.. 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.

:author: Michel Bierlaire
:date: Wed Nov  1 18:00:33 2023

.. GENERATED FROM PYTHON SOURCE LINES 11-35

.. code-block:: Python


    import pandas as pd
    from biogeme.sampling_of_alternatives import (
        SamplingContext,
        ChoiceSetsGeneration,
        GenerateModel,
        generate_segment_size,
    )
    from biogeme.expressions import Beta
    import biogeme.biogeme_logging as blog
    import biogeme.biogeme as bio
    from biogeme.nests import OneNestForCrossNestedLogit, NestsForCrossNestedLogit
    from specification_sampling import V, combined_variables
    from compare import compare
    from alternatives import (
        alternatives,
        ID_COLUMN,
        partitions,
        all_alternatives,
        asian_and_downtown,
        only_downtown,
        only_asian,
    )








.. GENERATED FROM PYTHON SOURCE LINES 36-38

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 39-47

.. 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 48-52

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 53-57

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 58-59

We use all alternatives in the nest.

.. GENERATED FROM PYTHON SOURCE LINES 59-66

.. 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 67-68

Nests

.. GENERATED FROM PYTHON SOURCE LINES 70-71

Downtown

.. GENERATED FROM PYTHON SOURCE LINES 71-79

.. 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 80-81

Asian

.. GENERATED FROM PYTHON SOURCE LINES 81-92

.. 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 93-95

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 96-111

.. 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 112-114

.. 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 115-118

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 119-121

.. 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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    Defining new variables...:  70%|███████   | 7/10 [00:03<00:01,  1.98it/s]
    Defining new variables...:  80%|████████  | 8/10 [00:03<00:01,  1.98it/s]
    Defining new variables...:  90%|█████████ | 9/10 [00:04<00:00,  1.97it/s]
    Defining new variables...: 100%|██████████| 10/10 [00:05<00:00,  1.97it/s]
    Defining new variables...: 100%|██████████| 10/10 [00:37<00:00,  3.78s/it]
    File cnl_10_63.dat has been created. 




.. GENERATED FROM PYTHON SOURCE LINES 122-124

.. code-block:: Python

    logprob = the_model_generation.get_cross_nested_logit()








.. GENERATED FROM PYTHON SOURCE LINES 125-128

.. code-block:: Python

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





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

 .. code-block:: none

    Biogeme parameters read from biogeme.toml. 




.. GENERATED FROM PYTHON SOURCE LINES 129-130

Calculate the null log likelihood for reporting.

.. GENERATED FROM PYTHON SOURCE LINES 130-134

.. 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


    np.float64(-23025.850929942502)



.. GENERATED FROM PYTHON SOURCE LINES 135-136

Estimate the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 136-138

.. code-block:: Python

    results = the_biogeme.estimate(recycle=False)





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

 .. code-block:: none

    As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds" 
    *** Initial values of the parameters are obtained from the file __cnl_10_63.iter 
    Cannot read file __cnl_10_63.iter. Statement is ignored. 
    As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds" 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Iter.    beta_chinese  beta_ethiopian     beta_french     beta_indian   beta_japanese     beta_korean   beta_lebanese   beta_log_dist    beta_mexican      beta_price     beta_rating        mu_asian     mu_downtown     Function    Relgrad   Radius      Rho      
        0           -0.19          -0.051            0.18           -0.22            0.08           -0.21          -0.033              -1            0.96            -0.6            0.63               1             1.4      1.8e+04       0.15        1     0.68    + 
        1           -0.21          -0.019            0.26           -0.23           0.088           -0.23          -0.018           -0.58            0.97           -0.47            0.81             1.1               1      1.6e+04      0.072       10     0.93   ++ 
        2           -0.21          -0.019            0.26           -0.23           0.088           -0.23          -0.018           -0.58            0.97           -0.47            0.81             1.1               1      1.6e+04      0.072     0.78    -0.82    - 
        3           -0.48            0.27               1           -0.28            0.21           -0.56             0.2           -0.47             1.2           -0.38            0.93             1.3             1.2      1.6e+04      0.023     0.78     0.78    + 
        4           -0.34             0.4             1.2          -0.035            0.42           -0.31            0.52           -0.55             1.3           -0.46            0.94             1.1             1.1      1.6e+04     0.0054      7.8        1   ++ 
        5           -0.36            0.46             1.3          -0.023            0.48           -0.32            0.59           -0.61             1.4           -0.51               1               1               1      1.6e+04     0.0046       78     0.96   ++ 
        6           -0.36            0.46             1.3          -0.023            0.48           -0.32            0.59           -0.61             1.4           -0.51               1               1               1      1.6e+04    8.3e-05       78        1   ++ 
    Results saved in file cnl_10_63.html 
    Results saved in file cnl_10_63.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 139-141

.. 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:           -15815.23
    Likelihood ratio test (null):           14421.24
    Rho square (null):                      0.313
    Rho bar square (null):                  0.313
    Akaike Information Criterion:   31656.46
    Bayesian Information Criterion: 31750.19





.. GENERATED FROM PYTHON SOURCE LINES 142-145

.. code-block:: Python

    estimated_parameters = results.get_estimated_parameters()
    estimated_parameters






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>Value</th>
          <th>Rob. Std err</th>
          <th>Rob. t-test</th>
          <th>Rob. p-value</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>beta_chinese</th>
          <td>-0.355854</td>
          <td>0.065737</td>
          <td>-5.413305</td>
          <td>6.187183e-08</td>
        </tr>
        <tr>
          <th>beta_ethiopian</th>
          <td>0.470517</td>
          <td>0.048806</td>
          <td>9.640480</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>beta_french</th>
          <td>1.313453</td>
          <td>0.063627</td>
          <td>20.643022</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>beta_indian</th>
          <td>-0.014493</td>
          <td>0.054403</td>
          <td>-0.266405</td>
          <td>7.899274e-01</td>
        </tr>
        <tr>
          <th>beta_japanese</th>
          <td>0.494104</td>
          <td>0.052761</td>
          <td>9.364955</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>beta_korean</th>
          <td>-0.318190</td>
          <td>0.053328</td>
          <td>-5.966692</td>
          <td>2.421114e-09</td>
        </tr>
        <tr>
          <th>beta_lebanese</th>
          <td>0.607425</td>
          <td>0.065966</td>
          <td>9.208228</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>beta_log_dist</th>
          <td>-0.621389</td>
          <td>0.024518</td>
          <td>-25.344483</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>beta_mexican</th>
          <td>1.413177</td>
          <td>0.055236</td>
          <td>25.584268</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>beta_price</th>
          <td>-0.521240</td>
          <td>0.020715</td>
          <td>-25.161987</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>beta_rating</th>
          <td>1.044178</td>
          <td>0.037827</td>
          <td>27.604277</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>mu_asian</th>
          <td>1.016981</td>
          <td>0.037306</td>
          <td>27.260280</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>mu_downtown</th>
          <td>1.013238</td>
          <td>0.028033</td>
          <td>36.144043</td>
          <td>0.000000e+00</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 146-148

.. code-block:: Python

    df, msg = compare(estimated_parameters)








.. GENERATED FROM PYTHON SOURCE LINES 149-151

.. 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         1.044178  -7.777002
    1       beta_price       -0.40        -0.521240   5.852654
    2     beta_chinese        0.75        -0.355854  16.822418
    3    beta_japanese        1.25         0.494104  14.326799
    4      beta_korean        0.75        -0.318190  20.030660
    5      beta_indian        1.00        -0.014493  18.647743
    6      beta_french        0.75         1.313453  -8.855572
    7     beta_mexican        1.25         1.413177  -2.954174
    8    beta_lebanese        0.75         0.607425   2.161352
    9   beta_ethiopian        0.50         0.470517   0.604089
    10   beta_log_dist       -0.60        -0.621389   0.872401
    11        mu_asian        2.00         1.016981  26.349899
    12     mu_downtown        2.00         1.013238  35.199584




.. GENERATED FROM PYTHON SOURCE LINES 152-153

.. code-block:: Python

    print(msg)








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

   **Total running time of the script:** (4 minutes 31.760 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>`_