.. 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 ``scenarios.py``.

.. 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: {} 
    Analytical Hessian method: full 
    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         asc_car          asc_sm  beta_dist_male beta_dist_femal beta_dist_unrep       mu_no_car     Function    Relgrad   Radius      Rho      
        0               0               0               0               0               0               0               0               0               1      2.1e+03        1.3      0.5    0.067    - 
        1             0.5             0.5            -0.5             0.5            -0.5            -0.5            -0.5            -0.5             1.5      1.4e+03      0.067      0.5     0.21    + 
        2            0.32            0.39              -1            0.78           -0.22           -0.38            -0.5           -0.49             1.3      1.3e+03      0.031      0.5     0.39    + 
        3            0.32            0.39              -1            0.78           -0.22           -0.38            -0.5           -0.49             1.3      1.3e+03      0.031     0.25    0.072    - 
        4            0.23            0.42           -0.85            0.53           -0.14           -0.54           -0.63            -0.5             1.3      1.3e+03      0.013     0.25      0.8    + 
        5          -0.021            0.34           -0.86            0.72           0.018           -0.54           -0.75           -0.53             1.4      1.3e+03      0.029     0.25     0.44    + 
        6           -0.27            0.31           -0.75            0.49            0.26           -0.53           -0.78           -0.58             1.3      1.3e+03      0.027     0.25      0.3    + 
        7           -0.36            0.28           -0.72            0.51            0.16           -0.78           -0.82           -0.61             1.5      1.3e+03      0.019     0.25     0.21    + 
        8           -0.36            0.28           -0.72            0.51            0.16           -0.78           -0.82           -0.61             1.5      1.3e+03      0.019     0.12     -0.5    - 
        9           -0.46            0.21           -0.84            0.57            0.24           -0.66            -0.8           -0.62             1.4      1.3e+03      0.011     0.12     0.57    + 
       10           -0.51            0.21           -0.74            0.45            0.21           -0.67           -0.84           -0.64             1.4      1.3e+03      0.012     0.12     0.39    + 
       11           -0.63            0.13           -0.76            0.53            0.17           -0.67           -0.86           -0.67             1.5      1.3e+03       0.01     0.12     0.56    + 
       12           -0.63            0.13           -0.76            0.53            0.17           -0.67           -0.86           -0.67             1.5      1.3e+03       0.01    0.062   -0.036    - 
       13           -0.63            0.13           -0.76            0.53            0.17           -0.67           -0.86           -0.67             1.5      1.3e+03       0.01    0.031    -0.32    - 
       14           -0.67             0.1            -0.8            0.49            0.21           -0.64           -0.83            -0.7             1.4      1.3e+03     0.0046    0.031     0.58    + 
       15            -0.7           0.085           -0.76            0.46            0.17           -0.67           -0.84            -0.7             1.5      1.3e+03     0.0042    0.031     0.77    + 
       16           -0.73           0.054           -0.77            0.45            0.19           -0.66           -0.82            -0.7             1.4      1.3e+03     0.0038     0.31     0.92   ++ 
       17              -1           -0.14           -0.72            0.41            0.14           -0.71           -0.82            -0.7             1.5      1.3e+03     0.0077     0.31      0.7    + 
       18            -1.4           -0.34           -0.76            0.29            0.11           -0.61           -0.87           -0.69             1.5      1.3e+03      0.013     0.31     0.27    + 
       19            -1.4           -0.34           -0.76            0.29            0.11           -0.61           -0.87           -0.69             1.5      1.3e+03      0.013     0.16     -4.8    - 
       20            -1.4           -0.34           -0.76            0.29            0.11           -0.61           -0.87           -0.69             1.5      1.3e+03      0.013    0.078     -0.8    - 
       21            -1.4           -0.35           -0.74            0.31           0.088           -0.69           -0.84           -0.69             1.5      1.3e+03     0.0029    0.078     0.76    + 
       22            -1.4           -0.35           -0.74            0.31           0.088           -0.69           -0.84           -0.69             1.5      1.3e+03     0.0029    0.039    -0.79    - 
       23            -1.4           -0.35           -0.74            0.31           0.088           -0.69           -0.84           -0.69             1.5      1.3e+03     0.0029     0.02   0.0073    - 
       24            -1.4           -0.37           -0.74             0.3            0.11           -0.67           -0.82           -0.67             1.5      1.3e+03     0.0026     0.02     0.41    + 
       25            -1.4           -0.38           -0.72            0.31           0.094           -0.68           -0.82           -0.68             1.5      1.3e+03     0.0011     0.02     0.69    + 
       26            -1.4            -0.4           -0.73             0.3           0.092           -0.67           -0.82           -0.69             1.5      1.3e+03    0.00097     0.02     0.89    + 
       27            -1.4           -0.42           -0.73             0.3           0.083           -0.68           -0.82           -0.69             1.5      1.3e+03     0.0012     0.02     0.75    + 
       28            -1.4           -0.44           -0.73            0.29           0.086           -0.68           -0.82           -0.69             1.5      1.3e+03    0.00073      0.2     0.92   ++ 
       29            -1.4           -0.44           -0.73            0.29           0.086           -0.68           -0.82           -0.69             1.5      1.3e+03    0.00073    0.098     -4.8    - 
       30            -1.4           -0.44           -0.73            0.29           0.086           -0.68           -0.82           -0.69             1.5      1.3e+03    0.00073    0.049       -2    - 
       31            -1.4           -0.44           -0.73            0.29           0.086           -0.68           -0.82           -0.69             1.5      1.3e+03    0.00073    0.024    -0.38    - 
       32            -1.5           -0.46           -0.71            0.28           0.077           -0.67           -0.83            -0.7             1.5      1.3e+03     0.0014    0.024     0.37    + 
       33            -1.5           -0.48           -0.73            0.28           0.074           -0.69           -0.82            -0.7             1.5      1.3e+03     0.0019    0.024     0.57    + 
       34            -1.5           -0.48           -0.73            0.28           0.074           -0.69           -0.82            -0.7             1.5      1.3e+03     0.0019    0.012     -1.1    - 
       35            -1.5           -0.49           -0.72            0.28           0.087           -0.68           -0.83            -0.7             1.5      1.3e+03     0.0014    0.012     0.54    + 
       36            -1.5           -0.49           -0.72            0.28           0.087           -0.68           -0.83            -0.7             1.5      1.3e+03     0.0014   0.0061    0.066    - 
       37            -1.5           -0.49           -0.72            0.28           0.081           -0.69           -0.83            -0.7             1.5      1.3e+03    0.00051   0.0061     0.88    + 
       38            -1.5           -0.49           -0.72            0.28           0.078           -0.68           -0.83            -0.7             1.5      1.3e+03    0.00052   0.0061     0.83    + 
       39            -1.5            -0.5           -0.72            0.28           0.074           -0.68           -0.83            -0.7             1.5      1.3e+03    0.00043   0.0061     0.85    + 
       40            -1.5            -0.5           -0.72            0.27           0.074           -0.68           -0.83            -0.7             1.5      1.3e+03    0.00044    0.061     0.94   ++ 
       41            -1.6           -0.55           -0.72            0.26           0.064           -0.68           -0.83            -0.7             1.5      1.3e+03    0.00039     0.61     0.94   ++ 
       42            -1.6           -0.55           -0.72            0.26           0.064           -0.68           -0.83            -0.7             1.5      1.3e+03    0.00039    0.064      -31    - 
       43            -1.6           -0.55           -0.72            0.26           0.064           -0.68           -0.83            -0.7             1.5      1.3e+03    0.00039    0.032      -21    - 
       44            -1.6           -0.55           -0.72            0.26           0.064           -0.68           -0.83            -0.7             1.5      1.3e+03    0.00039    0.016     -9.4    - 
       45            -1.6           -0.55           -0.72            0.26           0.064           -0.68           -0.83            -0.7             1.5      1.3e+03    0.00039    0.008     -5.4    - 
       46            -1.6           -0.55           -0.72            0.26           0.064           -0.68           -0.83            -0.7             1.5      1.3e+03    0.00039    0.004     -2.9    - 
       47            -1.6           -0.55           -0.72            0.26           0.064           -0.68           -0.83            -0.7             1.5      1.3e+03    0.00039    0.002     -1.2    - 
       48            -1.6           -0.55           -0.72            0.26           0.062           -0.69           -0.83            -0.7             1.5      1.3e+03     0.0003    0.002     0.12    + 
       49            -1.6           -0.55           -0.72            0.26           0.064           -0.69           -0.83            -0.7             1.5      1.3e+03    7.9e-05    0.002     0.68    + 
       50            -1.6           -0.55           -0.72            0.26           0.064           -0.69           -0.83            -0.7             1.5      1.3e+03    5.6e-05    0.002     0.72    + 
       51            -1.6           -0.55           -0.72            0.26           0.064           -0.69           -0.83            -0.7             1.5      1.3e+03    5.6e-05    0.001     -1.5    - 
       52            -1.6           -0.55           -0.72            0.26           0.064           -0.69           -0.83            -0.7             1.5      1.3e+03    5.6e-05   0.0005    -0.21    - 
       53            -1.6           -0.55           -0.72            0.26           0.064           -0.69           -0.83            -0.7             1.5      1.3e+03    7.4e-05   0.0005     0.34    + 
       54            -1.6           -0.55           -0.72            0.26           0.064           -0.69           -0.83            -0.7             1.5      1.3e+03    3.9e-05   0.0005     0.76    + 
       55            -1.6           -0.55           -0.72            0.26           0.064           -0.69           -0.83            -0.7             1.5      1.3e+03    3.8e-05   0.0005     0.86    + 
       56            -1.6           -0.55           -0.72            0.26           0.064           -0.69           -0.83            -0.7             1.5      1.3e+03    3.1e-05    0.005     0.96   ++ 
       57            -1.6           -0.55           -0.72            0.26           0.064           -0.69           -0.83            -0.7             1.5      1.3e+03    3.1e-05   0.0025   -0.043    - 
       58            -1.6           -0.55           -0.72            0.26           0.063           -0.69           -0.83            -0.7             1.5      1.3e+03    6.1e-05   0.0025     0.53    + 
       59            -1.6           -0.55           -0.72            0.26           0.063           -0.69           -0.83            -0.7             1.5      1.3e+03    6.1e-05   0.0012     -1.1    - 
       60            -1.6           -0.55           -0.72            0.26           0.063           -0.69           -0.83            -0.7             1.5      1.3e+03    5.5e-05   0.0012     0.23    + 
       61            -1.6           -0.55           -0.72            0.26           0.063           -0.69           -0.83            -0.7             1.5      1.3e+03    5.5e-05  0.00062    -0.54    - 
       62            -1.6           -0.55           -0.72            0.26           0.063           -0.69           -0.83            -0.7             1.5      1.3e+03    5.5e-05  0.00031    -0.16    - 
       63            -1.6           -0.55           -0.72            0.26           0.063           -0.69           -0.83            -0.7             1.5      1.3e+03    5.1e-05  0.00031     0.47    + 
       64            -1.6           -0.55           -0.72            0.26           0.063           -0.69           -0.83            -0.7             1.5      1.3e+03    2.2e-05  0.00031     0.63    + 
       65            -1.6           -0.55           -0.72            0.26           0.063           -0.69           -0.83            -0.7             1.5      1.3e+03    7.8e-06  0.00031     0.84    + 
       66            -1.6           -0.55           -0.72            0.26           0.063           -0.69           -0.83            -0.7             1.5      1.3e+03    7.7e-06   0.0031      0.9   ++ 
       67            -1.6           -0.55           -0.72            0.26           0.063           -0.69           -0.83            -0.7             1.5      1.3e+03    7.7e-06  0.00063     -2.2    - 
       68            -1.6           -0.55           -0.72            0.26           0.063           -0.69           -0.83            -0.7             1.5      1.3e+03    2.5e-06  0.00063     0.87    - 
    Optimization algorithm has converged. 
    Relative gradient: 2.533919056890597e-06 
    Cause of termination: Relative gradient = 2.5e-06 <= 6.1e-06 
    Number of function evaluations: 154 
    Number of gradient evaluations: 85 
    Number of hessian evaluations: 0 
    Algorithm: BFGS with trust region for simple bound constraints 
    Number of iterations: 69 
    Proportion of Hessian calculation: 0/42 = 0.0% 
    Optimization time: 0:00:00.236321 
    Optimization is complete. Save recoverable results in b02estimation.yaml. 
    File b02estimation.yaml has been generated. 
    Calculate final gradient and BHHH 
    File b02estimation.yaml has been generated. 
    Calculate second derivatives 
    File b02estimation.yaml has been generated. 
    Re-estimate the model 100 times for bootstrapping 

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    File b02estimation.yaml has been generated. 
    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

    {'Estimated parameters':                    Name     Value  ...  Bootstrap t-stat.  Bootstrap p-value
    0    beta_time_fulltime -1.596770  ...          -4.728180       2.265417e-06
    1       beta_time_other -0.552927  ...          -1.731091       8.343550e-02
    2             beta_cost -0.719071  ...          -4.837448       1.315170e-06
    3               asc_car  0.258539  ...           2.579412       9.896880e-03
    4                asc_sm  0.063032  ...           0.300496       7.637990e-01
    5        beta_dist_male -0.687750  ...          -4.185995       2.839201e-05
    6      beta_dist_female -0.832195  ...          -4.847570       1.249832e-06
    7  beta_dist_unreported -0.704655  ...          -2.636356       8.380166e-03
    8             mu_no_car  1.523717  ...           5.376708       7.586019e-08

    [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

    [-0.65553838 -1.42281291 -0.13347955 ... -0.37368101 -0.29812698
     -0.27028586]




.. 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:     -1295.12025227902
    Simulated log likelihood: -1295.12025227902





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

   **Total running time of the script:** (0 minutes 22.521 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>`_