.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b08boxcox.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_b08boxcox.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_swissmetro_plot_b08boxcox.py:


Box-Cox transforms
==================

Example of a logit model, with a Box-Cox transform of variables.

:author: Michel Bierlaire, EPFL
:date: Sun Apr  9 17:58:15 2023

.. GENERATED FROM PYTHON SOURCE LINES 11-16

.. code-block:: default


    import biogeme.biogeme as bio
    from biogeme import models
    from biogeme.expressions import Beta








.. GENERATED FROM PYTHON SOURCE LINES 17-18

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

.. GENERATED FROM PYTHON SOURCE LINES 18-32

.. 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,
    )








.. GENERATED FROM PYTHON SOURCE LINES 33-34

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 34-41

.. 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)
    LAMBDA = Beta('LAMBDA', 0, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 42-43

Definition of the utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 43-51

.. code-block:: default

    V1 = (
        ASC_TRAIN
        + B_TIME * models.boxcox(TRAIN_TT_SCALED, LAMBDA)
        + B_COST * TRAIN_COST_SCALED
    )
    V2 = ASC_SM + B_TIME * models.boxcox(SM_TT_SCALED, LAMBDA) + B_COST * SM_COST_SCALED
    V3 = ASC_CAR + B_TIME * models.boxcox(CAR_TT_SCALED, LAMBDA) + B_COST * CAR_CO_SCALED








.. GENERATED FROM PYTHON SOURCE LINES 52-53

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 53-55

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 56-57

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 57-59

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 60-62

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

.. GENERATED FROM PYTHON SOURCE LINES 62-64

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 65-66

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 66-69

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, logprob)
    the_biogeme.modelName = 'b08boxcox'








.. GENERATED FROM PYTHON SOURCE LINES 70-71

Check the derivatives of the log liklelihood function around 0.

.. GENERATED FROM PYTHON SOURCE LINES 71-73

.. code-block:: default

    the_biogeme.checkDerivatives(beta=[0, 0, 0, 0, 0], verbose=True)





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

 .. code-block:: none


    (-6964.6629791922205, array([  -99.        , -1541.5       ,  -224.60833333, -1510.70259763,
               0.        ]), array([[-1246.        ,   623.        ,   113.97111111,  -216.89261174,
                0.        ],
           [  623.        , -1536.25      ,   154.53194444,  -754.54814588,
                0.        ],
           [  113.97111111,   154.53194444,  -633.136825  ,   164.98825122,
                0.        ],
           [ -216.89261174,  -754.54814588,   164.98825122,  -896.93691608,
             -290.96756803],
           [    0.        ,     0.        ,     0.        ,  -290.96756803,
                0.        ]]), array([-0.00035575, -0.00045858, -0.00030395, -0.00027485,  0.        ]), array([[-2.33821161e-05,  8.70677854e-06,  1.87785348e-05,
             1.28155432e-06,  0.00000000e+00],
           [-1.78165961e-04,  2.44009268e-05, -3.65803303e-05,
            -3.42056321e-05,  0.00000000e+00],
           [ 5.42033138e-06, -7.02175248e-06, -6.80464154e-07,
             1.17407737e-06,  0.00000000e+00],
           [ 3.55529107e-06,  8.99536622e-06,  6.05643180e-07,
            -5.55560746e-06,  2.10474028e-05],
           [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
             7.68242649e-06,  0.00000000e+00]]))



.. GENERATED FROM PYTHON SOURCE LINES 74-75

Estimate the parameters

.. GENERATED FROM PYTHON SOURCE LINES 75-77

.. code-block:: default

    results = the_biogeme.estimate()








.. GENERATED FROM PYTHON SOURCE LINES 78-80

.. code-block:: default

    print(results.short_summary())





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

 .. code-block:: none

    Results for model b08boxcox
    Nbr of parameters:              5
    Sample size:                    6768
    Excluded data:                  3960
    Final log likelihood:           -5292.095
    Akaike Information Criterion:   10594.19
    Bayesian Information Criterion: 10628.29





.. GENERATED FROM PYTHON SOURCE LINES 81-83

.. 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>-0.004624</td>
          <td>0.048008</td>
          <td>-0.096310</td>
          <td>9.232741e-01</td>
        </tr>
        <tr>
          <th>ASC_TRAIN</th>
          <td>-0.484974</td>
          <td>0.064398</td>
          <td>-7.530904</td>
          <td>5.040413e-14</td>
        </tr>
        <tr>
          <th>B_COST</th>
          <td>-1.078534</td>
          <td>0.068008</td>
          <td>-15.858881</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME</th>
          <td>-1.674909</td>
          <td>0.076558</td>
          <td>-21.877701</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>LAMBDA</th>
          <td>0.510059</td>
          <td>0.077305</td>
          <td>6.598023</td>
          <td>4.166778e-11</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** (0 minutes 0.482 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b08boxcox.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_b08boxcox.py <plot_b08boxcox.py>`

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

      :download:`Download Jupyter notebook: plot_b08boxcox.ipynb <plot_b08boxcox.ipynb>`


.. only:: html

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

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