.. 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 15-23

.. code-block:: default


    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








.. GENERATED FROM PYTHON SOURCE LINES 24-25

Version of Biogeme.

.. GENERATED FROM PYTHON SOURCE LINES 25-28

.. code-block:: default

    print(ver.getText())






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

 .. code-block:: none

    biogeme 3.2.13 [2023-12-23]
    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 29-30

Logger.

.. GENERATED FROM PYTHON SOURCE LINES 30-34

.. code-block:: default

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






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

 .. code-block:: none

    Logger initalized 




.. GENERATED FROM PYTHON SOURCE LINES 35-36

Definition of a database

.. GENERATED FROM PYTHON SOURCE LINES 36-50

.. code-block:: default

    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],
        }
    )
    myData = db.Database('test', df)








.. GENERATED FROM PYTHON SOURCE LINES 51-52

Data

.. GENERATED FROM PYTHON SOURCE LINES 52-55

.. code-block:: default

    myData.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 56-57

Definition of various expressions.

.. GENERATED FROM PYTHON SOURCE LINES 57-65

.. code-block:: default

    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
    dictOfExpressions = {'loglike': likelihood, 'beta1': beta1, 'simul': simul}








.. GENERATED FROM PYTHON SOURCE LINES 66-67

Creation of the BIOGEME object.

.. GENERATED FROM PYTHON SOURCE LINES 67-71

.. code-block:: default

    myBiogeme = bio.BIOGEME(myData, dictOfExpressions)
    myBiogeme.modelName = 'simple_example'
    print(myBiogeme)





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

 .. code-block:: none

    File biogeme.toml has been created 
    simple_example: database [test]{'loglike': ((((-(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 72-73

The data is stored in the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 73-75

.. code-block:: default

    myBiogeme.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 76-77

Log likelihood with the initial values of the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 77-79

.. code-block:: default

    myBiogeme.calculateInitLikelihood()





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

 .. code-block:: none


    -115.30029248549191



.. GENERATED FROM PYTHON SOURCE LINES 80-82

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 82-86

.. code-block:: default

    x = myBiogeme.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 87-89

.. code-block:: default

    myBiogeme.calculateLikelihood(xplus, scaled=True)





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

 .. code-block:: none


    -111.0



.. GENERATED FROM PYTHON SOURCE LINES 90-91

Calculate the log-likelihood function and its derivatives.

.. GENERATED FROM PYTHON SOURCE LINES 91-94

.. code-block:: default

    f, g, h, bhhh = myBiogeme.calculateLikelihoodAndDerivatives(
        xplus, scaled=True, hessian=True, bhhh=True
    )







.. GENERATED FROM PYTHON SOURCE LINES 95-97

.. code-block:: default

    print(f'f = {f}')





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

 .. code-block:: none

    f = -111.0




.. GENERATED FROM PYTHON SOURCE LINES 98-100

.. code-block:: default

    print(f'g = {g}')





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

 .. code-block:: none

    g = [ -90. -108.]




.. GENERATED FROM PYTHON SOURCE LINES 101-103

.. code-block:: default

    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>-270.0</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 104-106

.. code-block:: default

    pd.DataFrame(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 107-108

Now the unscaled version.

.. GENERATED FROM PYTHON SOURCE LINES 108-111

.. code-block:: default

    f, g, h, bhhh = myBiogeme.calculateLikelihoodAndDerivatives(
        xplus, scaled=False, hessian=True, bhhh=True
    )







.. GENERATED FROM PYTHON SOURCE LINES 112-114

.. code-block:: default

    print(f'f = {f}')





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

 .. code-block:: none

    f = -555.0




.. GENERATED FROM PYTHON SOURCE LINES 115-117

.. code-block:: default

    print(f'g = {g}')





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

 .. code-block:: none

    g = [-450. -540.]




.. GENERATED FROM PYTHON SOURCE LINES 118-120

.. code-block:: default

    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>-1350.0</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 121-124

.. code-block:: default

    pd.DataFrame(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 125-126

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

.. GENERATED FROM PYTHON SOURCE LINES 126-129

.. code-block:: default

    fin_diff_hessian = myBiogeme.likelihoodFiniteDifferenceHessian(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 130-133

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

.. GENERATED FROM PYTHON SOURCE LINES 133-135

.. code-block:: default

    f, g, h, gdiff, hdiff = myBiogeme.checkDerivatives(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           -1.350000E+03   -1.380000E+03   +3.000020E+01 
    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 136-137

.. code-block:: default

    print(f'f = {f}')




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

 .. code-block:: none

    f = -555.0




.. GENERATED FROM PYTHON SOURCE LINES 138-139

.. code-block:: default

    print(f'g = {g}')




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

 .. code-block:: none

    g = [-450. -540.]




.. GENERATED FROM PYTHON SOURCE LINES 140-141

.. code-block:: default

    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>-1350.0</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 142-144

.. code-block:: default

    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 {
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        }

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          <th></th>
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        </tr>
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      <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 145-148

.. code-block:: default

    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 {
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        }
    </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>30.000202</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 149-151

Estimation
----------

.. GENERATED FROM PYTHON SOURCE LINES 153-154

Estimation of the parameters, with bootstrapping

.. GENERATED FROM PYTHON SOURCE LINES 154-157

.. code-block:: default

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





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

 .. code-block:: none

    *** Initial values of the parameters are obtained from the file __simple_example.iter 
    Parameter values restored from __simple_example.iter 
    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           -0.23             2.1      1.8e+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            -1.3             1.2           67    6.8e-05    1e+05        1   ++ 
        5            -1.3             1.2           67    1.2e-08    1e+05        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             1.1           44      0.021       10        1   ++ 
        1            -1.3             1.1           44    5.9e-05    1e+02        1   ++ 
        2            -1.3             1.1           44    4.1e-08    1e+02        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           52     0.0069       10        1   ++ 
        1            -1.3             1.2           52    6.2e-06    1e+02        1   ++ 
        2            -1.3             1.2           52    1.3e-07    1e+02        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    1.4e-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             1.3           71    0.00023       10        1   ++ 
        1            -1.3             1.3           71    5.8e-09       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           52     0.0069       10        1   ++ 
        1            -1.3             1.2           52    6.2e-06    1e+02        1   ++ 
        2            -1.3             1.2           52    1.3e-07    1e+02        1   ++ 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for 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           71    0.00023       10        1   ++ 
        1            -1.3             1.3           71    5.8e-09       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           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             1.3           81     0.0026       10     0.99   ++ 
        1            -1.3             1.3           81    6.8e-07       10        1   ++ 

    100%|██████████| 10/10 [00:00<00:00, 266.42it/s]
    Results saved in file simple_example.html 
    Results saved in file simple_example.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 158-160

.. code-block:: default

    results.getEstimatedParameters()






.. 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>-1.273264</td>
          <td>0.013724</td>
          <td>-92.776769</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta2</th>
          <td>1.248769</td>
          <td>0.059086</td>
          <td>21.134795</td>
          <td>0.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 161-164

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 166-168

.. code-block:: default

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





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

 .. code-block:: none

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




.. GENERATED FROM PYTHON SOURCE LINES 169-171

.. code-block:: default

    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:           -67.06549
    Akaike Information Criterion:   138.131
    Bayesian Information Criterion: 137.3499





.. GENERATED FROM PYTHON SOURCE LINES 172-174

.. code-block:: default

    recycled_results.getEstimatedParameters()






.. 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>-1.273264</td>
          <td>0.013724</td>
          <td>-92.776769</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta2</th>
          <td>1.248769</td>
          <td>0.059086</td>
          <td>21.134795</td>
          <td>0.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 175-177

Simulation
----------

.. GENERATED FROM PYTHON SOURCE LINES 179-180

Simulate with the initial values for the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 180-183

.. code-block:: default

    simulation_with_default_betas = myBiogeme.simulate(myBiogeme.loglike.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>loglike</th>
          <th>beta1</th>
          <th>simul</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>-101.0</td>
          <td>0.0</td>
          <td>0.15</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-131.0</td>
          <td>0.0</td>
          <td>0.06</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-131.0</td>
          <td>0.0</td>
          <td>0.06</td>
        </tr>
        <tr>
          <th>3</th>
          <td>-131.0</td>
          <td>0.0</td>
          <td>0.06</td>
        </tr>
        <tr>
          <th>4</th>
          <td>-101.0</td>
          <td>0.0</td>
          <td>0.15</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 184-185

Simulate with the estimated values for the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 187-189

.. code-block:: default

    print(results.getBetaValues())





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

 .. code-block:: none

    {'beta1': -1.273263915009374, 'beta2': 1.248768825523196}




.. GENERATED FROM PYTHON SOURCE LINES 190-193

.. code-block:: default

    simulation_with_estimated_betas = myBiogeme.simulate(results.getBetaValues())
    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>loglike</th>
          <th>beta1</th>
          <th>simul</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>-9.752666</td>
          <td>-1.273264</td>
          <td>-0.574194</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-20.733962</td>
          <td>-1.273264</td>
          <td>-0.229677</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-20.733962</td>
          <td>-1.273264</td>
          <td>-0.229677</td>
        </tr>
        <tr>
          <th>3</th>
          <td>-20.733962</td>
          <td>-1.273264</td>
          <td>-0.229677</td>
        </tr>
        <tr>
          <th>4</th>
          <td>-9.752666</td>
          <td>-1.273264</td>
          <td>-0.574194</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 194-196

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

.. GENERATED FROM PYTHON SOURCE LINES 196-202

.. code-block:: default

    draws_from_betas = results.getBetasForSensitivityAnalysis(
        myBiogeme.id_manager.free_betas.names
    )
    for draw in draws_from_betas:
        print(draw)





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

 .. code-block:: none

    {'beta1': -1.304007541668053, 'beta2': 1.1122455742294828}
    {'beta1': -1.264979774201378, 'beta2': 1.2842631765105155}
    {'beta1': -1.292557821467689, 'beta2': 1.1643222175104226}
    {'beta1': -1.2873325336195227, 'beta2': 1.1875198317201634}
    {'beta1': -1.2690260405244749, 'beta2': 1.26696688383924}
    {'beta1': -1.292557821467689, 'beta2': 1.1643222175104226}
    {'beta1': -1.273263915009374, 'beta2': 1.248768825523196}
    {'beta1': -1.2690260405244749, 'beta2': 1.26696688383924}
    {'beta1': -1.264979774201378, 'beta2': 1.2842631765105155}
    {'beta1': -1.2573978799517176, 'beta2': 1.3165120810083317}




.. GENERATED FROM PYTHON SOURCE LINES 203-205

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

.. GENERATED FROM PYTHON SOURCE LINES 205-208

.. code-block:: default

    left, right = myBiogeme.confidenceIntervals(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>loglike</th>
          <th>beta1</th>
          <th>simul</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>-9.958158</td>
          <td>-1.301431</td>
          <td>-0.594518</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-21.652272</td>
          <td>-1.301431</td>
          <td>-0.237807</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-21.652272</td>
          <td>-1.301431</td>
          <td>-0.237807</td>
        </tr>
        <tr>
          <th>3</th>
          <td>-21.652272</td>
          <td>-1.301431</td>
          <td>-0.237807</td>
        </tr>
        <tr>
          <th>4</th>
          <td>-9.958158</td>
          <td>-1.301431</td>
          <td>-0.594518</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 209-211

.. code-block:: default

    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>loglike</th>
          <th>beta1</th>
          <th>simul</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>-9.619739</td>
          <td>-1.259104</td>
          <td>-0.564089</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-20.485149</td>
          <td>-1.259104</td>
          <td>-0.225636</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-20.485149</td>
          <td>-1.259104</td>
          <td>-0.225636</td>
        </tr>
        <tr>
          <th>3</th>
          <td>-20.485149</td>
          <td>-1.259104</td>
          <td>-0.225636</td>
        </tr>
        <tr>
          <th>4</th>
          <td>-9.619739</td>
          <td>-1.259104</td>
          <td>-0.564089</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 212-222

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 224-227

.. code-block:: default

    validationData = myData.split(slices=5)
    validation_results = myBiogeme.validate(results, validationData)





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

 .. code-block:: none

    /Users/bierlair/venv312/lib/python3.12/site-packages/numpy/core/fromnumeric.py:59: FutureWarning: 'DataFrame.swapaxes' is deprecated and will be removed in a future version. Please use 'DataFrame.transpose' instead.
      return bound(*args, **kwds)
    File biogeme.toml has been parsed. 
    *** 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. 
    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_1.html 
    Results saved in file simple_example_val_est_1.pickle 
    File biogeme.toml has been parsed. 
    File biogeme.toml has been parsed. 
    *** 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. 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Results saved in file simple_example_val_est_2.html 
    Results saved in file simple_example_val_est_2.pickle 
    File biogeme.toml has been parsed. 
    File biogeme.toml has been parsed. 
    *** 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. 
    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_3.html 
    Results saved in file simple_example_val_est_3.pickle 
    File biogeme.toml has been parsed. 
    File biogeme.toml has been parsed. 
    *** 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. 
    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_4.html 
    Results saved in file simple_example_val_est_4.pickle 
    File biogeme.toml has been parsed. 
    File biogeme.toml has been parsed. 
    *** 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. 
    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_5.html 
    Results saved in file simple_example_val_est_5.pickle 
    File biogeme.toml has been parsed. 
    Simulation results saved in file simple_example_validation.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 228-235

.. code-block:: default

    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: -17.145326446024075
    Log likelihood for 1 validation data: -13.413098095892746
    Log likelihood for 1 validation data: -9.81771976465043
    Log likelihood for 1 validation data: -6.341108765392212
    Log likelihood for 1 validation data: -21.03742136293277




.. GENERATED FROM PYTHON SOURCE LINES 236-238

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

.. GENERATED FROM PYTHON SOURCE LINES 238-239

.. code-block:: default

    myBiogeme.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 0.232 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-python

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

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

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


.. only:: html

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

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