.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b01logit.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_b01logit.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_swissmetro_plot_b01logit.py:


Estimation of a logit model
===========================

 Three alternatives:

   - train,
   - car and,
   - Swissmetro.

 Stated preferences data.

:author: Michel Bierlaire, EPFL
:date: Sun Apr  9 17:02:18 2023

.. GENERATED FROM PYTHON SOURCE LINES 18-22

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 23-24

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

.. GENERATED FROM PYTHON SOURCE LINES 24-38

.. 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,
    )








.. 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)









.. 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 62-64

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

.. GENERATED FROM PYTHON SOURCE LINES 64-66

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 67-68

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 68-71

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, logprob)
    the_biogeme.modelName = 'b01logit'








.. GENERATED FROM PYTHON SOURCE LINES 72-73

Calculate the null log likelihood for reporting.

.. GENERATED FROM PYTHON SOURCE LINES 73-75

.. code-block:: default

    the_biogeme.calculateNullLoglikelihood(av)





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

 .. code-block:: none


    -6964.662979191462



.. GENERATED FROM PYTHON SOURCE LINES 76-77

Estimate the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 77-79

.. code-block:: default

    results = the_biogeme.estimate()








.. GENERATED FROM PYTHON SOURCE LINES 80-82

.. code-block:: default

    print(results.short_summary())





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

 .. code-block:: none

    Results for model b01logit
    Nbr of parameters:              4
    Sample size:                    6768
    Excluded data:                  3960
    Null log likelihood:            -6964.663
    Final log likelihood:           -5331.252
    Likelihood ratio test (null):           3266.822
    Rho square (null):                      0.235
    Rho bar square (null):                  0.234
    Akaike Information Criterion:   10670.5
    Bayesian Information Criterion: 10697.78





.. GENERATED FROM PYTHON SOURCE LINES 83-84

Get the results in a pandas table

.. GENERATED FROM PYTHON SOURCE LINES 84-86

.. code-block:: default

    pandas_results = results.getEstimatedParameters()
    print(pandas_results)




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

 .. code-block:: none

                  Value  Rob. Std err  Rob. t-test  Rob. p-value
    ASC_CAR   -0.154633      0.058163    -2.658590      0.007847
    ASC_TRAIN -0.701187      0.082562    -8.492857      0.000000
    B_COST    -1.083790      0.068225   -15.885521      0.000000
    B_TIME    -1.277859      0.104254   -12.257120      0.000000





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

   **Total running time of the script:** (0 minutes 0.660 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b01logit.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_b01logit.py <plot_b01logit.py>`

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

      :download:`Download Jupyter notebook: plot_b01logit.ipynb <plot_b01logit.ipynb>`


.. only:: html

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

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