.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/indicators/plot_b09wtp.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_b09wtp.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_indicators_plot_b09wtp.py:


Calculation of willingness to pay
=================================

We calculate and plot willingness to pay.
Details about this example are available in Section 4 of `Bierlaire (2018)
Calculating indicators with PandasBiogeme
<http://transp-or.epfl.ch/documents/technicalReports/Bier18a.pdf>`_

Michel Bierlaire, EPFL
Sat Jun 28 2025, 21:00:12

.. GENERATED FROM PYTHON SOURCE LINES 15-34

.. code-block:: Python


    import sys

    import numpy as np
    import pandas as pd
    from IPython.core.display_functions import display
    from biogeme.biogeme import BIOGEME
    from biogeme.results_processing import EstimationResults

    try:
        import matplotlib.pyplot as plt

        can_plot = True
    except ModuleNotFoundError:
        can_plot = False
    from biogeme.expressions import Derive
    from biogeme.data.optima import read_data, normalized_weight
    from scenarios import scenario








.. GENERATED FROM PYTHON SOURCE LINES 35-37

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

.. GENERATED FROM PYTHON SOURCE LINES 37-42

.. code-block:: Python

    v, _, _, _ = scenario()

    v_pt = v[0]
    v_car = v[1]








.. GENERATED FROM PYTHON SOURCE LINES 43-44

Calculation of the willingness to pay using derivatives.

.. GENERATED FROM PYTHON SOURCE LINES 44-47

.. code-block:: Python

    wtp_pt_time = Derive(v_pt, 'TimePT') / Derive(v_pt, 'MarginalCostPT')
    wtp_car_time = Derive(v_car, 'TimeCar') / Derive(v_car, 'CostCarCHF')








.. GENERATED FROM PYTHON SOURCE LINES 48-49

Formulas to simulate.

.. GENERATED FROM PYTHON SOURCE LINES 49-55

.. code-block:: Python

    simulate = {
        'weight': normalized_weight,
        'WTP PT time': wtp_pt_time,
        'WTP CAR time': wtp_car_time,
    }








.. GENERATED FROM PYTHON SOURCE LINES 56-57

Read the data

.. GENERATED FROM PYTHON SOURCE LINES 57-59

.. code-block:: Python

    database = read_data()








.. GENERATED FROM PYTHON SOURCE LINES 60-61

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 61-63

.. code-block:: Python

    the_biogeme = BIOGEME(database, simulate)








.. GENERATED FROM PYTHON SOURCE LINES 64-65

Read the estimation results from the file.

.. GENERATED FROM PYTHON SOURCE LINES 65-75

.. code-block:: Python

    try:
        results = EstimationResults.from_yaml_file(
            filename='saved_results/b02estimation.yaml'
        )
    except FileNotFoundError:
        sys.exit(
            'Run first the script b02estimation.py in order to generate '
            'the file b02estimation.yaml.'
        )








.. GENERATED FROM PYTHON SOURCE LINES 76-78

`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 78-81

.. code-block:: Python

    simulated_values = the_biogeme.simulate(results.get_beta_values())
    display(simulated_values)





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

 .. code-block:: none

            weight  WTP PT time  WTP CAR time
    0     0.893779     0.038447      0.038447
    1     0.868674     0.038447      0.038447
    2     0.868674     0.038447      0.038447
    3     0.965766     0.111038      0.111038
    4     0.868674     0.038447      0.038447
    ...        ...          ...           ...
    1894  2.053830     0.038447      0.038447
    1895  0.868674     0.111038      0.111038
    1896  0.868674     0.111038      0.111038
    1897  0.965766     0.038447      0.038447
    1898  0.965766     0.038447      0.038447

    [1899 rows x 3 columns]




.. GENERATED FROM PYTHON SOURCE LINES 82-83

Note the multiplication by 60 to have the valus of time per hour and not per minute.

.. GENERATED FROM PYTHON SOURCE LINES 83-85

.. code-block:: Python

    wtpcar = (60 * simulated_values['WTP CAR time'] * simulated_values['weight']).mean()








.. GENERATED FROM PYTHON SOURCE LINES 86-87

Calculate confidence intervals

.. GENERATED FROM PYTHON SOURCE LINES 87-89

.. code-block:: Python

    b = results.get_betas_for_sensitivity_analysis()








.. GENERATED FROM PYTHON SOURCE LINES 90-92

Returns data frame containing, for each simulated value, the left
and right bounds of the confidence interval calculated by simulation.

.. GENERATED FROM PYTHON SOURCE LINES 92-94

.. code-block:: Python

    left, right = the_biogeme.confidence_intervals(b, 0.9)





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

 .. code-block:: none


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.. GENERATED FROM PYTHON SOURCE LINES 95-96

Lower bounds of the confidence intervals

.. GENERATED FROM PYTHON SOURCE LINES 96-97

.. code-block:: Python

    display(left)




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

 .. code-block:: none

            weight  WTP PT time  WTP CAR time
    0     0.893779     0.011250      0.011250
    1     0.868674     0.011250      0.011250
    2     0.868674     0.011250      0.011250
    3     0.965766     0.067402      0.067402
    4     0.868674     0.011250      0.011250
    ...        ...          ...           ...
    1894  2.053830     0.011250      0.011250
    1895  0.868674     0.067402      0.067402
    1896  0.868674     0.067402      0.067402
    1897  0.965766     0.011250      0.011250
    1898  0.965766     0.011250      0.011250

    [1899 rows x 3 columns]




.. GENERATED FROM PYTHON SOURCE LINES 98-99

Upper bounds of the confidence intervals

.. GENERATED FROM PYTHON SOURCE LINES 99-101

.. code-block:: Python

    display(right)





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

 .. code-block:: none

            weight  WTP PT time  WTP CAR time
    0     0.893779     0.083276      0.083276
    1     0.868674     0.083276      0.083276
    2     0.868674     0.083276      0.083276
    3     0.965766     0.195056      0.195056
    4     0.868674     0.083276      0.083276
    ...        ...          ...           ...
    1894  2.053830     0.083276      0.083276
    1895  0.868674     0.195056      0.195056
    1896  0.868674     0.195056      0.195056
    1897  0.965766     0.083276      0.083276
    1898  0.965766     0.083276      0.083276

    [1899 rows x 3 columns]




.. GENERATED FROM PYTHON SOURCE LINES 102-103

Lower and upper bounds of the willingness to pay.

.. GENERATED FROM PYTHON SOURCE LINES 103-109

.. code-block:: Python

    wtpcar_left = (60 * left['WTP CAR time'] * left['weight']).mean()
    wtpcar_right = (60 * right['WTP CAR time'] * right['weight']).mean()
    print(
        f'Average WTP for car: {wtpcar:.3g} ' f'CI:[{wtpcar_left:.3g}, {wtpcar_right:.3g}]'
    )





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

 .. code-block:: none

    Average WTP for car: 3.89 CI:[1.9, 7.44]




.. GENERATED FROM PYTHON SOURCE LINES 110-112

In this specific case, there are only two distinct values in the
population: for workers and non workers

.. GENERATED FROM PYTHON SOURCE LINES 112-118

.. code-block:: Python

    print(
        'Unique values:      ',
        [f'{i:.3g}' for i in 60 * simulated_values['WTP CAR time'].unique()],
    )






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

 .. code-block:: none

    Unique values:       ['2.31', '6.66']




.. GENERATED FROM PYTHON SOURCE LINES 119-120

Function calculating the willingness to pay for a group.

.. GENERATED FROM PYTHON SOURCE LINES 120-139

.. code-block:: Python

    def wtp_for_subgroup(the_filter: 'pd.Series[np.bool_]') -> tuple[float, float, float]:
        """
        Check the value for groups of the population. Define a function that
        works for any filter to avoid repeating code.

        :param the_filter: pandas filter

        :return: willingness-to-pay for car and confidence interval
        """
        size = the_filter.sum()
        sim = simulated_values[the_filter]
        total_weight = sim['weight'].sum()
        weight = sim['weight'] * size / total_weight
        _wtpcar = (60 * sim['WTP CAR time'] * weight).mean()
        _wtpcar_left = (60 * left[the_filter]['WTP CAR time'] * weight).mean()
        _wtpcar_right = (60 * right[the_filter]['WTP CAR time'] * weight).mean()
        return _wtpcar, _wtpcar_left, _wtpcar_right









.. GENERATED FROM PYTHON SOURCE LINES 140-141

Full time workers.

.. GENERATED FROM PYTHON SOURCE LINES 141-145

.. code-block:: Python

    a_filter = database.dataframe['OccupStat'] == 1
    w, l, r = wtp_for_subgroup(a_filter)
    print(f'WTP car for workers: {w:.3g} CI:[{l:.3g}, {r:.3g}]')





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

 .. code-block:: none

    WTP car for workers: 6.66 CI:[4.04, 11.7]




.. GENERATED FROM PYTHON SOURCE LINES 146-147

Females.

.. GENERATED FROM PYTHON SOURCE LINES 147-151

.. code-block:: Python

    a_filter = database.dataframe['Gender'] == 2
    w, l, r = wtp_for_subgroup(a_filter)
    print(f'WTP car for females: {w:.3g} CI:[{l:.3g}, {r:.3g}]')





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

 .. code-block:: none

    WTP car for females: 3.09 CI:[1.28, 6.21]




.. GENERATED FROM PYTHON SOURCE LINES 152-153

Males.

.. GENERATED FROM PYTHON SOURCE LINES 153-157

.. code-block:: Python

    a_filter = database.dataframe['Gender'] == 1
    w, l, r = wtp_for_subgroup(a_filter)
    print(f'WTP car for males  : {w:.3g} CI:[{l:.3g}, {r:.3g}]')





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

 .. code-block:: none

    WTP car for males  : 4.89 CI:[2.67, 8.98]




.. GENERATED FROM PYTHON SOURCE LINES 158-160

We plot the distribution of WTP in the population. In this case,
there are only two values

.. GENERATED FROM PYTHON SOURCE LINES 160-168

.. code-block:: Python

    if can_plot:
        plt.hist(
            60 * simulated_values['WTP CAR time'],
            weights=simulated_values['weight'],
        )
        plt.xlabel('WTP (CHF/hour)')
        plt.ylabel('Individuals')
        plt.show()



.. image-sg:: /auto_examples/indicators/images/sphx_glr_plot_b09wtp_001.png
   :alt: plot b09wtp
   :srcset: /auto_examples/indicators/images/sphx_glr_plot_b09wtp_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 8.147 seconds)


.. _sphx_glr_download_auto_examples_indicators_plot_b09wtp.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

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

      :download:`Download Jupyter notebook: plot_b09wtp.ipynb <plot_b09wtp.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_b09wtp.py <plot_b09wtp.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_b09wtp.zip <plot_b09wtp.zip>`


.. only:: html

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

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