.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b10nested_bottom.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_b10nested_bottom.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_swissmetro_plot_b10nested_bottom.py:


Nested logit model normalized from bottom
=========================================

Example of a nested logit model where the normalization is done at the
 bottom level.

:author: Michel Bierlaire, EPFL
:date: Tue Oct 24 13:40:46 2023

.. GENERATED FROM PYTHON SOURCE LINES 13-20

.. code-block:: default


    import biogeme.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 21-22

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

.. GENERATED FROM PYTHON SOURCE LINES 22-39

.. 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 b10nested_bottom.py')





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

 .. code-block:: none

    Example b10nested_bottom.py 




.. GENERATED FROM PYTHON SOURCE LINES 40-41

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 41-47

.. 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)








.. GENERATED FROM PYTHON SOURCE LINES 48-54

This is the scale parameter of the choice model. It is usually
normalized to one. In this example, we normalize the nest parameter
instead, and estimate the scale parameter for the model.  If the
lower bound is set to zero, the model cannot be evaluated.
Therefore, we set the lower bound to a small number, strictly larger
than zero.

.. GENERATED FROM PYTHON SOURCE LINES 54-56

.. code-block:: default

    MU = Beta('MU', 0.5, 0.000001, 1.0, 0)








.. GENERATED FROM PYTHON SOURCE LINES 57-58

Definition of the utility functions

.. GENERATED FROM PYTHON SOURCE LINES 58-62

.. 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 63-64

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 64-66

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 67-68

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 68-70

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 71-73

Definition of nests. Only the non trival nests must be defined. A
trivial nest is a nest containing exactly one alternative.

.. GENERATED FROM PYTHON SOURCE LINES 73-80

.. code-block:: default


    existing = OneNestForNestedLogit(
        nest_param=1.0, list_of_alternatives=[1, 3], name='existing'
    )

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








.. GENERATED FROM PYTHON SOURCE LINES 81-85

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,
where the scale parameter mu is explicitly involved.

.. GENERATED FROM PYTHON SOURCE LINES 85-87

.. code-block:: default

    logprob = models.lognestedMevMu(V, av, nests, CHOICE, MU)








.. GENERATED FROM PYTHON SOURCE LINES 88-89

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 89-92

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, logprob)
    the_biogeme.modelName = 'b10nested_bottom'





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

 .. code-block:: none

    File biogeme.toml has been parsed. 




.. GENERATED FROM PYTHON SOURCE LINES 93-94

Estimate the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 94-96

.. 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 __b10nested_bottom.iter 
    Cannot read file __b10nested_bottom.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             0.4           -0.85           -0.96           -0.86               1      5.7e+03       0.13        1     0.74    + 
        1          -0.069           -0.81              -1            -1.2               1      5.3e+03      0.019       10        1   ++ 
        2          -0.069           -0.81              -1            -1.2               1      5.3e+03      0.019      0.5     -2.3    - 
        3           -0.19           -0.93            -1.2            -1.5             0.5      5.3e+03      0.017      0.5     0.74    + 
        4            -0.3           -0.99            -1.6            -1.8            0.54      5.2e+03    0.00089        5     0.97   ++ 
        5           -0.35            -1.1            -1.8            -1.9            0.48      5.2e+03    0.00059        5     0.87    + 
        6           -0.34            -1.1            -1.8            -1.8            0.49      5.2e+03    5.7e-05       50        1   ++ 
        7           -0.34            -1.1            -1.8            -1.8            0.49      5.2e+03    9.3e-08       50        1   ++ 
    Results saved in file b10nested_bottom.html 
    Results saved in file b10nested_bottom.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 97-99

.. code-block:: default

    print(results.short_summary())





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

 .. code-block:: none

    Results for model b10nested_bottom
    Nbr of parameters:              5
    Sample size:                    6768
    Excluded data:                  3960
    Final log likelihood:           -5236.9
    Akaike Information Criterion:   10483.8
    Bayesian Information Criterion: 10517.9





.. GENERATED FROM PYTHON SOURCE LINES 100-102

.. 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>-0.343348</td>
          <td>0.118827</td>
          <td>-2.889482</td>
          <td>3.858768e-03</td>
        </tr>
        <tr>
          <th>ASC_TRAIN</th>
          <td>-1.051575</td>
          <td>0.164976</td>
          <td>-6.374109</td>
          <td>1.840299e-10</td>
        </tr>
        <tr>
          <th>B_COST</th>
          <td>-1.759647</td>
          <td>0.149310</td>
          <td>-11.785219</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME</th>
          <td>-1.845915</td>
          <td>0.225653</td>
          <td>-8.180332</td>
          <td>2.220446e-16</td>
        </tr>
        <tr>
          <th>MU</th>
          <td>0.486839</td>
          <td>0.038918</td>
          <td>12.509269</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 0.487 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b10nested_bottom.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_b10nested_bottom.py <plot_b10nested_bottom.py>`

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

      :download:`Download Jupyter notebook: plot_b10nested_bottom.ipynb <plot_b10nested_bottom.ipynb>`


.. only:: html

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

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