.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/indicators/plot_b08arc_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_b08arc_elasticities.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_indicators_plot_b08arc_elasticities.py:


Arc elasticities
================

We use a previously estimated nested logit model and calculate arc 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 21:00:10 2023

.. GENERATED FROM PYTHON SOURCE LINES 16-25

.. code-block:: default


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








.. GENERATED FROM PYTHON SOURCE LINES 26-28

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

.. GENERATED FROM PYTHON SOURCE LINES 28-30

.. code-block:: default

    V, nests, _, MarginalCostPT = scenario()








.. GENERATED FROM PYTHON SOURCE LINES 31-32

Obtain the expression for the choice probability of the public transportation.

.. GENERATED FROM PYTHON SOURCE LINES 32-34

.. code-block:: default

    prob_PT = models.nested(V, None, nests, 0)








.. GENERATED FROM PYTHON SOURCE LINES 35-37

We investigate a scenario where the price for public transportation
increases by 20%. We extract the corresponding scenario.

.. GENERATED FROM PYTHON SOURCE LINES 37-40

.. code-block:: default

    V_after, _, _, MarginalCostPT_after = scenario(factor=1.2)
    prob_PT_after = models.nested(V_after, None, nests, 0)








.. GENERATED FROM PYTHON SOURCE LINES 41-42

Disaggregate elasticities

.. GENERATED FROM PYTHON SOURCE LINES 42-48

.. code-block:: default

    direct_elas_pt = (
        (prob_PT_after - prob_PT)
        * MarginalCostPT
        / (prob_PT * (MarginalCostPT_after - MarginalCostPT))
    )








.. GENERATED FROM PYTHON SOURCE LINES 49-50

Formulas to simulate.

.. GENERATED FROM PYTHON SOURCE LINES 50-56

.. code-block:: default

    simulate = {
        'weight': normalized_weight,
        'Prob. PT': prob_PT,
        'direct_elas_pt': direct_elas_pt,
    }








.. GENERATED FROM PYTHON SOURCE LINES 57-58

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 58-60

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, simulate)








.. GENERATED FROM PYTHON SOURCE LINES 61-62

Read the estimation results from the file

.. GENERATED FROM PYTHON SOURCE LINES 62-70

.. 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 71-73

`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 73-76

.. 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. PT</th>
          <th>direct_elas_pt</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.886023</td>
          <td>0.476807</td>
          <td>0.000000</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.861136</td>
          <td>0.238681</td>
          <td>-0.212447</td>
        </tr>
        <tr>
          <th>3</th>
          <td>0.861136</td>
          <td>0.119136</td>
          <td>-1.362762</td>
        </tr>
        <tr>
          <th>4</th>
          <td>0.957386</td>
          <td>0.051136</td>
          <td>-0.941739</td>
        </tr>
        <tr>
          <th>5</th>
          <td>0.861136</td>
          <td>0.257192</td>
          <td>-0.508224</td>
        </tr>
        <tr>
          <th>...</th>
          <td>...</td>
          <td>...</td>
          <td>...</td>
        </tr>
        <tr>
          <th>2259</th>
          <td>2.036009</td>
          <td>0.285872</td>
          <td>-0.514608</td>
        </tr>
        <tr>
          <th>2261</th>
          <td>0.861136</td>
          <td>0.149688</td>
          <td>-0.819720</td>
        </tr>
        <tr>
          <th>2262</th>
          <td>0.861136</td>
          <td>0.205901</td>
          <td>-0.407408</td>
        </tr>
        <tr>
          <th>2263</th>
          <td>0.957386</td>
          <td>0.219850</td>
          <td>-0.667577</td>
        </tr>
        <tr>
          <th>2264</th>
          <td>0.957386</td>
          <td>0.209149</td>
          <td>-0.727399</td>
        </tr>
      </tbody>
    </table>
    <p>1906 rows × 3 columns</p>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 77-78

We calculate the aggregate elasticities.

.. GENERATED FROM PYTHON SOURCE LINES 80-81

First, the weighted probabilities.

.. GENERATED FROM PYTHON SOURCE LINES 81-85

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 86-87

Then the denominator of the aggregate elasticity expression.

.. GENERATED FROM PYTHON SOURCE LINES 87-89

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 90-91

And finally the aggregate elasticities themselves.

.. GENERATED FROM PYTHON SOURCE LINES 91-101

.. code-block:: default

    direct_elas_pt = (
        simulated_values['Weighted prob. PT']
        * simulated_values['direct_elas_pt']
        / denominator_pt
    ).sum()

    print(
        f'Aggregate direct arc elasticity of public transportation wrt cost: '
        f'{direct_elas_pt:.3g}'
    )




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

 .. code-block:: none

    Aggregate direct arc elasticity of public transportation wrt cost: -0.299





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

   **Total running time of the script:** (0 minutes 0.456 seconds)


.. _sphx_glr_download_auto_examples_indicators_plot_b08arc_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_b08arc_elasticities.py <plot_b08arc_elasticities.py>`

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

      :download:`Download Jupyter notebook: plot_b08arc_elasticities.ipynb <plot_b08arc_elasticities.ipynb>`


.. only:: html

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

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