.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b02weight.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_b02weight.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_swissmetro_plot_b02weight.py:


WESML
=====

 Example of a logit model with Weighted Exogenous Sample Maximum
 Likelihood (WESML).

:author: Michel Bierlaire, EPFL
:date: Sun Apr  9 17:02:59 2023

.. GENERATED FROM PYTHON SOURCE LINES 13-18

.. code-block:: default


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








.. GENERATED FROM PYTHON SOURCE LINES 19-20

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

.. GENERATED FROM PYTHON SOURCE LINES 20-35

.. 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,
        GROUP,
    )








.. GENERATED FROM PYTHON SOURCE LINES 36-38

Parameters to be estimated.


.. GENERATED FROM PYTHON SOURCE LINES 38-44

.. 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 45-47

Definition of the utility functions.


.. GENERATED FROM PYTHON SOURCE LINES 47-51

.. 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 52-54

Associate utility functions with the numbering of alternatives.


.. GENERATED FROM PYTHON SOURCE LINES 54-56

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 57-59

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 the model.


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

.. GENERATED FROM PYTHON SOURCE LINES 66-68

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 69-71

Definition of the weight.


.. GENERATED FROM PYTHON SOURCE LINES 71-73

.. code-block:: default

    weight = 8.890991e-01 * (1.0 * (GROUP == 2) + 1.2 * (GROUP == 3))








.. GENERATED FROM PYTHON SOURCE LINES 74-75

These notes will be included as such in the report file.

.. GENERATED FROM PYTHON SOURCE LINES 75-82

.. code-block:: default

    USER_NOTES = (
        'Example of a logit model with three alternatives: '
        'Train, Car and Swissmetro.'
        ' Weighted Exogenous Sample Maximum Likelihood estimator (WESML)'
    )









.. GENERATED FROM PYTHON SOURCE LINES 83-84

Create the Biogeme object

.. GENERATED FROM PYTHON SOURCE LINES 84-88

.. code-block:: default

    formulas = {'loglike': logprob, 'weight': weight}
    the_biogeme = bio.BIOGEME(database, formulas, userNotes=USER_NOTES)
    the_biogeme.modelName = 'b02weight'








.. GENERATED FROM PYTHON SOURCE LINES 89-92

It is possible to control the generation of the HTML and the pickle
files. Note that these parameters can also be modified in the .TOML
configuration file.

.. GENERATED FROM PYTHON SOURCE LINES 92-95

.. code-block:: default

    the_biogeme.generate_html = True
    the_biogeme.generate_pickle = False








.. GENERATED FROM PYTHON SOURCE LINES 96-97

Estimate the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 97-100

.. code-block:: default

    results = the_biogeme.estimate()
    print(results.short_summary())





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

 .. code-block:: none

    Results for model b02weight
    Nbr of parameters:              4
    Sample size:                    6768
    Excluded data:                  3960
    Final log likelihood:           -5273.743
    Akaike Information Criterion:   10555.49
    Bayesian Information Criterion: 10582.77





.. GENERATED FROM PYTHON SOURCE LINES 101-102

Get the results in a pandas table

.. GENERATED FROM PYTHON SOURCE LINES 102-104

.. 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>-0.114315</td>
          <td>0.058312</td>
          <td>-1.960402</td>
          <td>0.049949</td>
        </tr>
        <tr>
          <th>ASC_TRAIN</th>
          <td>-0.756521</td>
          <td>0.083257</td>
          <td>-9.086524</td>
          <td>0.000000</td>
        </tr>
        <tr>
          <th>B_COST</th>
          <td>-1.119658</td>
          <td>0.067679</td>
          <td>-16.543708</td>
          <td>0.000000</td>
        </tr>
        <tr>
          <th>B_TIME</th>
          <td>-1.321529</td>
          <td>0.103658</td>
          <td>-12.748875</td>
          <td>0.000000</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** (0 minutes 0.214 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b02weight.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_b02weight.py <plot_b02weight.py>`

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

      :download:`Download Jupyter notebook: plot_b02weight.ipynb <plot_b02weight.ipynb>`


.. only:: html

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

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