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

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

.. _sphx_glr_auto_examples_programmers_plot_results.py:


biogeme.results
===============

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: Wed Nov 29 09:44:41 2023

.. GENERATED FROM PYTHON SOURCE LINES 15-23

.. code-block:: default

    import pandas as pd
    from biogeme.version import getText
    import biogeme.biogeme as bio
    import biogeme.database as db
    import biogeme.results as res
    from biogeme.expressions import Beta, Variable, exp









.. GENERATED FROM PYTHON SOURCE LINES 24-25

Version of Biogeme.

.. GENERATED FROM PYTHON SOURCE LINES 25-27

.. code-block:: default

    print(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 28-29

Definition of a database

.. GENERATED FROM PYTHON SOURCE LINES 29-43

.. 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],
        }
    )
    df






.. 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 44-46

.. code-block:: default

    my_data = db.Database('test', df)








.. GENERATED FROM PYTHON SOURCE LINES 47-48

Definition of various expressions

.. GENERATED FROM PYTHON SOURCE LINES 48-56

.. 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
    dict_of_expressions = {'loglike': likelihood, 'beta1': beta1, 'simul': simul}








.. GENERATED FROM PYTHON SOURCE LINES 57-58

Creation of the BIOGEME object

.. GENERATED FROM PYTHON SOURCE LINES 58-64

.. code-block:: default

    my_biogeme = bio.BIOGEME(my_data, dict_of_expressions)
    my_biogeme.modelName = 'simple_example'
    my_biogeme.bootstrap_samples = 10
    results = my_biogeme.estimate(run_bootstrap=True)
    print(results)





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

 .. code-block:: none


      0%|          | 0/10 [00:00<?, ?it/s]
    100%|██████████| 10/10 [00:00<00:00, 629.72it/s]

    Results for model simple_example
    Output file (HTML):                     simple_example~00.html
    Nbr of parameters:              2
    Sample size:                    5
    Excluded data:                  0
    Init log likelihood:            -67.38866
    Final log likelihood:           -67.06549
    Likelihood ratio test (init):           0.64633
    Rho square (init):                      0.0048
    Rho bar square (init):                  -0.0249
    Akaike Information Criterion:   138.131
    Bayesian Information Criterion: 137.3499
    Final gradient norm:            8.367978e-05
    beta1          : -1.27[0.115 -11.1 0][0.0137 -92.8 0][0.0111 -115 0]
    beta2          : 1.25[0.0848 14.7 0][0.0591 21.1 0][0.0478 26.1 0]
    ('beta2', 'beta1'):     0.00167 0.171   19.3    0       0.000811        1       55.6    0





.. GENERATED FROM PYTHON SOURCE LINES 65-66

Dump results on a file

.. GENERATED FROM PYTHON SOURCE LINES 66-69

.. code-block:: default

    the_pickle_file = results.writePickle()
    print(the_pickle_file)





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

 .. code-block:: none

    simple_example~01.pickle




.. GENERATED FROM PYTHON SOURCE LINES 70-71

Results can be imported from a file previously generated

.. GENERATED FROM PYTHON SOURCE LINES 71-74

.. code-block:: default

    read_results = res.bioResults(pickleFile=the_pickle_file)
    print(read_results)





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

 .. code-block:: none


    Results for model simple_example
    Output file (HTML):                     simple_example~00.html
    Nbr of parameters:              2
    Sample size:                    5
    Excluded data:                  0
    Init log likelihood:            -67.38866
    Final log likelihood:           -67.06549
    Likelihood ratio test (init):           0.64633
    Rho square (init):                      0.0048
    Rho bar square (init):                  -0.0249
    Akaike Information Criterion:   138.131
    Bayesian Information Criterion: 137.3499
    Final gradient norm:            8.367978e-05
    beta1          : -1.27[0.115 -11.1 0][0.0137 -92.8 0][0.0111 -115 0]
    beta2          : 1.25[0.0848 14.7 0][0.0591 21.1 0][0.0478 26.1 0]
    ('beta2', 'beta1'):     0.00167 0.171   19.3    0       0.000811        1       55.6    0





.. GENERATED FROM PYTHON SOURCE LINES 75-76

Results can be formatted in LaTeX

.. GENERATED FROM PYTHON SOURCE LINES 76-78

.. code-block:: default

    print(read_results.getLaTeX())





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

 .. code-block:: none

    %% This file is designed to be included into a LaTeX document
    %% See http://www.latex-project.org for information about LaTeX
    %% simple_example - Report from biogeme 3.2.13 [2023-12-23]
    %% biogeme 3.2.13 [2023-12-23]
    %% Version entirely written in Python
    %% 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)

    %% This file has automatically been generated on 2023-12-23 19:11:07.608823</p>

    %%Database name: test

    %% General statistics
    \section{General statistics}
    \begin{tabular}{ll}
    Number of estimated parameters & 2 \\
    Sample size & 5 \\
    Excluded observations & 0 \\
    Init log likelihood & -67.38866 \\
    Final log likelihood & -67.06549 \\
    Likelihood ratio test for the init. model & 0.64633 \\
    Rho-square for the init. model & 0.0048 \\
    Rho-square-bar for the init. model & -0.0249 \\
    Akaike Information Criterion & 138.131 \\
    Bayesian Information Criterion & 137.3499 \\
    Final gradient norm & 8.3680E-05 \\
    Bootstrapping time & 0:00:00.016320 \\
    Nbr of threads & 12 \\
    Relative gradient & \verb$1.5409993756401287e-06$ \\
    Cause of termination & \verb$Relative gradient = 1.5e-06 <= 6.1e-06$ \\
    Number of function evaluations & \verb$3$ \\
    Number of gradient evaluations & \verb$3$ \\
    Number of hessian evaluations & \verb$2$ \\
    Algorithm & \verb$Newton with trust region for simple bound constraints$ \\
    Number of iterations & \verb$2$ \\
    Proportion of Hessian calculation & \verb$2/2 = 100.0%$ \\
    Optimization time & \verb$0:00:00.003161$ \\
    \end{tabular}

    %%Parameter estimates
    \section{Parameter estimates}
    \begin{tabular}{lrrrr}
     & Value & Rob. Std err & Rob. t-test & Rob. p-value \\
    beta1 & -1.27 & 0.0137 & -92.8 & 0.0 \\
    beta2 & 1.25 & 0.0591 & 21.1 & 0.0 \\
    \end{tabular}

    %%Correlation
    \section{Correlation}
    \begin{tabular}{lrrrrrrrrrrrr}
     & Covariance & Correlation & t-test & p-value & Rob. cov. & Rob. corr. & Rob. t-test & Rob. p-value & Boot. cov. & Boot. corr. & Boot. t-test & Boot. p-value \\
    beta2-beta1 & 0.00167 & 0.171 & 19.3 & 0.0 & 0.000811 & 1.0 & 55.6 & 0.0 & 0.000531 & 1.0 & 68.6 & 0.0 \\
    \end{tabular}





.. GENERATED FROM PYTHON SOURCE LINES 79-80

Results can be formatted in HTML

.. GENERATED FROM PYTHON SOURCE LINES 80-82

.. code-block:: default

    print(read_results.getHtml())





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

 .. code-block:: none

    <html>
    <head>
    <script src="http://transp-or.epfl.ch/biogeme/sorttable.js"></script>
    <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
    <title>simple_example - Report from biogeme 3.2.13 [2023-12-23]</title>
    <meta name="keywords" content="biogeme, discrete choice, random utility">
    <meta name="description" content="Report from biogeme 3.2.13 [2023-12-23]">
    <meta name="author" content="{bv.author}">
    <style type=text/css>
    .biostyle
            {font-size:10.0pt;
            font-weight:400;
            font-style:normal;
            font-family:Courier;}
    .boundstyle
            {font-size:10.0pt;
            font-weight:400;
            font-style:normal;
            font-family:Courier;
            color:red}
    </style>
    </head>
    <body bgcolor="#ffffff">
    <p>biogeme 3.2.13 [2023-12-23]</p>
    <p><a href="https://www.python.org/" target="_blank">Python</a> package</p>
    <p>Home page: <a href="http://biogeme.epfl.ch" target="_blank">http://biogeme.epfl.ch</a></p>
    <p>Submit questions to <a href="https://groups.google.com/d/forum/biogeme" target="_blank">https://groups.google.com/d/forum/biogeme</a></p>
    <p><a href="http://people.epfl.ch/michel.bierlaire">Michel Bierlaire</a>, <a href="http://transp-or.epfl.ch">Transport and Mobility Laboratory</a>, <a href="http://www.epfl.ch">Ecole Polytechnique F&#233;d&#233;rale de Lausanne (EPFL)</a></p>
    <p>This file has automatically been generated on 2023-12-23 19:11:07.630521</p>
    <table>
    <tr class=biostyle><td align=right><strong>Report file</strong>:        </td><td>simple_example~00.html</td></tr>
    <tr class=biostyle><td align=right><strong>Database name</strong>:      </td><td>test</td></tr>
    </table>
    <h1>Estimation report</h1>
    <table border="0">
    <tr class=biostyle><td align=right ><strong>Number of estimated parameters</strong>: </td> <td>2</td></tr>
    <tr class=biostyle><td align=right ><strong>Sample size</strong>: </td> <td>5</td></tr>
    <tr class=biostyle><td align=right ><strong>Excluded observations</strong>: </td> <td>0</td></tr>
    <tr class=biostyle><td align=right ><strong>Init log likelihood</strong>: </td> <td>-67.38866</td></tr>
    <tr class=biostyle><td align=right ><strong>Final log likelihood</strong>: </td> <td>-67.06549</td></tr>
    <tr class=biostyle><td align=right ><strong>Likelihood ratio test for the init. model</strong>: </td> <td>0.64633</td></tr>
    <tr class=biostyle><td align=right ><strong>Rho-square for the init. model</strong>: </td> <td>0.0048</td></tr>
    <tr class=biostyle><td align=right ><strong>Rho-square-bar for the init. model</strong>: </td> <td>-0.0249</td></tr>
    <tr class=biostyle><td align=right ><strong>Akaike Information Criterion</strong>: </td> <td>138.131</td></tr>
    <tr class=biostyle><td align=right ><strong>Bayesian Information Criterion</strong>: </td> <td>137.3499</td></tr>
    <tr class=biostyle><td align=right ><strong>Final gradient norm</strong>: </td> <td>8.3680E-05</td></tr>
    <tr class=biostyle><td align=right ><strong>Bootstrapping time</strong>: </td> <td>0:00:00.016320</td></tr>
    <tr class=biostyle><td align=right ><strong>Nbr of threads</strong>: </td> <td>12</td></tr>
    <tr class=biostyle><td align=right ><strong>Relative gradient</strong>: </td> <td>1.5409993756401287e-06</td></tr>
    <tr class=biostyle><td align=right ><strong>Cause of termination</strong>: </td> <td>Relative gradient = 1.5e-06 <= 6.1e-06</td></tr>
    <tr class=biostyle><td align=right ><strong>Number of function evaluations</strong>: </td> <td>3</td></tr>
    <tr class=biostyle><td align=right ><strong>Number of gradient evaluations</strong>: </td> <td>3</td></tr>
    <tr class=biostyle><td align=right ><strong>Number of hessian evaluations</strong>: </td> <td>2</td></tr>
    <tr class=biostyle><td align=right ><strong>Algorithm</strong>: </td> <td>Newton with trust region for simple bound constraints</td></tr>
    <tr class=biostyle><td align=right ><strong>Number of iterations</strong>: </td> <td>2</td></tr>
    <tr class=biostyle><td align=right ><strong>Proportion of Hessian calculation</strong>: </td> <td>2/2 = 100.0%</td></tr>
    <tr class=biostyle><td align=right ><strong>Optimization time</strong>: </td> <td>0:00:00.003161</td></tr>
    </table>
    <h1>Estimated parameters</h1>
    <table border="1">
    <tr class=biostyle><th>Name</th><th>Value</th><th>Rob. Std err</th><th>Rob. t-test</th><th>Rob. p-value</th></tr>
    <tr class=biostyle><td>beta1</td><td>-1.27</td><td>0.0137</td><td>-92.8</td><td>0</td></tr>
    <tr class=biostyle><td>beta2</td><td>1.25</td><td>0.0591</td><td>21.1</td><td>0</td></tr>
    </table>
    <h2>Correlation of coefficients</h2>
    <table border="1">
    <tr class=biostyle><th>Coefficient1</th><th>Coefficient2</th><th>Covariance</th><th>Correlation</th><th>t-test</th><th>p-value</th><th>Rob. cov.</th><th>Rob. corr.</th><th>Rob. t-test</th><th>Rob. p-value</th><th>Boot. cov.</th><th>Boot. corr.</th><th>Boot. t-test</th><th>Boot. p-value</th></tr>
    <tr class=biostyle><td>beta2</td><td>beta1</td><td>0.00167</td><td>0.171</td><td>19.3</td><td>0</td><td>0.000811</td><td>1</td><td>55.6</td><td>0</td><td>0.000531</td><td>1</td><td>68.6</td><td>0</td></tr>
    </table>
    <p>Smallest eigenvalue: 73.054</p>
    <p>Largest eigenvalue: 147.802</p>
    <p>Condition number: 2.02319</p>
    </html>




.. GENERATED FROM PYTHON SOURCE LINES 83-84

General statistics, including a suggested format.

.. GENERATED FROM PYTHON SOURCE LINES 84-87

.. code-block:: default

    statistics = read_results.getGeneralStatistics()
    statistics





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

 .. code-block:: none


    {'Number of estimated parameters': GeneralStatistic(value=2, format=''), 'Sample size': GeneralStatistic(value=5, format=''), 'Excluded observations': GeneralStatistic(value=0, format=''), 'Init log likelihood': GeneralStatistic(value=-67.38865550201763, format='.7g'), 'Final log likelihood': GeneralStatistic(value=-67.0654904794877, format='.7g'), 'Likelihood ratio test for the init. model': GeneralStatistic(value=0.646330045059841, format='.7g'), 'Rho-square for the init. model': GeneralStatistic(value=0.004795540438111923, format='.3g'), 'Rho-square-bar for the init. model': GeneralStatistic(value=-0.024883045447017027, format='.3g'), 'Akaike Information Criterion': GeneralStatistic(value=138.1309809589754, format='.7g'), 'Bayesian Information Criterion': GeneralStatistic(value=137.34985678384362, format='.7g'), 'Final gradient norm': GeneralStatistic(value=8.367978491514103e-05, format='.4E'), 'Bootstrapping time': GeneralStatistic(value=datetime.timedelta(microseconds=16320), format=''), 'Nbr of threads': GeneralStatistic(value=12, format='')}



.. GENERATED FROM PYTHON SOURCE LINES 88-89

The suggested format can be used as follows

.. GENERATED FROM PYTHON SOURCE LINES 89-92

.. code-block:: default

    for k, (v, p) in statistics.items():
        print(f'{k}:\t{v:{p}}')





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

 .. code-block:: none

    Number of estimated parameters: 2
    Sample size:    5
    Excluded observations:  0
    Init log likelihood:    -67.38866
    Final log likelihood:   -67.06549
    Likelihood ratio test for the init. model:      0.64633
    Rho-square for the init. model: 0.0048
    Rho-square-bar for the init. model:     -0.0249
    Akaike Information Criterion:   138.131
    Bayesian Information Criterion: 137.3499
    Final gradient norm:    8.3680E-05
    Bootstrapping time:     0:00:00.016320
    Nbr of threads: 12




.. GENERATED FROM PYTHON SOURCE LINES 93-94

This result can be generated directly with the following function

.. GENERATED FROM PYTHON SOURCE LINES 94-96

.. code-block:: default

    print(results.printGeneralStatistics())





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

 .. code-block:: none

    Number of estimated parameters: 2
    Sample size:    5
    Excluded observations:  0
    Init log likelihood:    -67.38866
    Final log likelihood:   -67.06549
    Likelihood ratio test for the init. model:      0.64633
    Rho-square for the init. model: 0.0048
    Rho-square-bar for the init. model:     -0.0249
    Akaike Information Criterion:   138.131
    Bayesian Information Criterion: 137.3499
    Final gradient norm:    8.3680E-05
    Bootstrapping time:     0:00:00.016320
    Nbr of threads: 12





.. GENERATED FROM PYTHON SOURCE LINES 97-98

Estimated parameters as pandas dataframe

.. GENERATED FROM PYTHON SOURCE LINES 98-100

.. code-block:: default

    read_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>-92.776551</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta2</th>
          <td>1.248769</td>
          <td>0.059086</td>
          <td>21.134825</td>
          <td>0.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 101-102

Correlation results

.. GENERATED FROM PYTHON SOURCE LINES 102-104

.. code-block:: default

    read_results.getCorrelationResults()






.. 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>Covariance</th>
          <th>Correlation</th>
          <th>t-test</th>
          <th>p-value</th>
          <th>Rob. cov.</th>
          <th>Rob. corr.</th>
          <th>Rob. t-test</th>
          <th>Rob. p-value</th>
          <th>Boot. cov.</th>
          <th>Boot. corr.</th>
          <th>Boot. t-test</th>
          <th>Boot. p-value</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>beta2-beta1</th>
          <td>0.001671</td>
          <td>0.171121</td>
          <td>19.280045</td>
          <td>0.0</td>
          <td>0.000811</td>
          <td>1.0</td>
          <td>55.598081</td>
          <td>0.0</td>
          <td>0.000531</td>
          <td>0.999983</td>
          <td>68.644339</td>
          <td>0.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 105-106

Obtain the values of the parameters

.. GENERATED FROM PYTHON SOURCE LINES 106-108

.. code-block:: default

    read_results.getBetaValues()





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

 .. code-block:: none


    {'beta1': -1.2732639720980743, 'beta2': 1.2487693919282536}



.. GENERATED FROM PYTHON SOURCE LINES 109-110

Obtain the value of one or several specific parameters

.. GENERATED FROM PYTHON SOURCE LINES 110-112

.. code-block:: default

    read_results.getBetaValues(myBetas=['beta2'])





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

 .. code-block:: none


    {'beta2': 1.2487693919282536}



.. GENERATED FROM PYTHON SOURCE LINES 113-114

Variance-covariance matrix (Rao-Cramer)

.. GENERATED FROM PYTHON SOURCE LINES 114-116

.. code-block:: default

    read_results.getVarCovar()






.. 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>beta1</th>
          <th>beta2</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>beta1</th>
          <td>0.013258</td>
          <td>0.001671</td>
        </tr>
        <tr>
          <th>beta2</th>
          <td>0.001671</td>
          <td>0.007196</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 117-118

Variance-covariance matrix (robust)

.. GENERATED FROM PYTHON SOURCE LINES 118-120

.. code-block:: default

    read_results.getRobustVarCovar()






.. 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>beta1</th>
          <th>beta2</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>beta1</th>
          <td>0.000188</td>
          <td>0.000811</td>
        </tr>
        <tr>
          <th>beta2</th>
          <td>0.000811</td>
          <td>0.003491</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 121-122

Variance-covaraince matrix (bootstrap)

.. GENERATED FROM PYTHON SOURCE LINES 122-124

.. code-block:: default

    read_results.getBootstrapVarCovar()






.. 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>beta1</th>
          <th>beta2</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>beta1</th>
          <td>0.000123</td>
          <td>0.000531</td>
        </tr>
        <tr>
          <th>beta2</th>
          <td>0.000531</td>
          <td>0.002289</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 125-128

Draws for sensitivity analysis are generated using
bootstrapping. Any indicator can be generated by the model for each
draw, and its empirical distribution can be investigate .

.. GENERATED FROM PYTHON SOURCE LINES 128-130

.. code-block:: default

    read_results.getBetasForSensitivityAnalysis(['beta1', 'beta2'], size=10)





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

 .. code-block:: none


    [{'beta1': -1.2873325336225045, 'beta2': 1.1875198317410949}, {'beta1': -1.2823937362841489, 'beta2': 1.2091956038649867}, {'beta1': -1.2690260405244391, 'beta2': 1.2669668838389574}, {'beta1': -1.2823937362841489, 'beta2': 1.2091956038649867}, {'beta1': -1.2573978799505356, 'beta2': 1.3165120809997202}, {'beta1': -1.2873325336225045, 'beta2': 1.1875198317410949}, {'beta1': -1.269026040524439, 'beta2': 1.2669668838389574}, {'beta1': -1.2777126116343218, 'beta2': 1.2295568140736606}, {'beta1': -1.2573978799505356, 'beta2': 1.3165120809997202}, {'beta1': -1.2732639720980743, 'beta2': 1.2487693919282536}]



.. GENERATED FROM PYTHON SOURCE LINES 131-132

Results can be produced in the ALOGIT F12 format

.. GENERATED FROM PYTHON SOURCE LINES 132-134

.. code-block:: default

    print(read_results.getF12())





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

 .. code-block:: none

                                                                     simple_example
    From biogeme 3.2.13                                     2023-12-23 19:11:07  
    END
       0      beta1 F  -1.273263972098e+00 +1.372398469903e-02
       0      beta2 F  +1.248769391928e+00 +5.908586258958e-02
      -1
           5                  0                   0 -6.706549047949e+01
       0   0  2023-12-23 19:11:07
      99999





.. GENERATED FROM PYTHON SOURCE LINES 135-136

Miscellaneous functions

.. GENERATED FROM PYTHON SOURCE LINES 138-139

Likelihood ratio test. Let's first estimate a constrained model

.. GENERATED FROM PYTHON SOURCE LINES 141-152

.. code-block:: default

    beta2_constrained = Beta('beta2_constrained', 2.0, -3, 10, 1)
    likelihood_constrained = (
        -(beta1**2) * Variable1
        - exp(beta2_constrained * beta1) * Variable2
        - beta2_constrained**4
    )
    my_biogeme_constrained = bio.BIOGEME(my_data, likelihood_constrained)
    my_biogeme_constrained.modelName = 'simple_example_constrained'
    results_constrained = my_biogeme_constrained.estimate()
    print(results_constrained.short_summary())





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

 .. code-block:: none

    Results for model simple_example_constrained
    Nbr of parameters:              1
    Sample size:                    5
    Excluded data:                  0
    Final log likelihood:           -114.7702
    Akaike Information Criterion:   231.5403
    Bayesian Information Criterion: 231.1498





.. GENERATED FROM PYTHON SOURCE LINES 153-154

We can now perform a likelihood ratio test.

.. GENERATED FROM PYTHON SOURCE LINES 154-159

.. code-block:: default

    test_results = results.likelihood_ratio_test(results_constrained, 0.95)
    print(test_results.message)
    print(f'Statistic: {test_results.statistic}')
    print(f'Threshold: {test_results.threshold}')





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

 .. code-block:: none

    H0 can be rejected at level 95.0%
    Statistic: 95.40936413211196
    Threshold: 0.003932140000019531




.. GENERATED FROM PYTHON SOURCE LINES 160-161

Calculation of the :math:`p`-value

.. GENERATED FROM PYTHON SOURCE LINES 161-163

.. code-block:: default

    res.calcPValue(1.96)





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

 .. code-block:: none


    0.04999579029644097



.. GENERATED FROM PYTHON SOURCE LINES 164-165

Compilation of results

.. GENERATED FROM PYTHON SOURCE LINES 165-167

.. code-block:: default

    dict_of_results = {'Model A': read_results, 'Model B': the_pickle_file}








.. GENERATED FROM PYTHON SOURCE LINES 168-170

.. code-block:: default

    df = res.compile_estimation_results(dict_of_results)
    df




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

 .. code-block:: none


    (                                       Model A         Model B
    Number of estimated parameters               2               2
    Sample size                                  5               5
    Final log likelihood                 -67.06549       -67.06549
    Akaike Information Criterion        138.130981      138.130981
    Bayesian Information Criterion      137.349857      137.349857
    beta1 (t-test)                  -1.27  (-92.8)  -1.27  (-92.8)
    beta2 (t-test)                    1.25  (21.1)    1.25  (21.1), {'Model A': 'Model A', 'Model B': 'Model B'})




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

   **Total running time of the script:** (0 minutes 0.081 seconds)


.. _sphx_glr_download_auto_examples_programmers_plot_results.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_results.py <plot_results.py>`

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

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


.. only:: html

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

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