.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b18ordinal_logit.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_b18ordinal_logit.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_swissmetro_plot_b18ordinal_logit.py:


Ordinal logit model
===================

Example of an ordinal logit model.  This is just to illustrate the
syntax, as the data are not ordered.  But the example assume, for the
sake of it, that the alternatives are ordered as 1->2->3

:author: Michel Bierlaire, EPFL
:date: Mon Apr 10 12:15:28 2023

.. GENERATED FROM PYTHON SOURCE LINES 14-20

.. code-block:: Python


    import biogeme.biogeme_logging as blog
    import biogeme.biogeme as bio
    from biogeme.models import ordered_logit
    from biogeme.expressions import Beta, log, Elem








.. GENERATED FROM PYTHON SOURCE LINES 21-22

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

.. GENERATED FROM PYTHON SOURCE LINES 22-32

.. code-block:: Python

    from swissmetro_data import (
        database,
        CHOICE,
        TRAIN_TT_SCALED,
        TRAIN_COST_SCALED,
    )

    logger = blog.get_screen_logger(level=blog.INFO)
    logger.info('Example b18ordinal_logit.py')





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

 .. code-block:: none

    Example b18ordinal_logit.py 




.. GENERATED FROM PYTHON SOURCE LINES 33-34

Parameters to be estimated

.. GENERATED FROM PYTHON SOURCE LINES 34-37

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 38-39

Threshold parameters for the ordered logit.

.. GENERATED FROM PYTHON SOURCE LINES 41-42

:math:`\tau_1 \leq 0`.

.. GENERATED FROM PYTHON SOURCE LINES 42-44

.. code-block:: Python

    tau1 = Beta('tau1', -1, None, 0, 0)








.. GENERATED FROM PYTHON SOURCE LINES 45-46

:math:`\delta_2 \geq 0`.

.. GENERATED FROM PYTHON SOURCE LINES 46-48

.. code-block:: Python

    delta2 = Beta('delta2', 2, 0, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 49-50

:math:`\tau_2 = \tau_1 + \delta_2`

.. GENERATED FROM PYTHON SOURCE LINES 50-52

.. code-block:: Python

    tau2 = tau1 + delta2








.. GENERATED FROM PYTHON SOURCE LINES 53-54

Utility.

.. GENERATED FROM PYTHON SOURCE LINES 54-56

.. code-block:: Python

    U = B_TIME * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED








.. GENERATED FROM PYTHON SOURCE LINES 57-62

Associate each discrete indicator with an interval.

  1. :math:`-\infty \to \tau_1`,
  2. :math:`\tau_1 \to \tau_2`,
  3. :math:`\tau_2 \to +\infty`.

.. GENERATED FROM PYTHON SOURCE LINES 62-68

.. code-block:: Python

    the_proba = ordered_logit(
        continuous_value=U,
        list_of_discrete_values=[1, 2, 3],
        tau_parameter=tau1,
    )








.. GENERATED FROM PYTHON SOURCE LINES 69-70

Extract from the dict the formula associated with the observed choice.

.. GENERATED FROM PYTHON SOURCE LINES 70-72

.. code-block:: Python

    the_chosen_proba = Elem(the_proba, CHOICE)








.. GENERATED FROM PYTHON SOURCE LINES 73-75

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

.. GENERATED FROM PYTHON SOURCE LINES 75-77

.. code-block:: Python

    logprob = log(the_chosen_proba)








.. GENERATED FROM PYTHON SOURCE LINES 78-79

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 79-82

.. code-block:: Python

    the_biogeme = bio.BIOGEME(database, logprob)
    the_biogeme.modelName = 'b18ordinal_logit'





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

 .. code-block:: none

    Biogeme parameters read from biogeme.toml. 




.. GENERATED FROM PYTHON SOURCE LINES 83-84

Estimate the parameters

.. GENERATED FROM PYTHON SOURCE LINES 84-86

.. 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 __b18ordinal_logit.iter 
    Cannot read file __b18ordinal_logit.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.          B_COST          B_TIME            tau1     tau1_diff_2     Function    Relgrad   Radius      Rho      
        0            0.71         -0.0041           -0.55             1.7      6.6e+03       0.27       10      1.3   ++ 
        1               1           -0.02           -0.82             2.6      5.9e+03       0.12    1e+02      1.2   ++ 
        2             1.2          -0.024           -0.99             3.1      5.8e+03      0.023    1e+03      1.1   ++ 
        3             1.3          -0.022              -1             3.2      5.8e+03    0.00097    1e+04        1   ++ 
        4             1.3          -0.022              -1             3.2      5.8e+03      2e-06    1e+04        1   ++ 
    Results saved in file b18ordinal_logit.html 
    Results saved in file b18ordinal_logit.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 87-89

.. code-block:: Python

    print(results.short_summary())





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

 .. code-block:: none

    Results for model b18ordinal_logit
    Nbr of parameters:              4
    Sample size:                    6768
    Excluded data:                  3960
    Final log likelihood:           -5789.309
    Akaike Information Criterion:   11586.62
    Bayesian Information Criterion: 11613.9





.. GENERATED FROM PYTHON SOURCE LINES 90-92

.. 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>B_COST</th>
          <td>1.262893</td>
          <td>0.058542</td>
          <td>21.572527</td>
          <td>0.0000</td>
        </tr>
        <tr>
          <th>B_TIME</th>
          <td>-0.022081</td>
          <td>0.040060</td>
          <td>-0.551195</td>
          <td>0.5815</td>
        </tr>
        <tr>
          <th>tau1</th>
          <td>-1.030098</td>
          <td>0.067967</td>
          <td>-15.155781</td>
          <td>0.0000</td>
        </tr>
        <tr>
          <th>tau1_diff_2</th>
          <td>3.233237</td>
          <td>0.044509</td>
          <td>72.642216</td>
          <td>0.0000</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** (0 minutes 0.095 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b18ordinal_logit.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_b18ordinal_logit.ipynb <plot_b18ordinal_logit.ipynb>`

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

      :download:`Download Python source code: plot_b18ordinal_logit.py <plot_b18ordinal_logit.py>`

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

      :download:`Download zipped: plot_b18ordinal_logit.zip <plot_b18ordinal_logit.zip>`


.. only:: html

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