.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/indicators/plot_b07cross_elasticities.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_indicators_plot_b07cross_elasticities.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_indicators_plot_b07cross_elasticities.py:


Cross point elasticities
========================

We use a previously estimated nested logit model and calculate
disaggregate and aggregate cross point elasticities.

Details about this example are available in Section 3 of `Bierlaire (2018)
Calculating indicators with PandasBiogeme
<http://transp-or.epfl.ch/documents/technicalReports/Bier18a.pdf>`_

:author: Michel Bierlaire, EPFL
:date: Wed Apr 12 21:00:58 2023

.. GENERATED FROM PYTHON SOURCE LINES 17-35

.. code-block:: default


    import sys
    import biogeme.biogeme as bio
    from biogeme import models
    import biogeme.exceptions as excep
    import biogeme.results as res
    from biogeme.expressions import Derive
    from optima_data import database, normalized_weight

    from scenarios import (
        scenario,
        TimePT,
        TimeCar,
        MarginalCostPT,
        CostCarCHF,
    )









.. GENERATED FROM PYTHON SOURCE LINES 36-38

Obtain the specification for the default scenario
The definition of the scenarios is available in :ref:`scenarios`.

.. GENERATED FROM PYTHON SOURCE LINES 38-40

.. code-block:: default

    V, nests, _, _ = scenario()








.. GENERATED FROM PYTHON SOURCE LINES 41-42

Obtain the expression for the choice probability of each alternative.

.. GENERATED FROM PYTHON SOURCE LINES 42-46

.. code-block:: default

    prob_PT = models.nested(V, None, nests, 0)
    prob_CAR = models.nested(V, None, nests, 1)
    prob_SM = models.nested(V, None, nests, 2)








.. GENERATED FROM PYTHON SOURCE LINES 47-48

The choice model is a nested logit.

.. GENERATED FROM PYTHON SOURCE LINES 48-52

.. code-block:: default

    prob_PT = models.nested(V, None, nests, 0)
    prob_CAR = models.nested(V, None, nests, 1)
    prob_SM = models.nested(V, None, nests, 2)








.. GENERATED FROM PYTHON SOURCE LINES 53-55

Calculation of the cross elasticities.
We use the 'Derive' operator to calculate the derivatives.

.. GENERATED FROM PYTHON SOURCE LINES 55-60

.. code-block:: default

    cross_elas_pt_time = Derive(prob_PT, 'TimeCar') * TimeCar / prob_PT
    cross_elas_pt_cost = Derive(prob_PT, 'CostCarCHF') * CostCarCHF / prob_PT
    cross_elas_car_time = Derive(prob_CAR, 'TimePT') * TimePT / prob_CAR
    cross_elas_car_cost = Derive(prob_CAR, 'MarginalCostPT') * MarginalCostPT / prob_CAR








.. GENERATED FROM PYTHON SOURCE LINES 61-62

Formulas to simulate.

.. GENERATED FROM PYTHON SOURCE LINES 62-73

.. code-block:: default

    simulate = {
        'weight': normalized_weight,
        'Prob. car': prob_CAR,
        'Prob. public transportation': prob_PT,
        'Prob. slow modes': prob_SM,
        'cross_elas_pt_time': cross_elas_pt_time,
        'cross_elas_pt_cost': cross_elas_pt_cost,
        'cross_elas_car_time': cross_elas_car_time,
        'cross_elas_car_cost': cross_elas_car_cost,
    }








.. GENERATED FROM PYTHON SOURCE LINES 74-75

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 75-77

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, simulate)








.. GENERATED FROM PYTHON SOURCE LINES 78-79

Read the estimation results from the file

.. GENERATED FROM PYTHON SOURCE LINES 79-87

.. code-block:: default

    try:
        results = res.bioResults(pickleFile='saved_results/b02estimation.pickle')
    except excep.BiogemeError:
        sys.exit(
            'Run first the script b02estimation.py in order to generate '
            'the file b02estimation.pickle.'
        )








.. GENERATED FROM PYTHON SOURCE LINES 88-90

`simulated_values` is a Panda dataframe with the same number of rows as
the database, and as many columns as formulas to simulate.

.. GENERATED FROM PYTHON SOURCE LINES 90-93

.. code-block:: default

    simulated_values = the_biogeme.simulate(results.getBetaValues())
    simulated_values






.. 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>weight</th>
          <th>Prob. car</th>
          <th>Prob. public transportation</th>
          <th>Prob. slow modes</th>
          <th>cross_elas_pt_time</th>
          <th>cross_elas_pt_cost</th>
          <th>cross_elas_car_time</th>
          <th>cross_elas_car_cost</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.886023</td>
          <td>0.521791</td>
          <td>0.476807</td>
          <td>0.001402</td>
          <td>0.048202</td>
          <td>0.169661</td>
          <td>0.116998</td>
          <td>0.000000</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.861136</td>
          <td>0.563268</td>
          <td>0.238681</td>
          <td>0.198051</td>
          <td>0.009756</td>
          <td>0.025818</td>
          <td>0.056500</td>
          <td>0.051282</td>
        </tr>
        <tr>
          <th>3</th>
          <td>0.861136</td>
          <td>0.875824</td>
          <td>0.119136</td>
          <td>0.005040</td>
          <td>0.058152</td>
          <td>0.212013</td>
          <td>0.036800</td>
          <td>0.204779</td>
        </tr>
        <tr>
          <th>4</th>
          <td>0.957386</td>
          <td>0.814110</td>
          <td>0.051136</td>
          <td>0.134754</td>
          <td>0.091014</td>
          <td>0.096788</td>
          <td>0.077585</td>
          <td>0.039553</td>
        </tr>
        <tr>
          <th>5</th>
          <td>0.861136</td>
          <td>0.732059</td>
          <td>0.257192</td>
          <td>0.010749</td>
          <td>0.042266</td>
          <td>0.142084</td>
          <td>0.086126</td>
          <td>0.176831</td>
        </tr>
        <tr>
          <th>...</th>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
        </tr>
        <tr>
          <th>2259</th>
          <td>2.036009</td>
          <td>0.714085</td>
          <td>0.285872</td>
          <td>0.000043</td>
          <td>0.082457</td>
          <td>0.287419</td>
          <td>0.122138</td>
          <td>0.212928</td>
        </tr>
        <tr>
          <th>2261</th>
          <td>0.861136</td>
          <td>0.849040</td>
          <td>0.149688</td>
          <td>0.001272</td>
          <td>0.291538</td>
          <td>0.277282</td>
          <td>0.166150</td>
          <td>0.154376</td>
        </tr>
        <tr>
          <th>2262</th>
          <td>0.861136</td>
          <td>0.689083</td>
          <td>0.205901</td>
          <td>0.105016</td>
          <td>0.066032</td>
          <td>0.066625</td>
          <td>0.116739</td>
          <td>0.088479</td>
        </tr>
        <tr>
          <th>2263</th>
          <td>0.957386</td>
          <td>0.744274</td>
          <td>0.219850</td>
          <td>0.035876</td>
          <td>0.051566</td>
          <td>0.135393</td>
          <td>0.074890</td>
          <td>0.179498</td>
        </tr>
        <tr>
          <th>2264</th>
          <td>0.957386</td>
          <td>0.765468</td>
          <td>0.209149</td>
          <td>0.025383</td>
          <td>0.061873</td>
          <td>0.175431</td>
          <td>0.084528</td>
          <td>0.188736</td>
        </tr>
      </tbody>
    </table>
    <p>1906 rows × 8 columns</p>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 94-95

We calculate the aggregate elasticities.

.. GENERATED FROM PYTHON SOURCE LINES 97-98

First, the weighted probabilities.

.. GENERATED FROM PYTHON SOURCE LINES 98-105

.. code-block:: default

    simulated_values['Weighted prob. car'] = (
        simulated_values['weight'] * simulated_values['Prob. car']
    )
    simulated_values['Weighted prob. PT'] = (
        simulated_values['weight'] * simulated_values['Prob. public transportation']
    )








.. GENERATED FROM PYTHON SOURCE LINES 106-107

Then the denominators of the aggregate elasticity expressions.

.. GENERATED FROM PYTHON SOURCE LINES 107-110

.. code-block:: default

    denominator_car = simulated_values['Weighted prob. car'].sum()
    denominator_pt = simulated_values['Weighted prob. PT'].sum()








.. GENERATED FROM PYTHON SOURCE LINES 111-112

And finally the aggregate elasticities themselves.

.. GENERATED FROM PYTHON SOURCE LINES 114-115

Elasticity of car with respect to public transportation travel time.

.. GENERATED FROM PYTHON SOURCE LINES 115-124

.. code-block:: default

    cross_elas_term_car_time = (
        simulated_values['Weighted prob. car']
        * simulated_values['cross_elas_car_time']
        / denominator_car
    ).sum()
    print(
        f'Aggregate cross elasticity of car wrt PT time: ' f'{cross_elas_term_car_time:.3g}'
    )





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

 .. code-block:: none

    Aggregate cross elasticity of car wrt PT time: 0.107




.. GENERATED FROM PYTHON SOURCE LINES 125-126

Elasticity of car with respect to public transportation travel cost.

.. GENERATED FROM PYTHON SOURCE LINES 126-135

.. code-block:: default

    cross_elas_term_car_cost = (
        simulated_values['Weighted prob. car']
        * simulated_values['cross_elas_car_cost']
        / denominator_car
    ).sum()
    print(
        f'Aggregate cross elasticity of car wrt PT cost: ' f'{cross_elas_term_car_cost:.3g}'
    )





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

 .. code-block:: none

    Aggregate cross elasticity of car wrt PT cost: 0.123




.. GENERATED FROM PYTHON SOURCE LINES 136-137

Elasticity of public transportatiom with respect to car travel time.

.. GENERATED FROM PYTHON SOURCE LINES 137-146

.. code-block:: default

    cross_elas_term_pt_time = (
        simulated_values['Weighted prob. PT']
        * simulated_values['cross_elas_pt_time']
        / denominator_pt
    ).sum()
    print(
        f'Aggregate cross elasticity of PT wrt car time: ' f'{cross_elas_term_pt_time:.3g}'
    )





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

 .. code-block:: none

    Aggregate cross elasticity of PT wrt car time: 0.0953




.. GENERATED FROM PYTHON SOURCE LINES 147-148

Elasticity of public transportatiom with respect to car travel cost.

.. GENERATED FROM PYTHON SOURCE LINES 148-157

.. code-block:: default

    cross_elas_term_pt_cost = (
        simulated_values['Weighted prob. PT']
        * simulated_values['cross_elas_pt_cost']
        / denominator_pt
    ).sum()
    print(
        f'Aggregate cross direct elasticity of PT wrt car cost: '
        f'{cross_elas_term_pt_cost:.3g}'
    )




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

 .. code-block:: none

    Aggregate cross direct elasticity of PT wrt car cost: 0.2





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

   **Total running time of the script:** (0 minutes 1.187 seconds)


.. _sphx_glr_download_auto_examples_indicators_plot_b07cross_elasticities.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_b07cross_elasticities.py <plot_b07cross_elasticities.py>`

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

      :download:`Download Jupyter notebook: plot_b07cross_elasticities.ipynb <plot_b07cross_elasticities.ipynb>`


.. only:: html

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

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