  (-1.82)</td>
          <td></td>
          <td></td>
          <td></td>
          <td></td>
        </tr>
        <tr>
          <th>ASC_TRAIN (t-test)</th>
          <td>-1.79  (-15.4)</td>
          <td>-0.701  (-8.49)</td>
          <td>-0.814  (-9.45)</td>
          <td>-1.28  (-14)</td>
          <td>-1.37  (-14.7)</td>
        </tr>
        <tr>
          <th>ASC_TRAIN_GA (t-test)</th>
          <td>1.75  (19.1)</td>
          <td></td>
          <td></td>
          <td>1.97  (22.3)</td>
          <td>1.91  (21.5)</td>
        </tr>
        <tr>
          <th>ASC_TRAIN_one_lugg (t-test)</th>
          <td>0.635  (6.4)</td>
          <td></td>
          <td></td>
          <td></td>
          <td></td>
        </tr>
        <tr>
          <th>ASC_TRAIN_several_lugg (t-test)</th>
          <td>0.431  (2)</td>
          <td></td>
          <td></td>
          <td></td>
          <td></td>
        </tr>
        <tr>
          <th>B_COST (t-test)</th>
          <td>-1.25  (-15.3)</td>
          <td>-1.08  (-15.9)</td>
          <td>-1.23  (-16.6)</td>
          <td>-1.1  (-14.8)</td>
          <td>-1.26  (-15.3)</td>
        </tr>
        <tr>
          <th>B_TIME (t-test)</th>
          <td>-0.622  (-4.42)</td>
          <td>-1.28  (-12.3)</td>
          <td>-0.647  (-4.69)</td>
          <td>-1.18  (-11.3)</td>
          <td>-0.621  (-4.46)</td>
        </tr>
        <tr>
          <th>B_TIME_1st_class (t-test)</th>
          <td>-0.891  (-8.26)</td>
          <td></td>
          <td>-1.02  (-9.87)</td>
          <td></td>
          <td>-0.914  (-8.6)</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 169-170

Glossary.

.. GENERATED FROM PYTHON SOURCE LINES 170-172

.. code-block:: default

    for short_name, spec in pareto_specs.items():
        print(f'{short_name}\t{spec}')




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

 .. code-block:: none

    Model_000000    ASC:GA-LUGGAGE;B_TIME:FIRST
    Model_000001    ASC:no_seg;B_TIME:no_seg
    Model_000002    ASC:no_seg;B_TIME:FIRST
    Model_000003    ASC:GA;B_TIME:no_seg
    Model_000004    ASC:GA;B_TIME:FIRST





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

   **Total running time of the script:** (0 minutes 2.647 seconds)


.. _sphx_glr_download_auto_examples_assisted_plot_b04segmentation.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_b04segmentation.py <plot_b04segmentation.py>`

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

      :download:`Download Jupyter notebook: plot_b04segmentation.ipynb <plot_b04segmentation.ipynb>`


.. only:: html

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

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