.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b01logit_bis.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_swissmetro_plot_b01logit_bis.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_swissmetro_plot_b01logit_bis.py:


Illustration of additional features of Biogeme
==============================================

Same model as b01logit, using LinearUtility, segmentations

Michel Bierlaire, EPFL
Wed Jun 18 2025, 10:57:53

.. GENERATED FROM PYTHON SOURCE LINES 12-29

.. code-block:: Python


    import os

    from IPython.core.display_functions import display

    import biogeme.biogeme_logging as blog
    from biogeme.biogeme import BIOGEME
    from biogeme.exceptions import BiogemeError
    from biogeme.expressions import Beta, LinearTermTuple, LinearUtility
    from biogeme.models import loglogit
    from biogeme.results_processing import (
        EstimateVarianceCovariance,
        generate_html_file,
        get_pandas_estimated_parameters,
    )
    from biogeme.segmentation import Segmentation








.. GENERATED FROM PYTHON SOURCE LINES 30-31

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

.. GENERATED FROM PYTHON SOURCE LINES 31-50

.. code-block:: Python

    from swissmetro_data import (
        CAR_AV_SP,
        CAR_CO_SCALED,
        CAR_TT_SCALED,
        CHOICE,
        GA,
        MALE,
        SM_AV,
        SM_COST_SCALED,
        SM_TT_SCALED,
        TRAIN_AV_SP,
        TRAIN_COST_SCALED,
        TRAIN_TT_SCALED,
        database,
    )

    logger = blog.get_screen_logger(level=blog.INFO)
    logger.info('Example b01logit_bis.py')





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

 .. code-block:: none

    Example b01logit_bis.py 




.. GENERATED FROM PYTHON SOURCE LINES 51-52

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 52-55

.. code-block:: Python

    asc_car = Beta('asc_car', 0, None, None, 0)
    asc_train = Beta('asc_train', 0, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 56-58

Starting value.
We use starting values estimated from a previous run

.. GENERATED FROM PYTHON SOURCE LINES 58-61

.. code-block:: Python

    b_time = Beta('b_time', -1.28, None, None, 0)
    b_cost = Beta('b_cost', -1.08, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 62-63

Define segmentations.

.. GENERATED FROM PYTHON SOURCE LINES 63-76

.. code-block:: Python

    gender_segmentation = database.generate_segmentation(
        variable=MALE, mapping={0: 'female', 1: 'male'}
    )

    ga_segmentation = database.generate_segmentation(
        variable=GA, mapping={0: 'without_ga', 1: 'with_ga'}
    )

    segmentations_for_asc = [
        gender_segmentation,
        ga_segmentation,
    ]








.. GENERATED FROM PYTHON SOURCE LINES 77-78

Segmentation of the constants.

.. GENERATED FROM PYTHON SOURCE LINES 78-83

.. code-block:: Python

    asc_train_segmentation = Segmentation(asc_train, segmentations_for_asc)
    segmented_asc_train = asc_train_segmentation.segmented_beta()
    asc_car_segmentation = Segmentation(asc_car, segmentations_for_asc)
    segmented_asc_car = asc_car_segmentation.segmented_beta()








.. GENERATED FROM PYTHON SOURCE LINES 84-85

Definition of the utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 85-103

.. code-block:: Python

    terms1 = [
        LinearTermTuple(beta=b_time, x=TRAIN_TT_SCALED),
        LinearTermTuple(beta=b_cost, x=TRAIN_COST_SCALED),
    ]
    v_train = segmented_asc_train + LinearUtility(terms1)

    terms2 = [
        LinearTermTuple(beta=b_time, x=SM_TT_SCALED),
        LinearTermTuple(beta=b_cost, x=SM_COST_SCALED),
    ]
    v_swissmetro = LinearUtility(terms2)

    terms3 = [
        LinearTermTuple(beta=b_time, x=CAR_TT_SCALED),
        LinearTermTuple(beta=b_cost, x=CAR_CO_SCALED),
    ]
    v_car = segmented_asc_car + LinearUtility(terms3)








.. GENERATED FROM PYTHON SOURCE LINES 104-105

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 105-107

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 108-109

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 109-111

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 112-116

Definition of the model.

This is the contribution of each observation to the log likelihood
function.

.. GENERATED FROM PYTHON SOURCE LINES 116-118

.. code-block:: Python

    logprob = loglogit(v, av, CHOICE)








.. GENERATED FROM PYTHON SOURCE LINES 119-122

User notes.

These notes will be included as such in the report file.

.. GENERATED FROM PYTHON SOURCE LINES 122-130

.. code-block:: Python

    USER_NOTES = (
        'Example of a logit model with three alternatives: Train, Car and'
        ' Swissmetro. Same as 01logit and '
        'introducing some options and features. In particular, bioLinearUtility,'
        ' and automatic segmentation of parameters.'
    )









.. GENERATED FROM PYTHON SOURCE LINES 131-135

Create the Biogeme object. We include users notes, and we ask not to calculate the second derivatives.
The parameter 'calculating_second_derivatives' is a general instruction for Biogeme, In this case, the
second derivatives will not even be calculated after the algorithm has converged. It means that the statistics
will have to rely on bootstrap or BHHH.

.. GENERATED FROM PYTHON SOURCE LINES 135-144

.. code-block:: Python

    the_biogeme = BIOGEME(
        database,
        logprob,
        user_notes=USER_NOTES,
        save_iterations=False,
        bootstrap_samples=100,
        calculating_second_derivatives='never',
    )





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

 .. code-block:: none

    Biogeme parameters read from biogeme.toml. 




.. GENERATED FROM PYTHON SOURCE LINES 145-149

Calculate the null log likelihood for reporting.

As we have used starting values different from 0, the initial model
is not the equal probability model.

.. GENERATED FROM PYTHON SOURCE LINES 149-152

.. code-block:: Python

    the_biogeme.calculate_null_loglikelihood(av)
    the_biogeme.model_name = 'b01logit_bis'








.. GENERATED FROM PYTHON SOURCE LINES 153-155

Estimate the parameters.


.. GENERATED FROM PYTHON SOURCE LINES 155-157

.. code-block:: Python

    results = the_biogeme.estimate(run_bootstrap=True)





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

 .. code-block:: none

    Starting values for the algorithm: {} 
    As the model is rather complex, we cancel the calculation of second derivatives. If you want to control the parameters, change the algorithm from "automatic" to "simple_bounds" in the TOML file. 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: BFGS with trust region for simple bounds 
    Iter.   asc_train_ref asc_train_diff_ asc_train_diff_          b_time          b_cost     asc_car_ref asc_car_diff_ma asc_car_diff_wi     Function    Relgrad   Radius      Rho      
        0               0               0               0            -1.3            -1.1               0               0               0      5.5e+03       0.12      0.5    -0.69    - 
        1               0               0               0            -1.3            -1.1               0               0               0      5.5e+03       0.12     0.25   -0.051    - 
        2           -0.25           -0.25            0.25            -1.5           -0.83            0.25            0.25           -0.25      5.3e+03      0.079     0.25     0.41    + 
        3            -0.2            -0.5             0.5            -1.8           -0.58               0               0            -0.5      5.3e+03        0.1     0.25      0.2    + 
        4           -0.13           -0.55            0.67            -1.5            -0.8            0.13            0.17           -0.53      5.1e+03      0.041     0.25      0.9    + 
        5           -0.29            -0.8            0.92            -1.6            -1.1           -0.12          -0.077           -0.78      5.1e+03      0.069     0.25     0.49    + 
        6           -0.21           -0.84             1.1            -1.3            -1.1         -0.0014            0.11           -0.78        5e+03      0.041     0.25     0.46    + 
        7           -0.24           -0.99             1.4            -1.3              -1           -0.23           0.026           -0.78        5e+03      0.022     0.25     0.69    + 
        8           -0.44            -1.2             1.6            -1.3              -1           -0.23             0.2           -0.76        5e+03      0.024     0.25     0.17    + 
        9           -0.44            -1.2             1.6            -1.3              -1           -0.23             0.2           -0.76        5e+03      0.024     0.12    -0.21    - 
       10           -0.32            -1.2             1.7            -1.2              -1           -0.34            0.16           -0.76        5e+03       0.01     0.12      0.7    + 
       11           -0.44            -1.2             1.8            -1.2            -1.1           -0.46            0.23           -0.72        5e+03      0.013     0.12     0.54    + 
       12           -0.44            -1.2             1.9            -1.1            -1.1            -0.5            0.34           -0.68      4.9e+03      0.013     0.12     0.18    + 
       13           -0.56            -1.1             1.9            -1.2              -1           -0.63            0.45           -0.55      4.9e+03     0.0059     0.12     0.41    + 
       14           -0.56            -1.1             1.9            -1.2              -1           -0.63            0.45           -0.55      4.9e+03     0.0059    0.062   0.0044    - 
       15           -0.54            -1.1             1.9            -1.2            -1.1           -0.64            0.43           -0.55      4.9e+03     0.0028    0.062     0.75    + 
       16           -0.54            -1.1             1.9            -1.2            -1.1           -0.64            0.43           -0.55      4.9e+03     0.0028    0.031     -2.8    - 
       17           -0.54            -1.1             1.9            -1.2            -1.1           -0.64            0.43           -0.55      4.9e+03     0.0028    0.016    -0.29    - 
       18           -0.55            -1.1             1.9            -1.2            -1.1           -0.63            0.44           -0.54      4.9e+03     0.0021    0.016     0.44    + 
       19           -0.54            -1.1             1.9            -1.2            -1.1           -0.63            0.42           -0.53      4.9e+03     0.0021    0.016     0.46    + 
       20           -0.54            -1.1             1.9            -1.2            -1.1           -0.62            0.42           -0.51      4.9e+03    0.00047    0.016     0.83    + 
       21           -0.53            -1.1             1.9            -1.2            -1.1           -0.62            0.42            -0.5      4.9e+03     0.0014    0.016     0.42    + 
       22           -0.54            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.48      4.9e+03    0.00067    0.016     0.64    + 
       23           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.46      4.9e+03    0.00032    0.016     0.66    + 
       24           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.45      4.9e+03    0.00047    0.016     0.59    + 
       25           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.43      4.9e+03    0.00049    0.016     0.43    + 
       26           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.43      4.9e+03    0.00049   0.0078     -2.6    - 
       27           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.43      4.9e+03    0.00022   0.0078      0.5    + 
       28           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.43      4.9e+03    0.00022   0.0039     -2.3    - 
       29           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.43      4.9e+03    0.00022    0.002     -1.1    - 
       30           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.43      4.9e+03    0.00022  0.00098    0.064    - 
       31           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.43      4.9e+03    0.00017  0.00098     0.45    + 
       32           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.43      4.9e+03    7.4e-05  0.00098     0.84    + 
       33           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.43      4.9e+03    6.8e-05  0.00098     0.83    + 
       34           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.43      4.9e+03    6.2e-05  0.00098     0.87    + 
       35           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.43      4.9e+03    5.4e-05  0.00098     0.89    + 
       36           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.42      4.9e+03    5.3e-05  0.00098     0.89    + 
       37           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.42      4.9e+03    4.5e-05  0.00098     0.89    + 
       38           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.42      4.9e+03    4.3e-05  0.00098     0.89    + 
       39           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.42      4.9e+03    3.6e-05  0.00098     0.89    + 
       40           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.42      4.9e+03    3.4e-05  0.00098      0.9    + 
       41           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.42      4.9e+03    5.7e-05  0.00098     0.88    + 
       42           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.42      4.9e+03    2.4e-05   0.0098     0.94   ++ 
       43           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.42      4.9e+03    2.4e-05   0.0033     -9.7    - 
       44           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.42      4.9e+03      2e-05   0.0033     0.88    + 
       45           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.42      4.9e+03      2e-05   0.0017      -35    - 
       46           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.42      4.9e+03      2e-05  0.00084     -3.5    - 
       47           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.42      4.9e+03    3.8e-06  0.00084     0.86    - 
    Optimization algorithm has converged. 
    Relative gradient: 3.827951698290516e-06 
    Cause of termination: Relative gradient = 3.8e-06 <= 6.1e-06 
    Number of function evaluations: 119 
    Number of gradient evaluations: 71 
    Number of hessian evaluations: 0 
    Algorithm: BFGS with trust region for simple bound constraints 
    Number of iterations: 48 
    Proportion of Hessian calculation: 0/35 = 0.0% 
    Optimization time: 0:00:00.269941 
    Calculate BHHH 
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    100%|██████████| 100/100 [00:36<00:00,  2.73it/s]
    File b01logit_bis~00.html has been generated. 
    File b01logit_bis~00.yaml has been generated. 




.. GENERATED FROM PYTHON SOURCE LINES 158-160

Get the results in a pandas table.


.. GENERATED FROM PYTHON SOURCE LINES 160-165

.. code-block:: Python

    print('Parameters')
    print('----------')
    pandas_results = get_pandas_estimated_parameters(estimation_results=results)
    display(pandas_results)





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

 .. code-block:: none

    Parameters
    ----------
                         Name     Value  ...  Bootstrap t-stat.  Bootstrap p-value
    0           asc_train_ref -0.534241  ...          -4.877074       1.076712e-06
    1     asc_train_diff_male -1.103475  ...         -12.722500       0.000000e+00
    2  asc_train_diff_with_ga  1.889291  ...          18.925585       0.000000e+00
    3                  b_time -1.172988  ...         -11.299239       0.000000e+00
    4                  b_cost -1.089775  ...         -14.222431       0.000000e+00
    5             asc_car_ref -0.612850  ...          -6.348853       2.169263e-10
    6       asc_car_diff_male  0.408056  ...           3.940929       8.116649e-05
    7    asc_car_diff_with_ga -0.414881  ...          -2.072138       3.825259e-02

    [8 rows x 5 columns]




.. GENERATED FROM PYTHON SOURCE LINES 166-168

Get general statistics.


.. GENERATED FROM PYTHON SOURCE LINES 168-174

.. code-block:: Python

    print('General statistics')
    print('------------------')
    stats = results.get_general_statistics()
    for description, value in stats.items():
        print(f'{description}: {value}')





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

 .. code-block:: none

    General statistics
    ------------------
    Number of estimated parameters: 8
    Sample size: 6768
    Excluded observations: 3960
    Null log likelihood: -6964.663
    Init log likelihood: -5533.155
    Final log likelihood: -4943.895
    Likelihood ratio test for the null model: 4041.535
    Rho-square for the null model: 0.29
    Rho-square-bar for the null model: 0.289
    Likelihood ratio test for the init. model: 1178.519
    Rho-square for the init. model: 0.106
    Rho-square-bar for the init. model: 0.105
    Akaike Information Criterion: 9903.791
    Bayesian Information Criterion: 9958.351
    Final gradient norm: 3.7451E-02
    Bootstrapping time: 0:00:36.572809




.. GENERATED FROM PYTHON SOURCE LINES 175-177

Messages from the optimization algorithm.


.. GENERATED FROM PYTHON SOURCE LINES 177-182

.. code-block:: Python

    print('Optimization algorithm')
    print('----------------------')
    for description, message in results.optimization_messages.items():
        print(f'{description}:\t{message}')





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

 .. code-block:: none

    Optimization algorithm
    ----------------------
    Relative gradient:      3.827951698290516e-06
    Cause of termination:   Relative gradient = 3.8e-06 <= 6.1e-06
    Number of function evaluations: 119
    Number of gradient evaluations: 71
    Number of hessian evaluations:  0
    Algorithm:      BFGS with trust region for simple bound constraints
    Number of iterations:   48
    Proportion of Hessian calculation:      0/35 = 0.0%
    Optimization time:      0:00:00.269941




.. GENERATED FROM PYTHON SOURCE LINES 183-185

Try to generate the html output with the robust variance-covariance matrix. It does not work as the second derivatives
matrix is not calculated.

.. GENERATED FROM PYTHON SOURCE LINES 185-201

.. code-block:: Python

    try:
        robust_html_filename = f'{the_biogeme.model_name}_robust.html'
        # The following function assumes that the file does not exist.
        if os.path.exists(robust_html_filename):
            os.remove(robust_html_filename)
        generate_html_file(
            filename=robust_html_filename,
            estimation_results=results,
            variance_covariance_type=EstimateVarianceCovariance.ROBUST,
        )
        print(
            f'Estimation results with robust statistics generated: {robust_html_filename}'
        )
    except BiogemeError as e:
        print(f'BiogemeError: {e}')





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

 .. code-block:: none

    BiogemeError: Second derivatives matrix not available.




.. GENERATED FROM PYTHON SOURCE LINES 202-203

Generate the html output with the BHHH variance-covariance matrix

.. GENERATED FROM PYTHON SOURCE LINES 203-214

.. code-block:: Python

    bhhh_html_filename = f'{the_biogeme.model_name}_bhhh.html'
    # The following function assumes that the file does not exist.
    if os.path.exists(bhhh_html_filename):
        os.remove(bhhh_html_filename)
    generate_html_file(
        filename=bhhh_html_filename,
        estimation_results=results,
        variance_covariance_type=EstimateVarianceCovariance.BHHH,
    )
    print(f'Estimation results with BHHH statistics generated: {bhhh_html_filename}')





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

 .. code-block:: none

    File b01logit_bis_bhhh.html has been generated. 
    Estimation results with BHHH statistics generated: b01logit_bis_bhhh.html




.. GENERATED FROM PYTHON SOURCE LINES 215-217

Generate the file in Alogit format.


.. GENERATED FROM PYTHON SOURCE LINES 217-220

.. code-block:: Python

    f12_filename = results.write_f12()
    print(f'Estimation results in ALogit format generated: {f12_filename}')





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

 .. code-block:: none

    File b01logit_bis~03.F12 has been generated. 
    Estimation results in ALogit format generated: b01logit_bis~03.F12




.. GENERATED FROM PYTHON SOURCE LINES 221-223

Generate LaTeX code with the results.


.. GENERATED FROM PYTHON SOURCE LINES 223-225

.. code-block:: Python

    latex_filename = results.write_latex(include_begin_document=True)
    print(f'Estimation results in LaTeX format generated: {latex_filename}')




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

 .. code-block:: none

    File b01logit_bis~00.tex has been generated. 
    Estimation results in LaTeX format generated: b01logit_bis~00.tex





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

   **Total running time of the script:** (0 minutes 37.546 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b01logit_bis.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_b01logit_bis.ipynb <plot_b01logit_bis.ipynb>`

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

      :download:`Download Python source code: plot_b01logit_bis.py <plot_b01logit_bis.py>`

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

      :download:`Download zipped: plot_b01logit_bis.zip <plot_b01logit_bis.zip>`


.. only:: html

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

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