.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/sampling/plot_b03cnl.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_b03cnl.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_sampling_plot_b03cnl.py:


Cross-nested logit
==================

Estimation of a cross-nested logit model using sampling of alternatives.

Michel Bierlaire
Sat Jul 26 2025, 14:57:17

.. GENERATED FROM PYTHON SOURCE LINES 11-38

.. 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,
        all_alternatives,
        alternatives,
        asian_and_downtown,
        only_asian,
        only_downtown,
        partitions,
    )
    from biogeme.biogeme import BIOGEME
    from biogeme.expressions import Beta
    from biogeme.nests import NestsForCrossNestedLogit, OneNestForCrossNestedLogit
    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








.. GENERATED FROM PYTHON SOURCE LINES 39-41

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 42-50

.. code-block:: Python

    PARTITION = 'downtown'
    MEV_PARTITION = 'uniform_asian_or_downtown'
    SAMPLE_SIZE = 10  # out of 100 alternatives
    SAMPLE_SIZE_MEV = 63  # out of 63 alternatives
    CHOICE_COLUMN = 'cnl_3'
    MODEL_NAME = f'cnl_{SAMPLE_SIZE}_{SAMPLE_SIZE_MEV}'
    FILE_NAME = f'{MODEL_NAME}.dat'








.. GENERATED FROM PYTHON SOURCE LINES 51-55

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 56-60

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 61-62

We use all alternatives in the nest.

.. GENERATED FROM PYTHON SOURCE LINES 62-69

.. code-block:: Python

    mev_partition = partitions.get(MEV_PARTITION)
    if mev_partition is None:
        raise ValueError(f'Unknown partition: {MEV_PARTITION}')
    mev_segment_sizes = [
        SAMPLE_SIZE_MEV,
    ]








.. GENERATED FROM PYTHON SOURCE LINES 70-71

Nests

.. GENERATED FROM PYTHON SOURCE LINES 73-74

Downtown

.. GENERATED FROM PYTHON SOURCE LINES 74-82

.. code-block:: Python

    mu_downtown = Beta('mu_downtown', 1, 1, None, 0)
    downtown_alpha_dict = {i: 0.5 for i in asian_and_downtown} | {
        i: 1 for i in only_downtown
    }
    downtown_nest = OneNestForCrossNestedLogit(
        nest_param=mu_downtown, dict_of_alpha=downtown_alpha_dict, name='downtown'
    )








.. GENERATED FROM PYTHON SOURCE LINES 83-84

Asian

.. GENERATED FROM PYTHON SOURCE LINES 84-95

.. code-block:: Python

    mu_asian = Beta('mu_asian', 1, 1, None, 0)
    asian_alpha_dict = {i: 0.5 for i in asian_and_downtown} | {i: 1.0 for i in only_asian}
    asian_nest = OneNestForCrossNestedLogit(
        nest_param=mu_asian, dict_of_alpha=asian_alpha_dict, name='asian'
    )

    cnl_nests = NestsForCrossNestedLogit(
        choice_set=all_alternatives,
        tuple_of_nests=(downtown_nest, asian_nest),
    )





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

 .. code-block:: none

    The following elements do not appear in any nest and are assumed each to be alone in a separate nest: {2, 4, 5, 6, 8, 10, 12, 16, 19, 21, 23, 25, 26, 28, 29, 35, 39, 41, 42, 43, 44, 52, 53, 58, 59, 62, 64, 65, 66, 67, 69, 71, 73, 82, 85, 95, 96}. If it is not the intention, check the assignment of alternatives to nests. 




.. GENERATED FROM PYTHON SOURCE LINES 96-98

.. code-block:: Python

    observations = pd.read_csv('obs_choice.dat')








.. GENERATED FROM PYTHON SOURCE LINES 99-114

.. 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,
        mev_partition=mev_partition,
        mev_sample_sizes=mev_segment_sizes,
        cnl_nests=cnl_nests,
    )








.. GENERATED FROM PYTHON SOURCE LINES 115-117

.. 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 46, 54
    Main sample: 10: 5/46, 5/54
    Nbr of MEV alternatives: 63
    MEV partition: 1 segment(s) of size 63
    MEV sample: 63: 63/63
 




.. GENERATED FROM PYTHON SOURCE LINES 118-121

.. code-block:: Python

    the_data_generation = ChoiceSetsGeneration(context=context)
    the_model_generation = GenerateModel(context=context)








.. GENERATED FROM PYTHON SOURCE LINES 122-124

.. code-block:: Python

    biogeme_database = the_data_generation.sample_and_merge(recycle=False)





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

 .. code-block:: none

    Generating 10 + 63 alternatives for 10000 observations 

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    File cnl_10_63.dat has been created. 




.. GENERATED FROM PYTHON SOURCE LINES 125-127

.. code-block:: Python

    logprob = the_model_generation.get_cross_nested_logit()








.. GENERATED FROM PYTHON SOURCE LINES 128-131

.. code-block:: Python

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





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

 .. code-block:: none

    Biogeme parameters read from biogeme.toml. 




.. GENERATED FROM PYTHON SOURCE LINES 132-133

Calculate the null log likelihood for reporting.

.. GENERATED FROM PYTHON SOURCE LINES 133-137

.. code-block:: Python

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





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

 .. code-block:: none


    -23025.850929940458



.. GENERATED FROM PYTHON SOURCE LINES 138-139

Estimate the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 139-141

.. 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 __cnl_10_63.iter 
    Parameter values restored from __cnl_10_63.iter 
    Starting values for the algorithm: {'beta_rating': 0.7365266291094059, 'beta_price': -0.4239680674266754, 'beta_chinese': 0.738785241646357, 'beta_japanese': 1.2813341992881495, 'beta_korean': 0.7871329380842219, 'beta_indian': 1.078119718024791, 'beta_french': 0.7632288866575481, 'beta_mexican': 1.2593243502328455, 'beta_lebanese': 0.7497810818603908, 'beta_ethiopian': 0.5555323545985966, 'beta_log_dist': -0.5854142682626837, 'mu_downtown': 1.9338601890193694, 'mu_asian': 2.112962768508359} 
    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: 2.933940829781729e-07 
    Cause of termination: Relative gradient = 2.9e-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: 0:05:06.445139 
    Calculate second derivatives and BHHH 
    File cnl_10_63~00.html has been generated. 
    File cnl_10_63~00.yaml has been generated. 




.. GENERATED FROM PYTHON SOURCE LINES 142-144

.. code-block:: Python

    print(results.short_summary())





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

 .. code-block:: none

    Results for model cnl_10_63
    Nbr of parameters:              13
    Sample size:                    10000
    Excluded data:                  0
    Null log likelihood:            -23025.85
    Final log likelihood:           -14014.06
    Likelihood ratio test (null):           18023.57
    Rho square (null):                      0.391
    Rho bar square (null):                  0.391
    Akaike Information Criterion:   28054.13
    Bayesian Information Criterion: 28147.86





.. GENERATED FROM PYTHON SOURCE LINES 145-148

.. 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  0.736527         0.014947       49.277321             0.0
    1       beta_price -0.423968         0.012658      -33.493402             0.0
    2     beta_chinese  0.738785         0.062006       11.914783             0.0
    3    beta_japanese  1.281334         0.046413       27.607232             0.0
    4      beta_korean  0.787133         0.053694       14.659536             0.0
    5      beta_indian  1.078120         0.053553       20.131981             0.0
    6      beta_french  0.763229         0.049590       15.390741             0.0
    7     beta_mexican  1.259324         0.030265       41.609970             0.0
    8    beta_lebanese  0.749781         0.049632       15.106678             0.0
    9   beta_ethiopian  0.555532         0.041136       13.504778             0.0
    10   beta_log_dist -0.585414         0.012764      -45.864380             0.0
    11     mu_downtown  1.933860         0.030348       63.722869             0.0
    12        mu_asian  2.112963         0.068147       31.006151             0.0




.. GENERATED FROM PYTHON SOURCE LINES 149-151

.. code-block:: Python

    df, msg = compare(estimated_parameters)








.. GENERATED FROM PYTHON SOURCE LINES 152-154

.. 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         0.736527  0.901436
    1       beta_price       -0.40        -0.423968  1.893473
    2     beta_chinese        0.75         0.738785  0.180866
    3    beta_japanese        1.25         1.281334 -0.675117
    4      beta_korean        0.75         0.787133 -0.691563
    5      beta_indian        1.00         1.078120 -1.458748
    6      beta_french        0.75         0.763229 -0.266764
    7     beta_mexican        1.25         1.259324 -0.308091
    8    beta_lebanese        0.75         0.749781  0.004411
    9   beta_ethiopian        0.50         0.555532 -1.349970
    10   beta_log_dist       -0.60        -0.585414 -1.142722
    11        mu_asian        2.00         2.112963 -1.657644
    12     mu_downtown        2.00         1.933860  2.179381




.. GENERATED FROM PYTHON SOURCE LINES 155-156

.. code-block:: Python

    print(msg)








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

   **Total running time of the script:** (52 minutes 29.717 seconds)


.. _sphx_glr_download_auto_examples_sampling_plot_b03cnl.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_b03cnl.ipynb <plot_b03cnl.ipynb>`

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

      :download:`Download Python source code: plot_b03cnl.py <plot_b03cnl.py>`

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

      :download:`Download zipped: plot_b03cnl.zip <plot_b03cnl.zip>`


.. only:: html

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

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