.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/assisted/plot_b03alt_spec.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_b03alt_spec.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_assisted_plot_b03alt_spec.py:


Catalog for alternative specific coefficients
=============================================

Investigate alternative specific parameters:

    - two specifications for the travel time coefficient: generic, and
      alternative specific,
    - two specifications for the travel cost coefficient: generic, and
      alternative specific,

for a total of 4 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 22-47

.. code-block:: Python


    import biogeme.biogeme as bio
    import biogeme.biogeme_logging as blog
    from biogeme import models
    from biogeme.expressions import Beta
    from biogeme.catalog import generic_alt_specific_catalogs
    from biogeme.results import compile_estimation_results, pareto_optimal


    from biogeme.data.swissmetro import (
        read_data,
        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,
    )

    logger = blog.get_screen_logger(level=blog.INFO)








.. GENERATED FROM PYTHON SOURCE LINES 48-49

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 49-54

.. code-block:: Python

    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 55-56

Catalog for travel time coefficient.

.. GENERATED FROM PYTHON SOURCE LINES 56-60

.. code-block:: Python

    (B_TIME_catalog_dict,) = generic_alt_specific_catalogs(
        generic_name='B_TIME', beta_parameters=[B_TIME], alternatives=('TRAIN', 'SM', 'CAR')
    )








.. GENERATED FROM PYTHON SOURCE LINES 61-62

Catalog for travel cost coefficient.

.. GENERATED FROM PYTHON SOURCE LINES 62-66

.. code-block:: Python

    (B_COST_catalog_dict,) = generic_alt_specific_catalogs(
        generic_name='B_COST', beta_parameters=[B_COST], alternatives=('TRAIN', 'SM', 'CAR')
    )








.. GENERATED FROM PYTHON SOURCE LINES 67-68

Definition of the utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 68-83

.. code-block:: Python

    V1 = (
        ASC_TRAIN
        + B_TIME_catalog_dict['TRAIN'] * TRAIN_TT_SCALED
        + B_COST_catalog_dict['TRAIN'] * TRAIN_COST_SCALED
    )
    V2 = (
        B_TIME_catalog_dict['SM'] * SM_TT_SCALED
        + B_COST_catalog_dict['SM'] * SM_COST_SCALED
    )
    V3 = (
        ASC_CAR
        + B_TIME_catalog_dict['CAR'] * CAR_TT_SCALED
        + B_COST_catalog_dict['CAR'] * CAR_CO_SCALED
    )








.. GENERATED FROM PYTHON SOURCE LINES 84-85

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 85-87

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 88-89

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 89-91

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 92-94

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

.. GENERATED FROM PYTHON SOURCE LINES 94-96

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 97-98

Read the data

.. GENERATED FROM PYTHON SOURCE LINES 98-100

.. code-block:: Python

    database = read_data()








.. GENERATED FROM PYTHON SOURCE LINES 101-102

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 102-107

.. code-block:: Python

    the_biogeme = bio.BIOGEME(database, logprob)
    the_biogeme.modelName = 'b01alt_spec'
    the_biogeme.generate_html = False
    the_biogeme.generate_pickle = False





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

 .. code-block:: none

    Biogeme parameters read from biogeme.toml. 




.. GENERATED FROM PYTHON SOURCE LINES 108-109

Estimate the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 109-111

.. code-block:: Python

    dict_of_results = the_biogeme.estimate_catalog()





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

 .. code-block:: none

    Estimating 4 models. 
    Biogeme parameters read from biogeme.toml. 
    As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, 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 __b01alt_spec_000000.iter 
    Cannot read file __b01alt_spec_000000.iter. Statement is ignored. 
    As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, 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: Newton with trust region for simple bounds 
    Iter.         ASC_CAR       ASC_TRAIN          B_COST      B_TIME_CAR       B_TIME_SM    B_TIME_TRAIN     Function    Relgrad   Radius      Rho      
        0           -0.42           -0.77           -0.68           -0.78              -1           -0.88      8.8e+03      0.076       10      1.1   ++ 
        1           -0.53           -0.37           -0.78           -0.98            -1.4            -1.5      8.6e+03      0.025    1e+02      1.1   ++ 
        2           -0.54           -0.17           -0.79              -1            -1.5            -1.7      8.6e+03     0.0028    1e+03      1.1   ++ 
        3           -0.54           -0.17           -0.79              -1            -1.5            -1.7      8.6e+03      3e-05    1e+03        1   ++ 
    Biogeme parameters read from biogeme.toml. 
    As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, 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 __b01alt_spec_000001.iter 
    Cannot read file __b01alt_spec_000001.iter. Statement is ignored. 
    As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, 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: Newton with trust region for simple bounds 
    Iter.         ASC_CAR       ASC_TRAIN      B_COST_CAR       B_COST_SM    B_COST_TRAIN      B_TIME_CAR       B_TIME_SM    B_TIME_TRAIN     Function    Relgrad   Radius      Rho      
        0            -0.6          -0.032           -0.33            -0.8              -1            -1.2            -1.4            -1.6      8.6e+03      0.055       10     0.96   ++ 
        1           -0.59          -0.021           -0.64           -0.77            -1.6              -1            -1.5            -1.5      8.4e+03      0.016    1e+02      1.1   ++ 
        2           -0.59          -0.019           -0.66           -0.79            -1.8            -1.1            -1.5            -1.4      8.4e+03      0.002    1e+03      1.1   ++ 
        3           -0.59          -0.019           -0.66           -0.79            -1.8            -1.1            -1.5            -1.4      8.4e+03      3e-05    1e+03        1   ++ 
    Biogeme parameters read from biogeme.toml. 
    As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, 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 __b01alt_spec_000002.iter 
    Cannot read file __b01alt_spec_000002.iter. Statement is ignored. 
    As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, 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: Newton with trust region for simple bounds 
    Iter.         ASC_CAR       ASC_TRAIN          B_COST          B_TIME     Function    Relgrad   Radius      Rho      
        0           -0.16           -0.53           -0.66           -0.87      8.8e+03      0.048       10      1.1   ++ 
        1          -0.003           -0.63           -0.77            -1.2      8.7e+03     0.0073    1e+02      1.1   ++ 
        2           0.016           -0.65           -0.79            -1.3      8.7e+03    0.00016    1e+03        1   ++ 
        3           0.016           -0.65           -0.79            -1.3      8.7e+03    7.3e-08    1e+03        1   ++ 
    Biogeme parameters read from biogeme.toml. 
    As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, 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 __b01alt_spec_000003.iter 
    Cannot read file __b01alt_spec_000003.iter. Statement is ignored. 
    As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, 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: Newton with trust region for simple bounds 
    Iter.         ASC_CAR       ASC_TRAIN      B_COST_CAR       B_COST_SM    B_COST_TRAIN          B_TIME     Function    Relgrad   Radius      Rho      
        0           -0.39           0.098           -0.39           -0.81            -1.8            -1.3      8.5e+03      0.026        1      0.8    + 
        1           -0.42          -0.044           -0.38           -0.82            -1.9            -1.3      8.4e+03     0.0019       10        1   ++ 
        2           -0.42          -0.044           -0.38           -0.82            -1.9            -1.3      8.4e+03    1.5e-05       10        1   ++ 




.. GENERATED FROM PYTHON SOURCE LINES 112-113

Number of estimated models.

.. GENERATED FROM PYTHON SOURCE LINES 113-115

.. code-block:: Python

    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 4 models have been estimated




.. GENERATED FROM PYTHON SOURCE LINES 116-117

All estimation results

.. GENERATED FROM PYTHON SOURCE LINES 117-121

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 122-124

.. code-block:: Python

    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>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>Number of estimated parameters</th>
          <td>6</td>
          <td>8</td>
          <td>4</td>
          <td>6</td>
        </tr>
        <tr>
          <th>Sample size</th>
          <td>10719</td>
          <td>10719</td>
          <td>10719</td>
          <td>10719</td>
        </tr>
        <tr>
          <th>Final log likelihood</th>
          <td>-8579.524042</td>
          <td>-8430.710721</td>
          <td>-8670.163119</td>
          <td>-8448.605446</td>
        </tr>
        <tr>
          <th>Akaike Information Criterion</th>
          <td>17171.048085</td>
          <td>16877.421442</td>
          <td>17348.326237</td>
          <td>16909.210893</td>
        </tr>
        <tr>
          <th>Bayesian Information Criterion</th>
          <td>17214.726724</td>
          <td>16935.659627</td>
          <td>17377.44533</td>
          <td>16952.889531</td>
        </tr>
        <tr>
          <th>ASC_CAR (t-test)</th>
          <td>-0.544  (-7.24)</td>
          <td>-0.595  (-8.17)</td>
          <td>0.0162  (0.438)</td>
          <td>-0.415  (-7.36)</td>
        </tr>
        <tr>
          <th>ASC_TRAIN (t-test)</th>
          <td>-0.144  (-1.73)</td>
          <td>-0.0197  (-0.234)</td>
          <td>-0.652  (-12)</td>
          <td>-0.046  (-0.733)</td>
        </tr>
        <tr>
          <th>B_COST (t-test)</th>
          <td>-0.789  (-17)</td>
          <td></td>
          <td>-0.79  (-15.5)</td>
          <td></td>
        </tr>
        <tr>
          <th>B_TIME_CAR (t-test)</th>
          <td>-0.998  (-14.9)</td>
          <td>-1.06  (-11.1)</td>
          <td></td>
          <td></td>
        </tr>
        <tr>
          <th>B_TIME_SM (t-test)</th>
          <td>-1.47  (-14.3)</td>
          <td>-1.46  (-14.4)</td>
          <td></td>
          <td></td>
        </tr>
        <tr>
          <th>B_TIME_TRAIN (t-test)</th>
          <td>-1.76  (-23.4)</td>
          <td>-1.4  (-15.8)</td>
          <td></td>
          <td></td>
        </tr>
        <tr>
          <th>B_COST_CAR (t-test)</th>
          <td></td>
          <td>-0.659  (-6.68)</td>
          <td></td>
          <td>-0.383  (-5)</td>
        </tr>
        <tr>
          <th>B_COST_SM (t-test)</th>
          <td></td>
          <td>-0.787  (-14.8)</td>
          <td></td>
          <td>-0.823  (-15.5)</td>
        </tr>
        <tr>
          <th>B_COST_TRAIN (t-test)</th>
          <td></td>
          <td>-1.85  (-14.2)</td>
          <td></td>
          <td>-1.92  (-16.8)</td>
        </tr>
        <tr>
          <th>B_TIME (t-test)</th>
          <td></td>
          <td></td>
          <td>-1.28  (-19.5)</td>
          <td>-1.27  (-16.9)</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 125-126

Glossary

.. GENERATED FROM PYTHON SOURCE LINES 126-129

.. code-block:: Python

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





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

 .. code-block:: none

    Model_000000    B_COST_gen_altspec:generic;B_TIME_gen_altspec:altspec
    Model_000001    B_COST_gen_altspec:altspec;B_TIME_gen_altspec:altspec
    Model_000002    B_COST_gen_altspec:generic;B_TIME_gen_altspec:generic
    Model_000003    B_COST_gen_altspec:altspec;B_TIME_gen_altspec:generic




.. GENERATED FROM PYTHON SOURCE LINES 130-131

Estimation results of the Pareto optimal models.

.. GENERATED FROM PYTHON SOURCE LINES 131-136

.. code-block:: Python

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





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

 .. code-block:: none

    No Pareto file has been provided 




.. GENERATED FROM PYTHON SOURCE LINES 137-139

.. code-block:: Python

    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>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>Number of estimated parameters</th>
          <td>4</td>
          <td>8</td>
          <td>6</td>
        </tr>
        <tr>
          <th>Sample size</th>
          <td>10719</td>
          <td>10719</td>
          <td>10719</td>
        </tr>
        <tr>
          <th>Final log likelihood</th>
          <td>-8670.163119</td>
          <td>-8430.710721</td>
          <td>-8448.605446</td>
        </tr>
        <tr>
          <th>Akaike Information Criterion</th>
          <td>17348.326237</td>
          <td>16877.421442</td>
          <td>16909.210893</td>
        </tr>
        <tr>
          <th>Bayesian Information Criterion</th>
          <td>17377.44533</td>
          <td>16935.659627</td>
          <td>16952.889531</td>
        </tr>
        <tr>
          <th>ASC_CAR (t-test)</th>
          <td>0.0162  (0.438)</td>
          <td>-0.595  (-8.17)</td>
          <td>-0.415  (-7.36)</td>
        </tr>
        <tr>
          <th>ASC_TRAIN (t-test)</th>
          <td>-0.652  (-12)</td>
          <td>-0.0197  (-0.234)</td>
          <td>-0.046  (-0.733)</td>
        </tr>
        <tr>
          <th>B_COST (t-test)</th>
          <td>-0.79  (-15.5)</td>
          <td></td>
          <td></td>
        </tr>
        <tr>
          <th>B_TIME (t-test)</th>
          <td>-1.28  (-19.5)</td>
          <td></td>
          <td>-1.27  (-16.9)</td>
        </tr>
        <tr>
          <th>B_COST_CAR (t-test)</th>
          <td></td>
          <td>-0.659  (-6.68)</td>
          <td>-0.383  (-5)</td>
        </tr>
        <tr>
          <th>B_COST_SM (t-test)</th>
          <td></td>
          <td>-0.787  (-14.8)</td>
          <td>-0.823  (-15.5)</td>
        </tr>
        <tr>
          <th>B_COST_TRAIN (t-test)</th>
          <td></td>
          <td>-1.85  (-14.2)</td>
          <td>-1.92  (-16.8)</td>
        </tr>
        <tr>
          <th>B_TIME_CAR (t-test)</th>
          <td></td>
          <td>-1.06  (-11.1)</td>
          <td></td>
        </tr>
        <tr>
          <th>B_TIME_SM (t-test)</th>
          <td></td>
          <td>-1.46  (-14.4)</td>
          <td></td>
        </tr>
        <tr>
          <th>B_TIME_TRAIN (t-test)</th>
          <td></td>
          <td>-1.4  (-15.8)</td>
          <td></td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 140-141

Glossary.

.. GENERATED FROM PYTHON SOURCE LINES 141-143

.. code-block:: Python

    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    B_COST_gen_altspec:generic;B_TIME_gen_altspec:generic
    Model_000001    B_COST_gen_altspec:altspec;B_TIME_gen_altspec:altspec
    Model_000002    B_COST_gen_altspec:altspec;B_TIME_gen_altspec:generic





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

   **Total running time of the script:** (0 minutes 1.286 seconds)


.. _sphx_glr_download_auto_examples_assisted_plot_b03alt_spec.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

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

      :download:`Download Jupyter notebook: plot_b03alt_spec.ipynb <plot_b03alt_spec.ipynb>`

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

      :download:`Download Python source code: plot_b03alt_spec.py <plot_b03alt_spec.py>`

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

      :download:`Download zipped: plot_b03alt_spec.zip <plot_b03alt_spec.zip>`


.. only:: html

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

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