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

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

.. _sphx_glr_auto_examples_programmers_plot_biogeme.py:


biogeme.biogeme
===============

Examples of use of several functions.

This is designed for programmers who need examples of use of the
functions of the module. The examples are designed to illustrate the
syntax. They do not correspond to any meaningful model.

:author: Michel Bierlaire
:date: Thu Nov 16 18:36:35 2023

.. GENERATED FROM PYTHON SOURCE LINES 15-24

.. code-block:: Python


    import biogeme.version as ver
    import biogeme.biogeme as bio
    import biogeme.database as db
    import pandas as pd
    from biogeme.expressions import Beta, Variable, exp
    import biogeme.biogeme_logging as blog
    from biogeme.function_output import BiogemeFunctionOutput








.. GENERATED FROM PYTHON SOURCE LINES 25-26

Version of Biogeme.

.. GENERATED FROM PYTHON SOURCE LINES 26-29

.. code-block:: Python

    print(ver.get_text())






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

 .. code-block:: none

    biogeme 3.2.14 [2024-08-05]
    Home page: http://biogeme.epfl.ch
    Submit questions to https://groups.google.com/d/forum/biogeme
    Michel Bierlaire, Transport and Mobility Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL)





.. GENERATED FROM PYTHON SOURCE LINES 30-31

Logger.

.. GENERATED FROM PYTHON SOURCE LINES 31-35

.. code-block:: Python

    logger = blog.get_screen_logger(level=blog.INFO)
    logger.info('Logger initialized')






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

 .. code-block:: none

    Logger initialized 




.. GENERATED FROM PYTHON SOURCE LINES 36-37

Definition of a database

.. GENERATED FROM PYTHON SOURCE LINES 37-51

.. code-block:: Python

    df = pd.DataFrame(
        {
            'Person': [1, 1, 1, 2, 2],
            'Exclude': [0, 0, 1, 0, 1],
            'Variable1': [1, 2, 3, 4, 5],
            'Variable2': [10, 20, 30, 40, 50],
            'Choice': [1, 2, 3, 1, 2],
            'Av1': [0, 1, 1, 1, 1],
            'Av2': [1, 1, 1, 1, 1],
            'Av3': [0, 1, 1, 1, 1],
        }
    )
    my_data = db.Database('test', df)








.. GENERATED FROM PYTHON SOURCE LINES 52-53

Data

.. GENERATED FROM PYTHON SOURCE LINES 53-56

.. code-block:: Python

    my_data.data







.. 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>Person</th>
          <th>Exclude</th>
          <th>Variable1</th>
          <th>Variable2</th>
          <th>Choice</th>
          <th>Av1</th>
          <th>Av2</th>
          <th>Av3</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>1</td>
          <td>0</td>
          <td>1</td>
          <td>10</td>
          <td>1</td>
          <td>0</td>
          <td>1</td>
          <td>0</td>
        </tr>
        <tr>
          <th>1</th>
          <td>1</td>
          <td>0</td>
          <td>2</td>
          <td>20</td>
          <td>2</td>
          <td>1</td>
          <td>1</td>
          <td>1</td>
        </tr>
        <tr>
          <th>2</th>
          <td>1</td>
          <td>1</td>
          <td>3</td>
          <td>30</td>
          <td>3</td>
          <td>1</td>
          <td>1</td>
          <td>1</td>
        </tr>
        <tr>
          <th>3</th>
          <td>2</td>
          <td>0</td>
          <td>4</td>
          <td>40</td>
          <td>1</td>
          <td>1</td>
          <td>1</td>
          <td>1</td>
        </tr>
        <tr>
          <th>4</th>
          <td>2</td>
          <td>1</td>
          <td>5</td>
          <td>50</td>
          <td>2</td>
          <td>1</td>
          <td>1</td>
          <td>1</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 57-58

Definition of various expressions.

.. GENERATED FROM PYTHON SOURCE LINES 58-66

.. code-block:: Python

    Variable1 = Variable('Variable1')
    Variable2 = Variable('Variable2')
    beta1 = Beta('beta1', -1.0, -3, 3, 0)
    beta2 = Beta('beta2', 2.0, -3, 10, 0)
    likelihood = -(beta1**2) * Variable1 - exp(beta2 * beta1) * Variable2 - beta2**4
    simul = beta1 / Variable1 + beta2 / Variable2
    dict_of_expressions = {'log_like': likelihood, 'beta1': beta1, 'simul': simul}








.. GENERATED FROM PYTHON SOURCE LINES 67-68

Creation of the BIOGEME object.

.. GENERATED FROM PYTHON SOURCE LINES 68-72

.. code-block:: Python

    my_biogeme = bio.BIOGEME(my_data, dict_of_expressions)
    my_biogeme.modelName = 'simple_example'
    print(my_biogeme)





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

 .. code-block:: none

    Default values of the Biogeme parameters are used. 
    File biogeme.toml has been created 
    simple_example: database [test]{'log_like': ((((-Beta('beta1', -1.0, -3, 3, 0)**2.0) * Variable1) - (exp((Beta('beta2', 2.0, -3, 10, 0) * Beta('beta1', -1.0, -3, 3, 0))) * Variable2)) - Beta('beta2', 2.0, -3, 10, 0)**4.0), 'beta1': Beta('beta1', -1.0, -3, 3, 0), 'simul': ((Beta('beta1', -1.0, -3, 3, 0) / Variable1) + (Beta('beta2', 2.0, -3, 10, 0) / Variable2))}




.. GENERATED FROM PYTHON SOURCE LINES 73-74

The data is stored in the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 74-76

.. code-block:: Python

    my_biogeme.database.data






.. 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>Person</th>
          <th>Exclude</th>
          <th>Variable1</th>
          <th>Variable2</th>
          <th>Choice</th>
          <th>Av1</th>
          <th>Av2</th>
          <th>Av3</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>1</td>
          <td>0</td>
          <td>1</td>
          <td>10</td>
          <td>1</td>
          <td>0</td>
          <td>1</td>
          <td>0</td>
        </tr>
        <tr>
          <th>1</th>
          <td>1</td>
          <td>0</td>
          <td>2</td>
          <td>20</td>
          <td>2</td>
          <td>1</td>
          <td>1</td>
          <td>1</td>
        </tr>
        <tr>
          <th>2</th>
          <td>1</td>
          <td>1</td>
          <td>3</td>
          <td>30</td>
          <td>3</td>
          <td>1</td>
          <td>1</td>
          <td>1</td>
        </tr>
        <tr>
          <th>3</th>
          <td>2</td>
          <td>0</td>
          <td>4</td>
          <td>40</td>
          <td>1</td>
          <td>1</td>
          <td>1</td>
          <td>1</td>
        </tr>
        <tr>
          <th>4</th>
          <td>2</td>
          <td>1</td>
          <td>5</td>
          <td>50</td>
          <td>2</td>
          <td>1</td>
          <td>1</td>
          <td>1</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 77-78

Log likelihood with the initial values of the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 78-80

.. code-block:: Python

    my_biogeme.calculate_init_likelihood()





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

 .. code-block:: none


    -115.30029248549191



.. GENERATED FROM PYTHON SOURCE LINES 81-83

Calculate the log-likelihood with a different value of the
parameters. We retieve the current value and add 1 to each of them.

.. GENERATED FROM PYTHON SOURCE LINES 83-87

.. code-block:: Python

    x = my_biogeme.id_manager.free_betas_values
    xplus = [v + 1 for v in x]
    print(xplus)





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

 .. code-block:: none

    [0.0, 3.0]




.. GENERATED FROM PYTHON SOURCE LINES 88-90

.. code-block:: Python

    my_biogeme.calculate_likelihood(xplus, scaled=True)





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

 .. code-block:: none


    -111.0



.. GENERATED FROM PYTHON SOURCE LINES 91-92

Calculate the log-likelihood function and its derivatives.

.. GENERATED FROM PYTHON SOURCE LINES 92-97

.. code-block:: Python

    the_function_output: BiogemeFunctionOutput = (
        my_biogeme.calculate_likelihood_and_derivatives(
            xplus, scaled=True, hessian=True, bhhh=True
        )
    )







.. GENERATED FROM PYTHON SOURCE LINES 98-100

.. code-block:: Python

    print(f'f = {the_function_output.function}')





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

 .. code-block:: none

    f = -111.0




.. GENERATED FROM PYTHON SOURCE LINES 101-103

.. code-block:: Python

    print(f'g = {the_function_output.gradient}')





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

 .. code-block:: none

    g = [ -90. -108.]




.. GENERATED FROM PYTHON SOURCE LINES 104-106

.. code-block:: Python

    pd.DataFrame(the_function_output.hessian)






.. 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>0</th>
          <th>1</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>-276.0</td>
          <td>-30.0</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-30.0</td>
          <td>-108.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 107-109

.. code-block:: Python

    pd.DataFrame(the_function_output.bhhh)






.. 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>0</th>
          <th>1</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>9900.0</td>
          <td>9720.0</td>
        </tr>
        <tr>
          <th>1</th>
          <td>9720.0</td>
          <td>11664.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 110-111

Now the unscaled version.

.. GENERATED FROM PYTHON SOURCE LINES 111-114

.. code-block:: Python

    the_output: BiogemeFunctionOutput = my_biogeme.calculate_likelihood_and_derivatives(
        xplus, scaled=False, hessian=True, bhhh=True
    )







.. GENERATED FROM PYTHON SOURCE LINES 115-117

.. code-block:: Python

    print(f'f = {the_output.function}')





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

 .. code-block:: none

    f = -555.0




.. GENERATED FROM PYTHON SOURCE LINES 118-120

.. code-block:: Python

    print(f'g = {the_output.gradient}')





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

 .. code-block:: none

    g = [-450. -540.]




.. GENERATED FROM PYTHON SOURCE LINES 121-123

.. code-block:: Python

    pd.DataFrame(the_output.hessian)






.. 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>0</th>
          <th>1</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>-1380.0</td>
          <td>-150.0</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-150.0</td>
          <td>-540.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 124-127

.. code-block:: Python

    pd.DataFrame(the_output.bhhh)







.. 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>0</th>
          <th>1</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>49500.0</td>
          <td>48600.0</td>
        </tr>
        <tr>
          <th>1</th>
          <td>48600.0</td>
          <td>58320.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 128-129

Calculate the hessian of the log likelihood function using finite difference.

.. GENERATED FROM PYTHON SOURCE LINES 129-132

.. code-block:: Python

    fin_diff_hessian = my_biogeme.likelihood_finite_difference_hessian(xplus)
    pd.DataFrame(fin_diff_hessian)






.. 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>0</th>
          <th>1</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>-1380.000202</td>
          <td>-150.000000</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-150.000045</td>
          <td>-540.000054</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 133-136

Check numerically the derivatives' implementation. The analytical
derivatives are compared to the numerical derivatives obtains by
finite differences.

.. GENERATED FROM PYTHON SOURCE LINES 136-138

.. code-block:: Python

    f, g, h, gdiff, hdiff = my_biogeme.check_derivatives(xplus, verbose=True)





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

 .. code-block:: none

    x               Gradient        FinDiff         Difference 
    beta1           -4.500000E+02   -4.500001E+02   +6.934970E-05 
    beta2           -5.400000E+02   -5.400001E+02   +8.087011E-05 
    Row             Col             Hessian FinDiff         Difference 
    beta1           beta1           -1.380000E+03   -1.380000E+03   +2.022890E-04 
    beta1           beta2           -1.500000E+02   -1.500000E+02   +2.425509E-10 
    beta2           beta1           -1.500000E+02   -1.500000E+02   +4.509602E-05 
    beta2           beta2           -5.400000E+02   -5.400001E+02   +5.396423E-05 




.. GENERATED FROM PYTHON SOURCE LINES 139-140

.. code-block:: Python

    print(f'f = {f}')




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

 .. code-block:: none

    f = -555.0




.. GENERATED FROM PYTHON SOURCE LINES 141-142

.. code-block:: Python

    print(f'g = {g}')




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

 .. code-block:: none

    g = [-450. -540.]




.. GENERATED FROM PYTHON SOURCE LINES 143-144

.. code-block:: Python

    pd.DataFrame(h)





.. 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>0</th>
          <th>1</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>-1380.0</td>
          <td>-150.0</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-150.0</td>
          <td>-540.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 145-147

.. code-block:: Python

    pd.DataFrame(gdiff)
    # print(f'gdiff = {gdiff}')





.. 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>0</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.000069</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.000081</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 148-151

.. code-block:: Python

    pd.DataFrame(hdiff)
    # print(f'hdiff = {hdiff}')






.. 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>0</th>
          <th>1</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.000202</td>
          <td>2.425509e-10</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.000045</td>
          <td>5.396423e-05</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 152-154

Estimation
----------

.. GENERATED FROM PYTHON SOURCE LINES 156-157

Estimation of the parameters, with bootstrapping

.. GENERATED FROM PYTHON SOURCE LINES 157-160

.. code-block:: Python

    my_biogeme.bootstrap_samples = 10
    results = my_biogeme.estimate(run_bootstrap=True)





.. 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 __simple_example.iter 
    Parameter values restored from __simple_example.iter 
    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.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0           -0.22             2.1      1.9e+02      0.019       10      1.2   ++ 
        1            -0.6             1.5           93      0.013    1e+02      1.2   ++ 
        2              -1             1.3           70       0.01    1e+03      1.2   ++ 
        3            -1.2             1.3           67     0.0039    1e+04      1.1   ++ 
        4            -1.2             1.3           67    7.2e-05    1e+04        1   ++ 
    Re-estimate the model 10 times for bootstrapping 

      0%|          | 0/10 [00:00<?, ?it/s]Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Iter.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0            -1.3             1.3           74    0.00082       10     0.99   ++ 
        1            -1.3             1.3           74    7.1e-08       10        1   ++ 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Iter.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0            -1.3             1.2           67    1.1e-07        1        1      
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Iter.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0            -1.3             1.3           74    0.00082       10     0.99   ++ 
        1            -1.3             1.3           74    7.1e-08       10        1   ++ 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Iter.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0            -1.3             1.2           63     0.0003       10        1   ++ 
        1            -1.3             1.2           63      1e-08       10        1   ++ 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Iter.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0            -1.3             1.2           56     0.0034       10        1   ++ 
        1            -1.3             1.2           56    1.5e-06       10        1   ++ 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Iter.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0            -1.3             1.2           63     0.0003       10        1   ++ 
        1            -1.3             1.2           63      1e-08       10        1   ++ 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Iter.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0            -1.3             1.1           48      0.012       10        1   ++ 
        1            -1.3             1.1           48    2.1e-05       10        1   ++ 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Iter.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0            -1.3             1.2           63     0.0003       10        1   ++ 
        1            -1.3             1.2           63      1e-08       10        1   ++ 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Iter.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0            -1.3             1.3           78     0.0016       10     0.99   ++ 
        1            -1.3             1.3           78    2.8e-07       10        1   ++ 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Iter.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0            -1.3             1.3           71    0.00023       10        1   ++ 
        1            -1.3             1.3           71    5.8e-09       10        1   ++ 

    100%|██████████| 10/10 [00:00<00:00, 422.80it/s]
    Results saved in file simple_example.html 
    Results saved in file simple_example.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 161-163

.. code-block:: Python

    results.get_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>beta1</th>
          <td>-1.272838</td>
          <td>0.013630</td>
          <td>-93.387994</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta2</th>
          <td>1.248867</td>
          <td>0.059077</td>
          <td>21.139711</td>
          <td>0.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 164-167

If the model has already been estimated, it is possible to recycle
the estimation results. In that case, the other arguments are
ignored, and the results are whatever is in the file.

.. GENERATED FROM PYTHON SOURCE LINES 169-171

.. code-block:: Python

    recycled_results = my_biogeme.estimate(recycle=True, run_bootstrap=True)





.. 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" 
    Estimation results read from simple_example.pickle. There is no guarantee that they correspond to the specified model. 




.. GENERATED FROM PYTHON SOURCE LINES 172-174

.. code-block:: Python

    print(recycled_results.short_summary())





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

 .. code-block:: none

    Results for model simple_example
    Nbr of parameters:              2
    Sample size:                    5
    Excluded data:                  0
    Final log likelihood:           -67.0655
    Akaike Information Criterion:   138.131
    Bayesian Information Criterion: 137.3499





.. GENERATED FROM PYTHON SOURCE LINES 175-177

.. code-block:: Python

    recycled_results.get_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>beta1</th>
          <td>-1.272838</td>
          <td>0.013630</td>
          <td>-93.387994</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta2</th>
          <td>1.248867</td>
          <td>0.059077</td>
          <td>21.139711</td>
          <td>0.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 178-180

Simulation
----------

.. GENERATED FROM PYTHON SOURCE LINES 182-183

Simulate with the initial values for the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 183-188

.. code-block:: Python

    simulation_with_default_betas = my_biogeme.simulate(
        my_biogeme.log_like.get_beta_values()
    )
    simulation_with_default_betas






.. 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>log_like</th>
          <th>beta1</th>
          <th>simul</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>-20.733455</td>
          <td>-1.272838</td>
          <td>-0.229590</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-17.073277</td>
          <td>-1.272838</td>
          <td>-0.286988</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-17.073277</td>
          <td>-1.272838</td>
          <td>-0.286988</td>
        </tr>
        <tr>
          <th>3</th>
          <td>-9.752922</td>
          <td>-1.272838</td>
          <td>-0.573976</td>
        </tr>
        <tr>
          <th>4</th>
          <td>-6.092744</td>
          <td>-1.272838</td>
          <td>-1.147951</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 189-190

Simulate with the estimated values for the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 192-194

.. code-block:: Python

    print(results.get_beta_values())





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

 .. code-block:: none

    {'beta1': np.float64(-1.272838017207035), 'beta2': np.float64(1.248867015967332)}




.. GENERATED FROM PYTHON SOURCE LINES 195-198

.. code-block:: Python

    simulation_with_estimated_betas = my_biogeme.simulate(results.get_beta_values())
    simulation_with_estimated_betas






.. 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>log_like</th>
          <th>beta1</th>
          <th>simul</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>-20.733455</td>
          <td>-1.272838</td>
          <td>-0.229590</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-17.073277</td>
          <td>-1.272838</td>
          <td>-0.286988</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-17.073277</td>
          <td>-1.272838</td>
          <td>-0.286988</td>
        </tr>
        <tr>
          <th>3</th>
          <td>-9.752922</td>
          <td>-1.272838</td>
          <td>-0.573976</td>
        </tr>
        <tr>
          <th>4</th>
          <td>-6.092744</td>
          <td>-1.272838</td>
          <td>-1.147951</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 199-201

Confidence intervals.
First, we extract the values of betas from the bootstrapping draws.

.. GENERATED FROM PYTHON SOURCE LINES 201-207

.. code-block:: Python

    draws_from_betas = results.get_betas_for_sensitivity_analysis(
        my_biogeme.id_manager.free_betas.names
    )
    for draw in draws_from_betas:
        print(draw)





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

 .. code-block:: none

    {'beta1': np.float64(-1.2649797746053077), 'beta2': np.float64(1.284263176431638)}
    {'beta1': np.float64(-1.2732639061775262), 'beta2': np.float64(1.2487688275262538)}
    {'beta1': np.float64(-1.2649797746053077), 'beta2': np.float64(1.284263176431638)}
    {'beta1': np.float64(-1.2777126115403008), 'beta2': np.float64(1.2295568141100899)}
    {'beta1': np.float64(-1.2873325302586314), 'beta2': np.float64(1.1875198336493942)}
    {'beta1': np.float64(-1.2777126115403008), 'beta2': np.float64(1.2295568141100899)}
    {'beta1': np.float64(-1.2981043644725554), 'beta2': np.float64(1.1393509911926116)}
    {'beta1': np.float64(-1.2777126115403008), 'beta2': np.float64(1.22955681411009)}
    {'beta1': np.float64(-1.2611085824685073), 'beta2': np.float64(1.300751700054335)}
    {'beta1': np.float64(-1.2690260405818319), 'beta2': np.float64(1.2669668838241481)}




.. GENERATED FROM PYTHON SOURCE LINES 208-210

Then, we calculate the confidence intervals. The default interval
size is 0.9. Here, we use a different one.

.. GENERATED FROM PYTHON SOURCE LINES 210-213

.. code-block:: Python

    left, right = my_biogeme.confidence_intervals(draws_from_betas, interval_size=0.95)
    left






.. 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>log_like</th>
          <th>beta1</th>
          <th>simul</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>-21.416393</td>
          <td>-1.295681</td>
          <td>-0.236132</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-17.483798</td>
          <td>-1.295681</td>
          <td>-0.295165</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-17.483798</td>
          <td>-1.295681</td>
          <td>-0.295165</td>
        </tr>
        <tr>
          <th>3</th>
          <td>-9.907866</td>
          <td>-1.295681</td>
          <td>-0.590331</td>
        </tr>
        <tr>
          <th>4</th>
          <td>-6.369267</td>
          <td>-1.295681</td>
          <td>-1.180662</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 214-216

.. code-block:: Python

    right






.. 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>log_like</th>
          <th>beta1</th>
          <th>simul</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>-20.523662</td>
          <td>-1.26198</td>
          <td>-0.226455</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-16.985063</td>
          <td>-1.26198</td>
          <td>-0.283069</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-16.985063</td>
          <td>-1.26198</td>
          <td>-0.283069</td>
        </tr>
        <tr>
          <th>3</th>
          <td>-9.618608</td>
          <td>-1.26198</td>
          <td>-0.566138</td>
        </tr>
        <tr>
          <th>4</th>
          <td>-5.686012</td>
          <td>-1.26198</td>
          <td>-1.132275</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 217-227

Validation
----------
The validation consists in organizing the data into several slices
of about the same size, randomly defined.  Each slide is considered
as a validation dataset. The model is then re-estimated using all
the data except the slice, and the estimated model is applied on the
validation set (i.e. the slice). The value of the log likelihood for
each observation in the validation set is reported in a
dataframe. As this is done for each slice, the output is a list of
dataframes, each corresponding to one of these exercises.

.. GENERATED FROM PYTHON SOURCE LINES 229-232

.. code-block:: Python

    validationData = my_data.split(slices=5)
    validation_results = my_biogeme.validate(results, validationData)





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

 .. code-block:: none

    /Users/bierlair/venv312/lib/python3.12/site-packages/numpy/_core/fromnumeric.py:57: FutureWarning: 'DataFrame.swapaxes' is deprecated and will be removed in a future version. Please use 'DataFrame.transpose' instead.
      return bound(*args, **kwds)
    Biogeme parameters read from biogeme.toml. 
    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 __simple_example_val_est_1.iter 
    Cannot read file __simple_example_val_est_1.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.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0            -1.3             1.3           61     0.0012       10     0.99   ++ 
        1            -1.3             1.3           61    1.5e-07       10        1   ++ 
    Results saved in file simple_example_val_est_1.html 
    Results saved in file simple_example_val_est_1.pickle 
    Biogeme parameters read from biogeme.toml. 
    Biogeme parameters read from biogeme.toml. 
    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 __simple_example_val_est_2.iter 
    Cannot read file __simple_example_val_est_2.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.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0            -1.3             1.2           54    1.1e-07        1        1      
    Results saved in file simple_example_val_est_2.html 
    Results saved in file simple_example_val_est_2.pickle 
    Biogeme parameters read from biogeme.toml. 
    Biogeme parameters read from biogeme.toml. 
    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 __simple_example_val_est_3.iter 
    Cannot read file __simple_example_val_est_3.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.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0            -1.3             1.2           46     0.0022       10        1   ++ 
        1            -1.3             1.2           46      6e-07       10        1   ++ 
    Results saved in file simple_example_val_est_3.html 
    Results saved in file simple_example_val_est_3.pickle 
    Biogeme parameters read from biogeme.toml. 
    Biogeme parameters read from biogeme.toml. 
    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 __simple_example_val_est_4.iter 
    Cannot read file __simple_example_val_est_4.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.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0            -1.3             1.2           50    0.00048       10        1   ++ 
        1            -1.3             1.2           50    2.6e-08       10        1   ++ 
    Results saved in file simple_example_val_est_4.html 
    Results saved in file simple_example_val_est_4.pickle 
    Biogeme parameters read from biogeme.toml. 
    Biogeme parameters read from biogeme.toml. 
    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 __simple_example_val_est_5.iter 
    Cannot read file __simple_example_val_est_5.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.           beta1           beta2     Function    Relgrad   Radius      Rho      
        0            -1.3             1.3           57    0.00035       10        1   ++ 
        1            -1.3             1.3           57    1.3e-08       10        1   ++ 
    Results saved in file simple_example_val_est_5.html 
    Results saved in file simple_example_val_est_5.pickle 
    Biogeme parameters read from biogeme.toml. 
    Simulation results saved in file simple_example_validation.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 233-240

.. code-block:: Python

    for slide in validation_results:
        print(
            f'Log likelihood for {slide.shape[0]} '
            f'validation data: {slide["Loglikelihood"].sum()}'
        )






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

 .. code-block:: none

    Log likelihood for 1 validation data: -6.341108764653339
    Log likelihood for 1 validation data: -13.41309809589276
    Log likelihood for 1 validation data: -21.037421356430013
    Log likelihood for 1 validation data: -17.145326445763835
    Log likelihood for 1 validation data: -9.817719764565792




.. GENERATED FROM PYTHON SOURCE LINES 241-243

The following tools is used to find .py with the model name and a
specific extension.

.. GENERATED FROM PYTHON SOURCE LINES 243-244

.. code-block:: Python

    my_biogeme.files_of_type('pickle')




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

 .. code-block:: none


    ['simple_example.pickle']




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

   **Total running time of the script:** (0 minutes 0.161 seconds)


.. _sphx_glr_download_auto_examples_programmers_plot_biogeme.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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