.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b11cnl.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_b11cnl.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_swissmetro_plot_b11cnl.py:


Cross-nested logit
==================

 Example of a cross-nested logit model with two nests:

 - one with existing alternatives (car and train),
 - one with public transportation alternatives (train and Swissmetro)

:author: Michel Bierlaire, EPFL
:date: Sun Apr  9 18:06:44 2023

.. GENERATED FROM PYTHON SOURCE LINES 15-22

.. code-block:: Python


    import biogeme.biogeme_logging as blog
    import biogeme.biogeme as bio
    from biogeme import models
    from biogeme.expressions import Beta
    from biogeme.nests import OneNestForCrossNestedLogit, NestsForCrossNestedLogit








.. 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,
        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)
    logger.info('Example b11cnl.py')





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

 .. code-block:: none

    Example b11cnl.py 




.. GENERATED FROM PYTHON SOURCE LINES 42-43

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 43-49

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








.. GENERATED FROM PYTHON SOURCE LINES 50-53

.. code-block:: Python

    MU_EXISTING = Beta('MU_EXISTING', 1, 1, 5, 0)
    MU_PUBLIC = Beta('MU_PUBLIC', 1, 1, 5, 0)








.. GENERATED FROM PYTHON SOURCE LINES 54-55

Nest membership parameters.

.. GENERATED FROM PYTHON SOURCE LINES 55-58

.. code-block:: Python

    ALPHA_EXISTING = Beta('ALPHA_EXISTING', 0.5, 0, 1, 0)
    ALPHA_PUBLIC = 1 - ALPHA_EXISTING








.. GENERATED FROM PYTHON SOURCE LINES 59-60

Definition of the utility functions

.. GENERATED FROM PYTHON SOURCE LINES 60-64

.. code-block:: Python

    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 65-66

Associate utility functions with the numbering of alternatives

.. GENERATED FROM PYTHON SOURCE LINES 66-68

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 69-70

Associate the availability conditions with the alternatives

.. GENERATED FROM PYTHON SOURCE LINES 70-72

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 73-74

Definition of nests.

.. GENERATED FROM PYTHON SOURCE LINES 74-89

.. code-block:: Python


    nest_existing = OneNestForCrossNestedLogit(
        nest_param=MU_EXISTING,
        dict_of_alpha={1: ALPHA_EXISTING, 2: 0.0, 3: 1.0},
        name='existing',
    )

    nest_public = OneNestForCrossNestedLogit(
        nest_param=MU_PUBLIC, dict_of_alpha={1: ALPHA_PUBLIC, 2: 1.0, 3: 0.0}, name='public'
    )

    nests = NestsForCrossNestedLogit(
        choice_set=[1, 2, 3], tuple_of_nests=(nest_existing, nest_public)
    )








.. GENERATED FROM PYTHON SOURCE LINES 90-91

The choice model is a cross-nested logit, with availability conditions.

.. GENERATED FROM PYTHON SOURCE LINES 91-93

.. code-block:: Python

    logprob = models.logcnl(V, av, nests, CHOICE)








.. GENERATED FROM PYTHON SOURCE LINES 94-95

Create the Biogeme object

.. GENERATED FROM PYTHON SOURCE LINES 95-98

.. code-block:: Python

    the_biogeme = bio.BIOGEME(database, logprob)
    the_biogeme.modelName = 'b11cnl'





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

 .. code-block:: none

    Biogeme parameters read from biogeme.toml. 




.. GENERATED FROM PYTHON SOURCE LINES 99-100

Estimate the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 100-102

.. code-block:: Python

    results = the_biogeme.estimate()





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

 .. code-block:: none

    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 __b11cnl.iter 
    Cannot read file __b11cnl.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.  ALPHA_EXISTING         ASC_CAR       ASC_TRAIN          B_COST          B_TIME     MU_EXISTING       MU_PUBLIC     Function    Relgrad   Radius      Rho      
        0            0.57          -0.088           -0.83           -0.27              -1             1.5             1.5      5.6e+03      0.081        1     0.61    + 
        1            0.86           -0.29           -0.32            -1.3           -0.93             1.8             1.7      5.3e+03      0.049        1     0.63    + 
        2            0.86           -0.29           -0.32            -1.3           -0.93             1.8             1.7      5.3e+03      0.049      0.5    0.013    - 
        3            0.79           -0.12           -0.34           -0.77            -0.9               2             1.8      5.2e+03      0.012      0.5     0.79    + 
        4            0.56           -0.25            -0.1           -0.88            -0.8             2.5             2.2      5.2e+03      0.013      0.5     0.69    + 
        5            0.55           -0.25          -0.057           -0.86            -0.8             2.5             2.6      5.2e+03     0.0039        5      1.3   ++ 
        6            0.51           -0.25           0.049           -0.84           -0.79             2.5             3.3      5.2e+03     0.0054       50      1.2   ++ 
        7             0.5           -0.24           0.077           -0.83           -0.78             2.5             3.7      5.2e+03     0.0017    5e+02      1.2   ++ 
        8             0.5           -0.24           0.095           -0.82           -0.78             2.5               4      5.2e+03    0.00053    5e+03      1.1   ++ 
        9             0.5           -0.24           0.095           -0.82           -0.78             2.5               4      5.2e+03    3.3e-05    5e+03        1   ++ 
    Results saved in file b11cnl.html 
    Results saved in file b11cnl.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 103-105

.. code-block:: Python

    print(results.short_summary())





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

 .. code-block:: none

    Results for model b11cnl
    Nbr of parameters:              7
    Sample size:                    6768
    Excluded data:                  3960
    Final log likelihood:           -5214.049
    Akaike Information Criterion:   10442.1
    Bayesian Information Criterion: 10489.84





.. GENERATED FROM PYTHON SOURCE LINES 106-108

.. 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>ALPHA_EXISTING</th>
          <td>0.495086</td>
          <td>0.034723</td>
          <td>14.258046</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>ASC_CAR</th>
          <td>-0.240519</td>
          <td>0.053433</td>
          <td>-4.501346</td>
          <td>6.752446e-06</td>
        </tr>
        <tr>
          <th>ASC_TRAIN</th>
          <td>0.098094</td>
          <td>0.069916</td>
          <td>1.403026</td>
          <td>1.606089e-01</td>
        </tr>
        <tr>
          <th>B_COST</th>
          <td>-0.818963</td>
          <td>0.058942</td>
          <td>-13.894456</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME</th>
          <td>-0.776852</td>
          <td>0.102331</td>
          <td>-7.591581</td>
          <td>3.153033e-14</td>
        </tr>
        <tr>
          <th>MU_EXISTING</th>
          <td>2.514925</td>
          <td>0.248163</td>
          <td>10.134152</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>MU_PUBLIC</th>
          <td>4.108825</td>
          <td>0.494954</td>
          <td>8.301433</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 1.955 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b11cnl.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_b11cnl.ipynb <plot_b11cnl.ipynb>`

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

      :download:`Download Python source code: plot_b11cnl.py <plot_b11cnl.py>`

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

      :download:`Download zipped: plot_b11cnl.zip <plot_b11cnl.zip>`


.. only:: html

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

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