.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b09nested.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_b09nested.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_swissmetro_plot_b09nested.py:


Nested logit model
==================

Example of a nested logit model.

:author: Michel Bierlaire, EPFL
:date: Tue Oct 24 13:37:32 2023

.. GENERATED FROM PYTHON SOURCE LINES 12-19

.. code-block:: default


    from biogeme import biogeme_logging as blog
    import biogeme.biogeme as bio
    from biogeme import models
    from biogeme.expressions import Beta
    from biogeme.nests import OneNestForNestedLogit, NestsForNestedLogit








.. GENERATED FROM PYTHON SOURCE LINES 20-21

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

.. GENERATED FROM PYTHON SOURCE LINES 21-38

.. 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,
    )

    logger = blog.get_screen_logger(level=blog.INFO)
    logger.info('Example b09nested')





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

 .. code-block:: none

    Example b09nested 




.. GENERATED FROM PYTHON SOURCE LINES 39-40

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 40-47

.. 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)
    MU = Beta('MU', 1, 1, 10, 0)








.. GENERATED FROM PYTHON SOURCE LINES 48-49

Definition of the utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 49-53

.. 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 54-55

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 55-57

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 58-59

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 59-61

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 62-66

Definition of nests. Only the non trivial nests must be defined. A
trivial nest is a nest containing exactly one alternative.  In this
example, we create a nest for the existing modes, that is train (1)
and car (3).

.. GENERATED FROM PYTHON SOURCE LINES 66-73

.. code-block:: default


    existing = OneNestForNestedLogit(
        nest_param=MU, list_of_alternatives=[1, 3], name='existing'
    )

    nests = NestsForNestedLogit(choice_set=list(V), tuple_of_nests=(existing,))








.. GENERATED FROM PYTHON SOURCE LINES 74-77

Definition of the model. This is the contribution of each
observation to the log likelihood function.
The choice model is a nested logit, with availability conditions.

.. GENERATED FROM PYTHON SOURCE LINES 77-79

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 80-81

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 81-84

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, logprob)
    the_biogeme.modelName = "b09nested"





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

 .. code-block:: none

    File biogeme.toml has been parsed. 




.. GENERATED FROM PYTHON SOURCE LINES 85-86

Calculate the null log likelihood for reporting.

.. GENERATED FROM PYTHON SOURCE LINES 86-88

.. code-block:: default

    the_biogeme.calculateNullLoglikelihood(av)





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

 .. code-block:: none


    -6964.662979191462



.. GENERATED FROM PYTHON SOURCE LINES 89-90

Estimate the parameters

.. GENERATED FROM PYTHON SOURCE LINES 90-92

.. code-block:: default

    results = the_biogeme.estimate()





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

 .. code-block:: none

    *** Initial values of the parameters are obtained from the file __b09nested.iter 
    Cannot read file __b09nested.iter. Statement is ignored. 
    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              MU     Function    Relgrad   Radius      Rho      
        0             0.1           -0.75              -1            -0.8             1.5      5.4e+03      0.082       10     0.92   ++ 
        1           -0.22           -0.28           -0.82           -0.86             2.2      5.3e+03      0.076       10     0.44    + 
        2           -0.17           -0.52            -0.7            -0.7             2.7      5.3e+03      0.023       10     0.72    + 
        3           -0.17           -0.52            -0.7            -0.7             2.7      5.3e+03      0.023     0.84     -4.6    - 
        4           -0.14           -0.52           -0.87           -0.92             1.8      5.2e+03      0.006     0.84     0.63    + 
        5           -0.16           -0.51           -0.87           -0.91               2      5.2e+03     0.0014      8.4      1.1   ++ 
        6           -0.17           -0.51           -0.86            -0.9             2.1      5.2e+03    8.1e-05       84        1   ++ 
        7           -0.17           -0.51           -0.86            -0.9             2.1      5.2e+03    2.8e-07       84        1   ++ 
    Results saved in file b09nested.html 
    Results saved in file b09nested.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 93-95

.. code-block:: default

    print(results.short_summary())





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

 .. code-block:: none

    Results for model b09nested
    Nbr of parameters:              5
    Sample size:                    6768
    Excluded data:                  3960
    Null log likelihood:            -6964.663
    Final log likelihood:           -5236.9
    Likelihood ratio test (null):           3455.526
    Rho square (null):                      0.248
    Rho bar square (null):                  0.247
    Akaike Information Criterion:   10483.8
    Bayesian Information Criterion: 10517.9





.. GENERATED FROM PYTHON SOURCE LINES 96-99

.. 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>-0.167155</td>
          <td>0.054529</td>
          <td>-3.065428</td>
          <td>2.173586e-03</td>
        </tr>
        <tr>
          <th>ASC_TRAIN</th>
          <td>-0.511948</td>
          <td>0.079114</td>
          <td>-6.471047</td>
          <td>9.732637e-11</td>
        </tr>
        <tr>
          <th>B_COST</th>
          <td>-0.856667</td>
          <td>0.060035</td>
          <td>-14.269453</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME</th>
          <td>-0.898666</td>
          <td>0.107112</td>
          <td>-8.389947</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>MU</th>
          <td>2.054056</td>
          <td>0.164201</td>
          <td>12.509383</td>
          <td>0.000000e+00</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 100-102

We calculate the correlation between the error terms of the
alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 102-107

.. code-block:: default

    corr = nests.correlation(
        parameters=results.getBetaValues(),
        alternatives_names={1: 'Train', 2: 'Swissmetro', 3: 'Car'},
    )
    print(corr)




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

 .. code-block:: none

                Train  Swissmetro  Car
    Train         1.0         0.0  0.0
    Swissmetro    0.0         1.0  0.0
    Car           0.0         0.0  1.0





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

   **Total running time of the script:** (0 minutes 0.411 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b09nested.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_b09nested.py <plot_b09nested.py>`

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

      :download:`Download Jupyter notebook: plot_b09nested.ipynb <plot_b09nested.ipynb>`


.. only:: html

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

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