.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/indicators/plot_b06point_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_b06point_elasticities.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_indicators_plot_b06point_elasticities.py:


Direct point elasticities
=========================

We use a previously estimated nested logit model and calculate
 disaggregate and aggregate direct 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 21:01:41 2023

.. GENERATED FROM PYTHON SOURCE LINES 17-35

.. code-block:: default


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

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








.. 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 47-49

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

.. GENERATED FROM PYTHON SOURCE LINES 49-59

.. code-block:: default

    direct_elas_pt_time = Derive(prob_PT, 'TimePT') * TimePT / prob_PT

    direct_elas_pt_cost = Derive(prob_PT, 'MarginalCostPT') * MarginalCostPT / prob_PT

    direct_elas_car_time = Derive(prob_CAR, 'TimeCar') * TimeCar / prob_CAR

    direct_elas_car_cost = Derive(prob_CAR, 'CostCarCHF') * CostCarCHF / prob_CAR

    direct_elas_sm_dist = Derive(prob_SM, 'distance_km') * distance_km / prob_SM








.. GENERATED FROM PYTHON SOURCE LINES 60-61

Formulas to simulate.

.. GENERATED FROM PYTHON SOURCE LINES 61-73

.. code-block:: default

    simulate = {
        'weight': normalized_weight,
        'Prob. car': prob_CAR,
        'Prob. public transportation': prob_PT,
        'Prob. slow modes': prob_SM,
        'direct_elas_pt_time': direct_elas_pt_time,
        'direct_elas_pt_cost': direct_elas_pt_cost,
        'direct_elas_car_time': direct_elas_car_time,
        'direct_elas_car_cost': direct_elas_car_cost,
        'direct_elas_sm_dist': direct_elas_sm_dist,
    }








.. 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 Pandas 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>direct_elas_pt_time</th>
          <th>direct_elas_pt_cost</th>
          <th>direct_elas_car_time</th>
          <th>direct_elas_car_cost</th>
          <th>direct_elas_sm_dist</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>-0.128761</td>
          <td>0.000000</td>
          <td>-0.044176</td>
          <td>-0.155490</td>
          <td>-6.282280</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.861136</td>
          <td>0.563268</td>
          <td>0.238681</td>
          <td>0.198051</td>
          <td>-0.236955</td>
          <td>-0.215072</td>
          <td>-0.007565</td>
          <td>-0.020018</td>
          <td>-0.690123</td>
        </tr>
        <tr>
          <th>3</th>
          <td>0.861136</td>
          <td>0.875824</td>
          <td>0.119136</td>
          <td>0.005040</td>
          <td>-0.278714</td>
          <td>-1.550950</td>
          <td>-0.008245</td>
          <td>-0.030060</td>
          <td>-6.242559</td>
        </tr>
        <tr>
          <th>4</th>
          <td>0.957386</td>
          <td>0.814110</td>
          <td>0.051136</td>
          <td>0.134754</td>
          <td>-2.020961</td>
          <td>-1.030288</td>
          <td>-0.020782</td>
          <td>-0.022100</td>
          <td>-1.734068</td>
        </tr>
        <tr>
          <th>5</th>
          <td>0.861136</td>
          <td>0.732059</td>
          <td>0.257192</td>
          <td>0.010749</td>
          <td>-0.255844</td>
          <td>-0.525291</td>
          <td>-0.015470</td>
          <td>-0.052004</td>
          <td>-4.727090</td>
        </tr>
        <tr>
          <th>...</th>
          <td>...</td>
          <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>-0.305144</td>
          <td>-0.531971</td>
          <td>-0.033015</td>
          <td>-0.115081</td>
          <td>-10.671587</td>
        </tr>
        <tr>
          <th>2261</th>
          <td>0.861136</td>
          <td>0.849040</td>
          <td>0.149688</td>
          <td>0.001272</td>
          <td>-0.948767</td>
          <td>-0.881532</td>
          <td>-0.051836</td>
          <td>-0.049301</td>
          <td>-8.100940</td>
        </tr>
        <tr>
          <th>2262</th>
          <td>0.861136</td>
          <td>0.689083</td>
          <td>0.205901</td>
          <td>0.105016</td>
          <td>-0.551441</td>
          <td>-0.417948</td>
          <td>-0.029794</td>
          <td>-0.030061</td>
          <td>-1.862736</td>
        </tr>
        <tr>
          <th>2263</th>
          <td>0.957386</td>
          <td>0.744274</td>
          <td>0.219850</td>
          <td>0.035876</td>
          <td>-0.291011</td>
          <td>-0.697499</td>
          <td>-0.017718</td>
          <td>-0.046520</td>
          <td>-3.407459</td>
        </tr>
        <tr>
          <th>2264</th>
          <td>0.957386</td>
          <td>0.765468</td>
          <td>0.209149</td>
          <td>0.025383</td>
          <td>-0.342744</td>
          <td>-0.765284</td>
          <td>-0.018957</td>
          <td>-0.053750</td>
          <td>-3.969568</td>
        </tr>
      </tbody>
    </table>
    <p>1906 rows × 9 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 98-108

.. 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']
    )
    simulated_values['Weighted prob. SM'] = (
        simulated_values['weight'] * simulated_values['Prob. slow modes']
    )








.. GENERATED FROM PYTHON SOURCE LINES 109-110

Then the denominators of the aggregate elasticity expressions.

.. GENERATED FROM PYTHON SOURCE LINES 110-114

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 115-116

And finally the aggregate elasticities themselves.

.. GENERATED FROM PYTHON SOURCE LINES 118-119

Elasticity of car with respect to time.

.. GENERATED FROM PYTHON SOURCE LINES 119-130

.. code-block:: default

    direct_elas_term_car_time = (
        simulated_values['Weighted prob. car']
        * simulated_values['direct_elas_car_time']
        / denominator_car
    ).sum()

    print(
        f'Aggregate direct point elasticity of car wrt time: '
        f'{direct_elas_term_car_time:.3g}'
    )





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

 .. code-block:: none

    Aggregate direct point elasticity of car wrt time: -0.0441




.. GENERATED FROM PYTHON SOURCE LINES 131-132

Elasticity of car with respect to cost.

.. GENERATED FROM PYTHON SOURCE LINES 132-142

.. code-block:: default

    direct_elas_term_car_cost = (
        simulated_values['Weighted prob. car']
        * simulated_values['direct_elas_car_cost']
        / denominator_car
    ).sum()
    print(
        f'Aggregate direct point elasticity of car wrt cost: '
        f'{direct_elas_term_car_cost:.3g}'
    )





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

 .. code-block:: none

    Aggregate direct point elasticity of car wrt cost: -0.0906




.. GENERATED FROM PYTHON SOURCE LINES 143-144

Elasticity of public transportation with respect to time.

.. GENERATED FROM PYTHON SOURCE LINES 144-154

.. code-block:: default

    direct_elas_term_pt_time = (
        simulated_values['Weighted prob. PT']
        * simulated_values['direct_elas_pt_time']
        / denominator_pt
    ).sum()
    print(
        f'Aggregate direct point elasticity of PT wrt time: '
        f'{direct_elas_term_pt_time:.3g}'
    )





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

 .. code-block:: none

    Aggregate direct point elasticity of PT wrt time: -0.274




.. GENERATED FROM PYTHON SOURCE LINES 155-156

Elasticity of public transportation with respect to cost.

.. GENERATED FROM PYTHON SOURCE LINES 156-166

.. code-block:: default

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





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

 .. code-block:: none

    Aggregate direct point elasticity of PT wrt cost: -0.32




.. GENERATED FROM PYTHON SOURCE LINES 167-168

Elasticity of slow modes with respect to distance.

.. GENERATED FROM PYTHON SOURCE LINES 168-177

.. code-block:: default

    direct_elas_term_sm_dist = (
        simulated_values['Weighted prob. SM']
        * simulated_values['direct_elas_sm_dist']
        / denominator_sm
    ).sum()
    print(
        f'Aggregate direct point elasticity of SM wrt distance: '
        f'{direct_elas_term_sm_dist:.3g}'
    )




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

 .. code-block:: none

    Aggregate direct point elasticity of SM wrt distance: -1.09





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

   **Total running time of the script:** (0 minutes 1.444 seconds)


.. _sphx_glr_download_auto_examples_indicators_plot_b06point_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_b06point_elasticities.py <plot_b06point_elasticities.py>`

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

      :download:`Download Jupyter notebook: plot_b06point_elasticities.ipynb <plot_b06point_elasticities.ipynb>`


.. only:: html

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

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