.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/bayesian_swissmetro/plot_b01c_logit_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_bayesian_swissmetro_plot_b01c_logit_simul.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_bayesian_swissmetro_plot_b01c_logit_simul.py:


1c. Simulation of a logit model (traditional and Bayesian)
==========================================================

Example of simulation with a logit model

Michel Bierlaire, EPFL
Thu Oct 30 2025, 14:03:15

.. GENERATED FROM PYTHON SOURCE LINES 11-21

.. code-block:: Python


    import pandas as pd
    from IPython.core.display_functions import display

    import biogeme.biogeme_logging as blog
    from biogeme.bayesian_estimation import BayesianResults
    from biogeme.biogeme import BIOGEME
    from biogeme.expressions import Beta, Derive
    from biogeme.models import logit








.. GENERATED FROM PYTHON SOURCE LINES 22-23

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

.. GENERATED FROM PYTHON SOURCE LINES 23-38

.. code-block:: Python

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

    logger = blog.get_screen_logger(level=blog.INFO)








.. GENERATED FROM PYTHON SOURCE LINES 39-40

Parameters.

.. GENERATED FROM PYTHON SOURCE LINES 40-46

.. code-block:: Python

    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 47-50

Definition of the utility functions. As we will calculate the derivative with respect to TRAIN_TT, SM_TT and CAR_TT,
they must explicitly appear in the model. If not, the derivative will be zero. Therefore, we do not use the
`_SCALED` version of the attributes. We explicitly include their definition.

.. GENERATED FROM PYTHON SOURCE LINES 50-54

.. code-block:: Python

    v_train = asc_train + b_time * TRAIN_TT / 100 + b_cost * TRAIN_COST_SCALED
    v_swissmetro = asc_sm + b_time * SM_TT / 100 + b_cost * SM_COST_SCALED
    v_car = asc_car + b_time * CAR_TT / 100 + b_cost * CAR_CO_SCALED








.. GENERATED FROM PYTHON SOURCE LINES 55-56

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 56-58

.. code-block:: Python

    v = {1: v_train, 2: v_swissmetro, 3: v_car}








.. GENERATED FROM PYTHON SOURCE LINES 59-60

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 60-62

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 63-65

Choice probability.


.. GENERATED FROM PYTHON SOURCE LINES 65-67

.. code-block:: Python

    prob_train = logit(v, av, 1)








.. GENERATED FROM PYTHON SOURCE LINES 68-70

Elasticity.


.. GENERATED FROM PYTHON SOURCE LINES 70-72

.. code-block:: Python

    time_elasticity_train = Derive(prob_train, 'TRAIN_TT') * TRAIN_TT / prob_train








.. GENERATED FROM PYTHON SOURCE LINES 73-75

Quantities to be simulated.


.. GENERATED FROM PYTHON SOURCE LINES 75-82

.. code-block:: Python

    simulate = {
        'Prob. train': prob_train,
        'train time elasticity': time_elasticity_train,
        'Value of time': b_time / b_cost,
    }









.. GENERATED FROM PYTHON SOURCE LINES 83-87

Create the Biogeme object.

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

.. GENERATED FROM PYTHON SOURCE LINES 87-90

.. code-block:: Python

    biosim = BIOGEME(database, simulate)
    biosim.model_name = 'b01c_logit_simul'





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

 .. code-block:: none

    Biogeme parameters read from biogeme.toml. 




.. GENERATED FROM PYTHON SOURCE LINES 91-92

Retrieve the estimated values of the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 92-97

.. code-block:: Python

    RESULTS_FILE_NAME = 'saved_results/b01a_logit.nc'
    estimation_results = BayesianResults.from_netcdf(filename=RESULTS_FILE_NAME)
    betas = estimation_results.get_beta_values()






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

 .. code-block:: none

    Loaded NetCDF file size: 855.3 MB 
    load finished in 4448 ms (4.45 s)
    Diagnostics computation took 23.5 seconds (cached). 




.. GENERATED FROM PYTHON SOURCE LINES 98-99

Simulation using the posterior mean of each parameter

.. GENERATED FROM PYTHON SOURCE LINES 99-104

.. code-block:: Python


    print('Simulation using the posterior mean of each parameter')
    results = biosim.simulate(the_beta_values=betas)
    display(results)





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

 .. code-block:: none

    Simulation using the posterior mean of each parameter
          Prob. train  train time elasticity  Value of time
    0        0.167825              -1.192850       1.180578
    1        0.184090              -1.075555       1.180578
    2        0.142838              -1.426131       1.180578
    3        0.161141              -1.105807       1.180578
    4        0.139629              -1.431470       1.180578
    ...           ...                    ...            ...
    6763     0.172357              -1.143983       1.180578
    6764     0.164421              -1.154953       1.180578
    6765     0.149244              -1.175931       1.180578
    6766     0.134531              -1.417798       1.180578
    6767     0.176696              -1.137986       1.180578

    [6768 rows x 3 columns]




.. GENERATED FROM PYTHON SOURCE LINES 105-107

Bayesian simulation using the posterior draws


.. GENERATED FROM PYTHON SOURCE LINES 107-113

.. code-block:: Python

    print('Bayesian simulation')
    bayesian_results = biosim.simulate_bayesian(
        bayesian_estimation_results=estimation_results, percentage_of_draws_to_use=3
    )
    with pd.option_context('display.max_columns', None, 'display.expand_frame_repr', False):
        display(bayesian_results)




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

 .. code-block:: none

    Bayesian simulation
    Bayesian simulation performed with 3% of the draws, that is 240/8000 draws. Adjust the parameter "percentage_of_draws_to_use" if you need a different number of draws. 

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                                 Prob. train_mean  Prob. train_q025  Prob. train_q975  train time elasticity_mean  train time elasticity_q025  train time elasticity_q975  Value of time_mean  Value of time_q025  Value of time_q975
    __biogeme_internal_obs_id__                                                                                                                                                                                                      
    0                                    0.167515          0.157977          0.178539                   -1.189251                   -1.286882                   -1.088971            1.181914            1.049833            1.313146
    1                                    0.183722          0.172976          0.195906                   -1.072349                   -1.158776                   -0.983756            1.181914            1.049833            1.313146
    2                                    0.142630          0.135141          0.152021                   -1.421745                   -1.542036                   -1.297560            1.181914            1.049833            1.313146
    3                                    0.160822          0.151748          0.171163                   -1.102525                   -1.196037                   -1.006631            1.181914            1.049833            1.313146
    4                                    0.139444          0.131443          0.149657                   -1.427078                   -1.550104                   -1.300481            1.181914            1.049833            1.313146
    ...                                       ...               ...               ...                         ...                         ...                         ...                 ...                 ...                 ...
    6763                                 0.172081          0.163140          0.183298                   -1.140513                   -1.234750                   -1.043042            1.181914            1.049833            1.313146
    6764                                 0.164130          0.154941          0.175101                   -1.151497                   -1.248836                   -1.052276            1.181914            1.049833            1.313146
    6765                                 0.149016          0.141000          0.158921                   -1.172342                   -1.271547                   -1.069987            1.181914            1.049833            1.313146
    6766                                 0.134394          0.126414          0.144618                   -1.413400                   -1.535721                   -1.286135            1.181914            1.049833            1.313146
    6767                                 0.176372          0.166627          0.188252                   -1.134603                   -1.229517                   -1.038149            1.181914            1.049833            1.313146

    [6768 rows x 9 columns]





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

   **Total running time of the script:** (1 minutes 41.239 seconds)


.. _sphx_glr_download_auto_examples_bayesian_swissmetro_plot_b01c_logit_simul.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_b01c_logit_simul.ipynb <plot_b01c_logit_simul.ipynb>`

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

      :download:`Download Python source code: plot_b01c_logit_simul.py <plot_b01c_logit_simul.py>`

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

      :download:`Download zipped: plot_b01c_logit_simul.zip <plot_b01c_logit_simul.zip>`


.. only:: html

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

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