.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/indicators/plot_b02estimation.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_indicators_plot_b02estimation.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_indicators_plot_b02estimation.py:


Estimation and simulation of a nested logit model
=================================================

 We estimate a nested logit model, and we perform simulation using the
 estimated model.

Michel Bierlaire, EPFL
Sat Jun 28 2025, 16:08:07

.. GENERATED FROM PYTHON SOURCE LINES 12-26

.. code-block:: Python


    from IPython.core.display_functions import display

    import biogeme.biogeme_logging as blog
    from biogeme.biogeme import BIOGEME
    from biogeme.data.optima import read_data
    from biogeme.jax_calculator import get_value_c
    from biogeme.models import lognested
    from biogeme.results_processing import get_pandas_estimated_parameters
    from scenarios import scenario

    logger = blog.get_screen_logger(level=blog.INFO)
    logger.info('Example plot_b02estimation')





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

 .. code-block:: none

    Example plot_b02estimation 




.. GENERATED FROM PYTHON SOURCE LINES 27-29

Obtain the specification for the default scenario.
The definition of the scenarios is available in :ref:`scenarios`.

.. GENERATED FROM PYTHON SOURCE LINES 29-31

.. code-block:: Python

    V, nests, choice, _ = scenario()








.. GENERATED FROM PYTHON SOURCE LINES 32-34

The choice model is a nested logit, with availability conditions
For estimation, we need the log of the probability.

.. GENERATED FROM PYTHON SOURCE LINES 34-36

.. code-block:: Python

    log_probability = lognested(util=V, availability=None, nests=nests, choice=choice)








.. GENERATED FROM PYTHON SOURCE LINES 37-38

Get the database

.. GENERATED FROM PYTHON SOURCE LINES 38-39

.. code-block:: Python

    database = read_data()







.. GENERATED FROM PYTHON SOURCE LINES 40-41

Create the Biogeme object for estimation.

.. GENERATED FROM PYTHON SOURCE LINES 41-44

.. code-block:: Python

    the_biogeme = BIOGEME(database, log_probability)
    the_biogeme.model_name = 'b02estimation'





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

 .. code-block:: none

    Default values of the Biogeme parameters are used. 
    File biogeme.toml has been created 




.. GENERATED FROM PYTHON SOURCE LINES 45-46

Estimate the parameters. Perform bootstrapping.

.. GENERATED FROM PYTHON SOURCE LINES 46-48

.. code-block:: Python

    results = the_biogeme.estimate(run_bootstrap=True)





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

 .. code-block:: none

    *** Initial values of the parameters are obtained from the file __b02estimation.iter 
    Cannot read file __b02estimation.iter. Statement is ignored. 
    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. beta_time_fullt beta_time_other       beta_cost       mu_no_car          asc_sm  beta_dist_male beta_dist_femal beta_dist_unrep         asc_car     Function    Relgrad   Radius      Rho      
        0               0               0               0               1               0               0               0               0               0      2.1e+03        1.3      0.5    0.067    - 
        1             0.5             0.5            -0.5             1.5            -0.5            -0.5            -0.5            -0.5             0.5      1.4e+03      0.067      0.5     0.21    + 
        2            0.32            0.39              -1             1.3           -0.22           -0.38            -0.5           -0.49            0.78      1.3e+03      0.031      0.5     0.39    + 
        3            0.32            0.39              -1             1.3           -0.22           -0.38            -0.5           -0.49            0.78      1.3e+03      0.031     0.25    0.072    - 
        4            0.23            0.42           -0.85             1.3           -0.14           -0.54           -0.63            -0.5            0.53      1.3e+03      0.013     0.25      0.8    + 
        5          -0.021            0.34           -0.86             1.4           0.018           -0.54           -0.75           -0.53            0.72      1.3e+03      0.029     0.25     0.44    + 
        6           -0.27            0.31           -0.75             1.3            0.26           -0.53           -0.78           -0.58            0.49      1.3e+03      0.027     0.25      0.3    + 
        7           -0.36            0.28           -0.72             1.5            0.16           -0.78           -0.82           -0.61            0.51      1.3e+03      0.019     0.25     0.21    + 
        8           -0.36            0.28           -0.72             1.5            0.16           -0.78           -0.82           -0.61            0.51      1.3e+03      0.019     0.12     -0.5    - 
        9           -0.46            0.21           -0.84             1.4            0.24           -0.66            -0.8           -0.62            0.57      1.3e+03      0.011     0.12     0.57    + 
       10           -0.51            0.21           -0.74             1.4            0.21           -0.67           -0.84           -0.64            0.45      1.3e+03      0.012     0.12     0.39    + 
       11           -0.63            0.13           -0.76             1.5            0.17           -0.67           -0.86           -0.67            0.53      1.3e+03       0.01     0.12     0.56    + 
       12           -0.63            0.13           -0.76             1.5            0.17           -0.67           -0.86           -0.67            0.53      1.3e+03       0.01    0.062   -0.036    - 
       13           -0.63            0.13           -0.76             1.5            0.17           -0.67           -0.86           -0.67            0.53      1.3e+03       0.01    0.031    -0.32    - 
       14           -0.67             0.1            -0.8             1.4            0.21           -0.64           -0.83            -0.7            0.49      1.3e+03     0.0046    0.031     0.58    + 
       15            -0.7           0.085           -0.76             1.5            0.17           -0.67           -0.84            -0.7            0.46      1.3e+03     0.0042    0.031     0.77    + 
       16           -0.73           0.054           -0.77             1.4            0.19           -0.66           -0.82            -0.7            0.45      1.3e+03     0.0038     0.31     0.92   ++ 
       17              -1           -0.14           -0.72             1.5            0.14           -0.71           -0.82            -0.7            0.41      1.3e+03     0.0077     0.31      0.7    + 
       18            -1.4           -0.34           -0.76             1.5            0.11           -0.61           -0.87           -0.69            0.29      1.3e+03      0.013     0.31     0.27    + 
       19            -1.4           -0.34           -0.76             1.5            0.11           -0.61           -0.87           -0.69            0.29      1.3e+03      0.013     0.16     -4.8    - 
       20            -1.4           -0.34           -0.76             1.5            0.11           -0.61           -0.87           -0.69            0.29      1.3e+03      0.013    0.078     -0.8    - 
       21            -1.4           -0.35           -0.74             1.5           0.088           -0.69           -0.84           -0.69            0.31      1.3e+03     0.0029    0.078     0.76    + 
       22            -1.4           -0.35           -0.74             1.5           0.088           -0.69           -0.84           -0.69            0.31      1.3e+03     0.0029    0.039    -0.79    - 
       23            -1.4           -0.35           -0.74             1.5           0.088           -0.69           -0.84           -0.69            0.31      1.3e+03     0.0029     0.02   0.0073    - 
       24            -1.4           -0.37           -0.74             1.5            0.11           -0.67           -0.82           -0.67             0.3      1.3e+03     0.0026     0.02     0.41    + 
       25            -1.4           -0.38           -0.72             1.5           0.094           -0.68           -0.82           -0.68            0.31      1.3e+03     0.0011     0.02     0.69    + 
       26            -1.4            -0.4           -0.73             1.5           0.092           -0.67           -0.82           -0.69             0.3      1.3e+03    0.00097     0.02     0.89    + 
       27            -1.4           -0.42           -0.73             1.5           0.083           -0.68           -0.82           -0.69             0.3      1.3e+03     0.0012     0.02     0.75    + 
       28            -1.4           -0.44           -0.73             1.5           0.086           -0.68           -0.82           -0.69            0.29      1.3e+03    0.00073      0.2     0.92   ++ 
       29            -1.4           -0.44           -0.73             1.5           0.086           -0.68           -0.82           -0.69            0.29      1.3e+03    0.00073    0.098     -4.8    - 
       30            -1.4           -0.44           -0.73             1.5           0.086           -0.68           -0.82           -0.69            0.29      1.3e+03    0.00073    0.049       -2    - 
       31            -1.4           -0.44           -0.73             1.5           0.086           -0.68           -0.82           -0.69            0.29      1.3e+03    0.00073    0.024    -0.38    - 
       32            -1.5           -0.46           -0.71             1.5           0.077           -0.67           -0.83            -0.7            0.28      1.3e+03     0.0014    0.024     0.37    + 
       33            -1.5           -0.48           -0.73             1.5           0.074           -0.69           -0.82            -0.7            0.28      1.3e+03     0.0019    0.024     0.57    + 
       34            -1.5           -0.48           -0.73             1.5           0.074           -0.69           -0.82            -0.7            0.28      1.3e+03     0.0019    0.012     -1.1    - 
       35            -1.5           -0.49           -0.72             1.5           0.087           -0.68           -0.83            -0.7            0.28      1.3e+03     0.0014    0.012     0.54    + 
       36            -1.5           -0.49           -0.72             1.5           0.087           -0.68           -0.83            -0.7            0.28      1.3e+03     0.0014   0.0061    0.066    - 
       37            -1.5           -0.49           -0.72             1.5           0.081           -0.69           -0.83            -0.7            0.28      1.3e+03    0.00051   0.0061     0.88    + 
       38            -1.5           -0.49           -0.72             1.5           0.078           -0.68           -0.83            -0.7            0.28      1.3e+03    0.00052   0.0061     0.83    + 
       39            -1.5            -0.5           -0.72             1.5           0.074           -0.68           -0.83            -0.7            0.28      1.3e+03    0.00043   0.0061     0.85    + 
       40            -1.5            -0.5           -0.72             1.5           0.074           -0.68           -0.83            -0.7            0.27      1.3e+03    0.00044    0.061     0.94   ++ 
       41            -1.6           -0.55           -0.72             1.5           0.064           -0.68           -0.83            -0.7            0.26      1.3e+03    0.00039     0.61     0.94   ++ 
       42            -1.6           -0.55           -0.72             1.5           0.064           -0.68           -0.83            -0.7            0.26      1.3e+03    0.00039    0.064      -31    - 
       43            -1.6           -0.55           -0.72             1.5           0.064           -0.68           -0.83            -0.7            0.26      1.3e+03    0.00039    0.032      -21    - 
       44            -1.6           -0.55           -0.72             1.5           0.064           -0.68           -0.83            -0.7            0.26      1.3e+03    0.00039    0.016     -9.4    - 
       45            -1.6           -0.55           -0.72             1.5           0.064           -0.68           -0.83            -0.7            0.26      1.3e+03    0.00039    0.008     -5.4    - 
       46            -1.6           -0.55           -0.72             1.5           0.064           -0.68           -0.83            -0.7            0.26      1.3e+03    0.00039    0.004     -2.9    - 
       47            -1.6           -0.55           -0.72             1.5           0.064           -0.68           -0.83            -0.7            0.26      1.3e+03    0.00039    0.002     -1.2    - 
       48            -1.6           -0.55           -0.72             1.5           0.062           -0.69           -0.83            -0.7            0.26      1.3e+03    0.00031    0.002     0.12    + 
       49            -1.6           -0.55           -0.72             1.5           0.064           -0.69           -0.83            -0.7            0.26      1.3e+03    7.9e-05    0.002     0.68    + 
       50            -1.6           -0.55           -0.72             1.5           0.064           -0.69           -0.83            -0.7            0.26      1.3e+03    5.6e-05    0.002     0.71    + 
       51            -1.6           -0.55           -0.72             1.5           0.064           -0.69           -0.83            -0.7            0.26      1.3e+03    5.6e-05    0.001     -1.5    - 
       52            -1.6           -0.55           -0.72             1.5           0.064           -0.69           -0.83            -0.7            0.26      1.3e+03    5.6e-05   0.0005     -0.2    - 
       53            -1.6           -0.55           -0.72             1.5           0.064           -0.69           -0.83            -0.7            0.26      1.3e+03    7.3e-05   0.0005     0.35    + 
       54            -1.6           -0.55           -0.72             1.5           0.064           -0.69           -0.83            -0.7            0.26      1.3e+03    3.9e-05   0.0005     0.76    + 
       55            -1.6           -0.55           -0.72             1.5           0.064           -0.69           -0.83            -0.7            0.26      1.3e+03    3.8e-05   0.0005     0.86    + 
       56            -1.6           -0.55           -0.72             1.5           0.064           -0.69           -0.83            -0.7            0.26      1.3e+03    3.1e-05    0.005     0.96   ++ 
       57            -1.6           -0.55           -0.72             1.5           0.064           -0.69           -0.83            -0.7            0.26      1.3e+03    3.1e-05   0.0025   -0.051    - 
       58            -1.6           -0.55           -0.72             1.5           0.063           -0.69           -0.83            -0.7            0.26      1.3e+03    6.2e-05   0.0025     0.53    + 
       59            -1.6           -0.55           -0.72             1.5           0.063           -0.69           -0.83            -0.7            0.26      1.3e+03    6.2e-05   0.0012     -1.1    - 
       60            -1.6           -0.55           -0.72             1.5           0.063           -0.69           -0.83            -0.7            0.26      1.3e+03    5.7e-05   0.0012     0.21    + 
       61            -1.6           -0.55           -0.72             1.5           0.063           -0.69           -0.83            -0.7            0.26      1.3e+03    5.7e-05  0.00062    -0.51    - 
       62            -1.6           -0.55           -0.72             1.5           0.063           -0.69           -0.83            -0.7            0.26      1.3e+03    5.7e-05  0.00031    -0.11    - 
       63            -1.6           -0.55           -0.72             1.5           0.063           -0.69           -0.83            -0.7            0.26      1.3e+03    5.6e-05  0.00031     0.48    + 
       64            -1.6           -0.55           -0.72             1.5           0.063           -0.69           -0.83            -0.7            0.26      1.3e+03    2.3e-05  0.00031     0.59    + 
       65            -1.6           -0.55           -0.72             1.5           0.063           -0.69           -0.83            -0.7            0.26      1.3e+03    7.6e-06  0.00031     0.87    + 
       66            -1.6           -0.55           -0.72             1.5           0.063           -0.69           -0.83            -0.7            0.26      1.3e+03    1.1e-05  0.00031      0.7    + 
       67            -1.6           -0.55           -0.72             1.5           0.063           -0.69           -0.83            -0.7            0.26      1.3e+03    2.8e-06  0.00031     0.94    + 
    Optimization algorithm has converged. 
    Relative gradient: 2.7803605259079523e-06 
    Cause of termination: Relative gradient = 2.8e-06 <= 6.1e-06 
    Number of function evaluations: 153 
    Number of gradient evaluations: 85 
    Number of hessian evaluations: 0 
    Algorithm: BFGS with trust region for simple bound constraints 
    Number of iterations: 68 
    Proportion of Hessian calculation: 0/42 = 0.0% 
    Optimization time: 0:00:00.687495 
    Calculate second derivatives and BHHH 
    Re-estimate the model 100 times for bootstrapping 

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      warnings.warn(


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    File b02estimation.html has been generated. 
    File b02estimation.yaml has been generated. 




.. GENERATED FROM PYTHON SOURCE LINES 49-50

Get the results in a pandas table

.. GENERATED FROM PYTHON SOURCE LINES 50-54

.. code-block:: Python

    pandas_results = get_pandas_estimated_parameters(estimation_results=results)
    display(pandas_results)






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

 .. code-block:: none

                       Name     Value  ...  Bootstrap t-stat.  Bootstrap p-value
    0    beta_time_fulltime -1.596467  ...          -4.896418       9.759926e-07
    1       beta_time_other -0.552686  ...          -1.673272       9.427379e-02
    2             beta_cost -0.719072  ...          -5.182724       2.186688e-07
    3             mu_no_car  1.523716  ...           5.679133       1.353795e-08
    4                asc_sm  0.063000  ...           0.276633       7.820616e-01
    5        beta_dist_male -0.687677  ...          -3.446560       5.677721e-04
    6      beta_dist_female -0.832153  ...          -4.544143       5.515927e-06
    7  beta_dist_unreported -0.704737  ...          -2.221318       2.632942e-02
    8               asc_car  0.258607  ...           2.390527       1.682422e-02

    [9 rows x 5 columns]




.. GENERATED FROM PYTHON SOURCE LINES 55-56

Simulation

.. GENERATED FROM PYTHON SOURCE LINES 56-65

.. code-block:: Python

    simulated_choices = get_value_c(
        expression=log_probability,
        betas=results.get_beta_values(),
        database=database,
        numerically_safe=False,
        use_jit=True,
    )
    display(simulated_choices)





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

 .. code-block:: none


    Bootstraps:   0%|          | 0/100 [01:56<?, ?it/s]
    [-0.65553681 -1.42271161 -0.13348367 ... -0.37368096 -0.29814134
     -0.27030377]




.. GENERATED FROM PYTHON SOURCE LINES 66-76

.. code-block:: Python

    loglikelihood = get_value_c(
        expression=log_probability,
        betas=results.get_beta_values(),
        database=database,
        aggregation=True,
        numerically_safe=False,
        use_jit=True,
    )
    print(f'Final log likelihood:     {results.final_log_likelihood}')
    print(f'Simulated log likelihood: {loglikelihood}')




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

 .. code-block:: none

    Final log likelihood:     -1295.1202531057634
    Simulated log likelihood: -1295.1202531057634





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

   **Total running time of the script:** (2 minutes 0.270 seconds)


.. _sphx_glr_download_auto_examples_indicators_plot_b02estimation.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_b02estimation.ipynb <plot_b02estimation.ipynb>`

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

      :download:`Download Python source code: plot_b02estimation.py <plot_b02estimation.py>`

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

      :download:`Download zipped: plot_b02estimation.zip <plot_b02estimation.zip>`


.. only:: html

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

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