.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b01logit_simul.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_simul.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_swissmetro_plot_b01logit_simul.py:


Simulation of a logit model
===========================

Example of simulation with a logit model


:author: Michel Bierlaire, EPFL
:date: Sun Apr  9 17:13:23 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, Derive








.. GENERATED FROM PYTHON SOURCE LINES 19-20

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

.. GENERATED FROM PYTHON SOURCE LINES 20-36

.. code-block:: default

    from swissmetro_data import (
        database,
        SM_AV,
        CAR_AV_SP,
        TRAIN_AV_SP,
        TRAIN_TT,
        TRAIN_TT_SCALED,
        TRAIN_COST_SCALED,
        SM_TT,
        SM_TT_SCALED,
        SM_COST_SCALED,
        CAR_TT,
        CAR_TT_SCALED,
        CAR_CO_SCALED,
    )








.. GENERATED FROM PYTHON SOURCE LINES 37-38

Parameters.

.. 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 45-46

Definition of the utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 46-50

.. 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 51-52

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 52-54

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 55-56

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 56-58

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 59-61

Choice probability.


.. GENERATED FROM PYTHON SOURCE LINES 61-65

.. code-block:: default

    prob1 = models.logit(V, av, 1)
    prob2 = models.logit(V, av, 2)
    prob3 = models.logit(V, av, 3)








.. GENERATED FROM PYTHON SOURCE LINES 66-71

Elasticities.

Elasticities can be computed. We illustrate below two
formulas. Check in the output file that they produce the same
result.

.. GENERATED FROM PYTHON SOURCE LINES 73-76

First, the general definition of elasticities. This illustrates the
use of the Derive expression, and can be used with any model,
however complicated it is. Note the quotes in the Derive opertor.

.. GENERATED FROM PYTHON SOURCE LINES 76-81

.. code-block:: default


    genelas1 = Derive(prob1, 'TRAIN_TT') * TRAIN_TT / prob1
    genelas2 = Derive(prob2, 'SM_TT') * SM_TT / prob2
    genelas3 = Derive(prob3, 'CAR_TT') * CAR_TT / prob3








.. GENERATED FROM PYTHON SOURCE LINES 82-84

Second, the elasticity of logit models. See Ben-Akiva and Lerman for
the formula

.. GENERATED FROM PYTHON SOURCE LINES 84-89

.. code-block:: default


    logitelas1 = TRAIN_AV_SP * (1.0 - prob1) * TRAIN_TT_SCALED * B_TIME
    logitelas2 = SM_AV * (1.0 - prob2) * SM_TT_SCALED * B_TIME
    logitelas3 = CAR_AV_SP * (1.0 - prob3) * CAR_TT_SCALED * B_TIME








.. GENERATED FROM PYTHON SOURCE LINES 90-92

Quantities to be simulated.


.. GENERATED FROM PYTHON SOURCE LINES 92-105

.. code-block:: default

    simulate = {
        'Prob. train': prob1,
        'Prob. Swissmetro': prob2,
        'Prob. car': prob3,
        'logit elas. 1': logitelas1,
        'generic elas. 1': genelas1,
        'logit elas. 2': logitelas2,
        'generic elas. 2': genelas2,
        'logit elas. 3': logitelas3,
        'generic elas. 3': genelas3,
    }









.. GENERATED FROM PYTHON SOURCE LINES 106-110

Create the Biogeme object.

As we simulate the probability for all aternatives, even when one of
them is not available, Biogeme may trigger some warnings.

.. GENERATED FROM PYTHON SOURCE LINES 110-113

.. code-block:: default

    biosim = bio.BIOGEME(database, simulate)
    biosim.modelName = 'b01logit_simul'








.. GENERATED FROM PYTHON SOURCE LINES 114-115

Values of the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 115-123

.. code-block:: default

    betas = {
        'ASC_TRAIN': -0.701188,
        'B_TIME': -1.27786,
        'B_COST': -1.08379,
        'ASC_CAR': -0.154633,
    }









.. GENERATED FROM PYTHON SOURCE LINES 124-126

Simulation


.. GENERATED FROM PYTHON SOURCE LINES 126-128

.. code-block:: default

    results = biosim.simulate(theBetaValues=betas)
    results.describe()





.. 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>Prob. train</th>
          <th>Prob. Swissmetro</th>
          <th>Prob. car</th>
          <th>logit elas. 1</th>
          <th>generic elas. 1</th>
          <th>logit elas. 2</th>
          <th>generic elas. 2</th>
          <th>logit elas. 3</th>
          <th>generic elas. 3</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>count</th>
          <td>6768.000000</td>
          <td>6768.000000</td>
          <td>6768.000000</td>
          <td>6768.000000</td>
          <td>6768.0</td>
          <td>6768.000000</td>
          <td>6768.0</td>
          <td>6768.000000</td>
          <td>6768.0</td>
        </tr>
        <tr>
          <th>mean</th>
          <td>0.134161</td>
          <td>0.604315</td>
          <td>0.261525</td>
          <td>-1.872612</td>
          <td>0.0</td>
          <td>-0.447850</td>
          <td>0.0</td>
          <td>-1.136701</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>std</th>
          <td>0.060525</td>
          <td>0.182309</td>
          <td>0.203746</td>
          <td>0.886439</td>
          <td>0.0</td>
          <td>0.498262</td>
          <td>0.0</td>
          <td>1.074337</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>min</th>
          <td>0.000010</td>
          <td>0.000281</td>
          <td>0.000000</td>
          <td>-13.059604</td>
          <td>0.0</td>
          <td>-10.168912</td>
          <td>0.0</td>
          <td>-19.934616</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>25%</th>
          <td>0.093416</td>
          <td>0.487012</td>
          <td>0.095533</td>
          <td>-2.377303</td>
          <td>0.0</td>
          <td>-0.553065</td>
          <td>0.0</td>
          <td>-1.624370</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>50%</th>
          <td>0.128314</td>
          <td>0.611886</td>
          <td>0.247461</td>
          <td>-1.769928</td>
          <td>0.0</td>
          <td>-0.334896</td>
          <td>0.0</td>
          <td>-0.949290</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>75%</th>
          <td>0.166545</td>
          <td>0.753873</td>
          <td>0.384113</td>
          <td>-1.196807</td>
          <td>0.0</td>
          <td>-0.203747</td>
          <td>0.0</td>
          <td>-0.462240</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>max</th>
          <td>0.642731</td>
          <td>0.971398</td>
          <td>0.999710</td>
          <td>-0.232835</td>
          <td>0.0</td>
          <td>-0.024123</td>
          <td>0.0</td>
          <td>0.000000</td>
          <td>0.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** (0 minutes 2.601 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b01logit_simul.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_simul.py <plot_b01logit_simul.py>`

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

      :download:`Download Jupyter notebook: plot_b01logit_simul.ipynb <plot_b01logit_simul.ipynb>`


.. only:: html

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

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