.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/sampling/plot_b01logit.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_sampling_plot_b01logit.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_sampling_plot_b01logit.py:


Logit
=====

Estimation of a logit model using sampling of alternatives.

Michel Bierlaire
Fri Jul 25 2025, 17:36:23

.. GENERATED FROM PYTHON SOURCE LINES 11-28

.. code-block:: Python


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

    import biogeme.biogeme_logging as blog
    from alternatives import ID_COLUMN, alternatives, partitions
    from biogeme.biogeme import BIOGEME
    from biogeme.results_processing import get_pandas_estimated_parameters
    from biogeme.sampling_of_alternatives import (
        ChoiceSetsGeneration,
        GenerateModel,
        SamplingContext,
        generate_segment_size,
    )
    from compare import compare
    from specification_sampling import V, combined_variables





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

 .. code-block:: none

        ID  rating  price  ...   rest_lon    distance  downtown
    0    0       1      4  ...  42.220972   71.735518       1.0
    1    1       2      2  ...  50.549434  106.267205       0.0
    2    2       3      3  ...  97.830520  136.298409       0.0
    3    3       4      1  ...  69.152206   85.941147       0.0
    4    4       4      3  ...  89.145620   96.773021       0.0
    ..  ..     ...    ...  ...        ...         ...       ...
    95  95       4      3  ...   9.511387   84.166441       0.0
    96  96       1      1  ...  92.144641   95.601366       0.0
    97  97       4      2  ...  27.657518   30.440555       1.0
    98  98       4      4  ...  32.303213   45.027143       1.0
    99  99       4      1  ...  13.672495   25.703295       1.0

    [100 rows x 16 columns]
    Number of asian restaurants: 33




.. GENERATED FROM PYTHON SOURCE LINES 29-31

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 32-34

The data file contains several columns associated with synthetic
choices. Here we arbitrarily select `logit_4`.

.. GENERATED FROM PYTHON SOURCE LINES 34-36

.. code-block:: Python

    CHOICE_COLUMN = 'logit_4'








.. GENERATED FROM PYTHON SOURCE LINES 37-43

.. code-block:: Python

    SAMPLE_SIZE = 10
    PARTITION = 'asian'
    MODEL_NAME = f'logit_{PARTITION}_{SAMPLE_SIZE}_alt'
    FILE_NAME = f'{MODEL_NAME}.dat'
    OBS_FILE = 'obs_choice.dat'








.. GENERATED FROM PYTHON SOURCE LINES 44-48

.. code-block:: Python

    the_partition = partitions.get(PARTITION)
    if the_partition is None:
        raise ValueError(f'Unknown partition: {PARTITION}')








.. GENERATED FROM PYTHON SOURCE LINES 49-51

.. code-block:: Python

    segment_sizes = generate_segment_size(SAMPLE_SIZE, the_partition.number_of_segments())








.. GENERATED FROM PYTHON SOURCE LINES 52-54

.. code-block:: Python

    observations = pd.read_csv(OBS_FILE)








.. GENERATED FROM PYTHON SOURCE LINES 55-67

.. code-block:: Python

    context = SamplingContext(
        the_partition=the_partition,
        sample_sizes=segment_sizes,
        individuals=observations,
        choice_column=CHOICE_COLUMN,
        alternatives=alternatives,
        id_column=ID_COLUMN,
        biogeme_file_name=FILE_NAME,
        utility_function=V,
        combined_variables=combined_variables,
    )








.. GENERATED FROM PYTHON SOURCE LINES 68-70

.. code-block:: Python

    logger.info(context.reporting())





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

 .. code-block:: none

    Size of the choice set: 100
    Main partition: 2 segment(s) of size 33, 67
    Main sample: 10: 5/33, 5/67
 




.. GENERATED FROM PYTHON SOURCE LINES 71-73

.. code-block:: Python

    the_data_generation = ChoiceSetsGeneration(context=context)








.. GENERATED FROM PYTHON SOURCE LINES 74-76

.. code-block:: Python

    the_model_generation = GenerateModel(context=context)








.. GENERATED FROM PYTHON SOURCE LINES 77-79

.. code-block:: Python

    biogeme_database = the_data_generation.sample_and_merge(recycle=False)





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

 .. code-block:: none

    Generating 10 + 0 alternatives for 10000 observations 

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    File logit_asian_10_alt.dat has been created. 




.. GENERATED FROM PYTHON SOURCE LINES 80-82

.. code-block:: Python

    logprob = the_model_generation.get_logit()








.. GENERATED FROM PYTHON SOURCE LINES 83-86

.. code-block:: Python

    the_biogeme = BIOGEME(biogeme_database, logprob)
    the_biogeme.modelName = MODEL_NAME





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

 .. code-block:: none

    Biogeme parameters read from biogeme.toml. 
    /Users/bierlair/MyFiles/github/biogeme/docs/source/examples/sampling/plot_b01logit.py:84: DeprecationWarning: 'modelName' is deprecated. Please use 'model_name' instead.
      the_biogeme.modelName = MODEL_NAME




.. GENERATED FROM PYTHON SOURCE LINES 87-88

Calculate the null log likelihood for reporting.

.. GENERATED FROM PYTHON SOURCE LINES 88-90

.. code-block:: Python

    the_biogeme.calculate_null_loglikelihood({i: 1 for i in range(SAMPLE_SIZE)})





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

 .. code-block:: none


    -23025.850929940458



.. GENERATED FROM PYTHON SOURCE LINES 91-92

Estimate the parameters

.. GENERATED FROM PYTHON SOURCE LINES 92-94

.. code-block:: Python

    results = the_biogeme.estimate(recycle=False)





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

 .. code-block:: none

    *** Initial values of the parameters are obtained from the file __logit_asian_10_alt.iter 
    Parameter values restored from __logit_asian_10_alt.iter 
    Starting values for the algorithm: {'beta_rating': 0.7474053406335313, 'beta_price': -0.40656630678576633, 'beta_chinese': 0.6120193026885046, 'beta_japanese': 1.1876198392575683, 'beta_korean': 0.7100322440030521, 'beta_indian': 0.9377605509978457, 'beta_french': 0.6115512270994261, 'beta_mexican': 1.2233552157690688, 'beta_lebanese': 0.6578163784697699, 'beta_ethiopian': 0.47263438214296166, 'beta_log_dist': -0.6017924240399324} 
    As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Optimization algorithm has converged. 
    Relative gradient: 4.75385039567593e-07 
    Cause of termination: Relative gradient = 4.8e-07 <= 6.1e-06 
    Number of function evaluations: 1 
    Number of gradient evaluations: 1 
    Number of hessian evaluations: 0 
    Algorithm: Newton with trust region for simple bound constraints 
    Number of iterations: 0 
    Optimization time: 0:00:01.316658 
    Calculate second derivatives and BHHH 
    File logit_asian_10_alt~00.html has been generated. 
    File logit_asian_10_alt~00.yaml has been generated. 




.. GENERATED FROM PYTHON SOURCE LINES 95-97

.. code-block:: Python

    print(results.short_summary())





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

 .. code-block:: none

    Results for model logit_asian_10_alt
    Nbr of parameters:              11
    Sample size:                    10000
    Excluded data:                  0
    Null log likelihood:            -23025.85
    Final log likelihood:           -18389.31
    Likelihood ratio test (null):           9273.078
    Rho square (null):                      0.201
    Rho bar square (null):                  0.201
    Akaike Information Criterion:   36800.62
    Bayesian Information Criterion: 36879.94





.. GENERATED FROM PYTHON SOURCE LINES 98-101

.. code-block:: Python

    estimated_parameters = get_pandas_estimated_parameters(estimation_results=results)
    display(estimated_parameters)





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

 .. code-block:: none

                  Name     Value  Robust std err.  Robust t-stat.  Robust p-value
    0      beta_rating  0.747405         0.015277       48.922826             0.0
    1       beta_price -0.406566         0.012767      -31.843948             0.0
    2     beta_chinese  0.612019         0.050248       12.180081             0.0
    3    beta_japanese  1.187620         0.046358       25.618523             0.0
    4      beta_korean  0.710032         0.042348       16.766548             0.0
    5      beta_indian  0.937761         0.043111       21.752391             0.0
    6      beta_french  0.611551         0.061565        9.933479             0.0
    7     beta_mexican  1.223355         0.036539       33.480934             0.0
    8    beta_lebanese  0.657816         0.062525       10.520805             0.0
    9   beta_ethiopian  0.472634         0.050153        9.423939             0.0
    10   beta_log_dist -0.601792         0.015140      -39.748700             0.0




.. GENERATED FROM PYTHON SOURCE LINES 102-104

.. code-block:: Python

    df, msg = compare(estimated_parameters)








.. GENERATED FROM PYTHON SOURCE LINES 105-107

.. code-block:: Python

    print(df)





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

 .. code-block:: none

                  Name  True Value  Estimated Value    T-Test
    0      beta_rating        0.75         0.747405  0.169838
    1       beta_price       -0.40        -0.406566  0.514300
    2     beta_chinese        0.75         0.612019  2.746018
    3    beta_japanese        1.25         1.187620  1.345622
    4      beta_korean        0.75         0.710032  0.943790
    5      beta_indian        1.00         0.937761  1.443713
    6      beta_french        0.75         0.611551  2.248835
    7     beta_mexican        1.25         1.223355  0.729218
    8    beta_lebanese        0.75         0.657816  1.474341
    9   beta_ethiopian        0.50         0.472634  0.545648
    10   beta_log_dist       -0.60        -0.601792  0.118391




.. GENERATED FROM PYTHON SOURCE LINES 108-109

.. code-block:: Python

    print(msg)




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

 .. code-block:: none

    Parameters not estimated: ['mu_asian', 'mu_downtown']





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

   **Total running time of the script:** (0 minutes 16.427 seconds)


.. _sphx_glr_download_auto_examples_sampling_plot_b01logit.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.ipynb <plot_b01logit.ipynb>`

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

      :download:`Download Python source code: plot_b01logit.py <plot_b01logit.py>`

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

      :download:`Download zipped: plot_b01logit.zip <plot_b01logit.zip>`


.. only:: html

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

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