.. 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 15-24

.. code-block:: Python


    import pandas as pd
    from biogeme.version import get_text
    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 25-26

Version of Biogeme.

.. GENERATED FROM PYTHON SOURCE LINES 26-28

.. code-block:: Python

    print(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 29-30

Definition of a database

.. GENERATED FROM PYTHON SOURCE LINES 30-44

.. 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],
        }
    )
    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 45-47

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 48-49

Definition of various expressions

.. GENERATED FROM PYTHON SOURCE LINES 49-57

.. 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 58-59

Creation of the BIOGEME object

.. GENERATED FROM PYTHON SOURCE LINES 59-65

.. code-block:: Python

    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, 440.33it/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:            -67.08858
    Final log likelihood:           -67.06549
    Likelihood ratio test (init):           0.04618125
    Rho square (init):                      0.000344
    Rho bar square (init):                  -0.0295
    Akaike Information Criterion:   138.131
    Bayesian Information Criterion: 137.3499
    Final gradient norm:            3.900312e-07
    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 66-67

Dump results on a file

.. GENERATED FROM PYTHON SOURCE LINES 67-70

.. code-block:: Python

    the_pickle_file = results.write_pickle()
    print(the_pickle_file)





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

 .. code-block:: none

    simple_example~01.pickle




.. GENERATED FROM PYTHON SOURCE LINES 71-72

Results can be imported from a file previously generated

.. GENERATED FROM PYTHON SOURCE LINES 72-75

.. code-block:: Python

    read_results = res.bioResults(pickle_file=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:            -67.08858
    Final log likelihood:           -67.06549
    Likelihood ratio test (init):           0.04618125
    Rho square (init):                      0.000344
    Rho bar square (init):                  -0.0295
    Akaike Information Criterion:   138.131
    Bayesian Information Criterion: 137.3499
    Final gradient norm:            3.900312e-07
    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 76-77

Results can be formatted in LaTeX

.. GENERATED FROM PYTHON SOURCE LINES 77-79

.. code-block:: Python

    print(read_results.get_latex())





.. 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 3.2.14 [2024-08-05]
    %% biogeme 3.2.14 [2024-08-05]
    %% 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 2024-08-05 20:01:27.541772</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 & -67.08858 \\
    Final log likelihood & -67.06549 \\
    Likelihood ratio test for the init. model & 0.04618125 \\
    Rho-square for the init. model & 0.000344 \\
    Rho-square-bar for the init. model & -0.0295 \\
    Akaike Information Criterion & 138.131 \\
    Bayesian Information Criterion & 137.3499 \\
    Final gradient norm & 3.9003E-07 \\
    Bootstrapping time & 0:00:00.023199 \\
    Nbr of threads & 12 \\
    Relative gradient & \verb$7.1957442139436635e-09$ \\
    Cause of termination & \verb$Relative gradient = 7.2e-09 <= 0.00012$ \\
    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$0:00:00.003449$ \\
    \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 80-81

Results can be formatted in HTML

.. GENERATED FROM PYTHON SOURCE LINES 81-83

.. code-block:: Python

    print(read_results.get_html())





.. 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 3.2.14 [2024-08-05]</title>
    <meta name="keywords" content="biogeme, discrete choice, random utility">
    <meta name="description" content="Report from biogeme 3.2.14 [2024-08-05]">
    <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 3.2.14 [2024-08-05]</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 2024-08-05 20:01:27.544784</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>-67.08858</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>0.04618125</td></tr>
    <tr class=biostyle><td align=right ><strong>Rho-square for the init. model</strong>: </td> <td>0.000344</td></tr>
    <tr class=biostyle><td align=right ><strong>Rho-square-bar for the init. model</strong>: </td> <td>-0.0295</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>3.9003E-07</td></tr>
    <tr class=biostyle><td align=right ><strong>Bootstrapping time</strong>: </td> <td>0:00:00.023199</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>7.1957442139436635e-09</td></tr>
    <tr class=biostyle><td align=right ><strong>Cause of termination</strong>: </td> <td>Relative gradient = 7.2e-09 <= 0.00012</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>0:00:00.003449</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: 2.02318</p>
    </html>




.. GENERATED FROM PYTHON SOURCE LINES 84-85

General statistics, including a suggested format.

.. GENERATED FROM PYTHON SOURCE LINES 85-88

.. code-block:: Python

    statistics = read_results.get_general_statistics()
    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=-67.08858110351106, format='.7g'), 'Final log likelihood': GeneralStatistic(value=-67.06549047946356, format='.7g'), 'Likelihood ratio test for the init. model': GeneralStatistic(value=0.04618124809499591, format='.7g'), 'Rho-square for the init. model': GeneralStatistic(value=np.float64(0.00034418113586087706), format='.3g'), 'Rho-square-bar for the init. model': GeneralStatistic(value=np.float64(-0.029467151390522472), format='.3g'), 'Akaike Information Criterion': GeneralStatistic(value=138.13098095892713, format='.7g'), 'Bayesian Information Criterion': GeneralStatistic(value=np.float64(137.34985678379533), format='.7g'), 'Final gradient norm': GeneralStatistic(value=3.9003122659206894e-07, format='.4E'), 'Bootstrapping time': GeneralStatistic(value=datetime.timedelta(microseconds=23199), format=''), 'Nbr of threads': GeneralStatistic(value=12, format='')}



.. GENERATED FROM PYTHON SOURCE LINES 89-90

The suggested format can be used as follows

.. GENERATED FROM PYTHON SOURCE LINES 90-93

.. code-block:: Python

    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:    -67.08858
    Final log likelihood:   -67.06549
    Likelihood ratio test for the init. model:      0.04618125
    Rho-square for the init. model: 0.000344
    Rho-square-bar for the init. model:     -0.0295
    Akaike Information Criterion:   138.131
    Bayesian Information Criterion: 137.3499
    Final gradient norm:    3.9003E-07
    Bootstrapping time:     0:00:00.023199
    Nbr of threads: 12




.. GENERATED FROM PYTHON SOURCE LINES 94-95

This result can be generated directly with the following function

.. GENERATED FROM PYTHON SOURCE LINES 95-97

.. code-block:: Python

    print(results.print_general_statistics())





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

 .. code-block:: none

    Number of estimated parameters: 2
    Sample size:    5
    Excluded observations:  0
    Init log likelihood:    -67.08858
    Final log likelihood:   -67.06549
    Likelihood ratio test for the init. model:      0.04618125
    Rho-square for the init. model: 0.000344
    Rho-square-bar for the init. model:     -0.0295
    Akaike Information Criterion:   138.131
    Bayesian Information Criterion: 137.3499
    Final gradient norm:    3.9003E-07
    Bootstrapping time:     0:00:00.023199
    Nbr of threads: 12





.. GENERATED FROM PYTHON SOURCE LINES 98-99

Estimated parameters as pandas dataframe

.. GENERATED FROM PYTHON SOURCE LINES 99-101

.. code-block:: Python

    read_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>-1.273264</td>
          <td>0.013724</td>
          <td>-92.776663</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta2</th>
          <td>1.248769</td>
          <td>0.059086</td>
          <td>21.134794</td>
          <td>0.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 102-103

Correlation results

.. GENERATED FROM PYTHON SOURCE LINES 103-105

.. code-block:: Python

    read_results.get_correlation_results()






.. 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>19.280039</td>
          <td>0.0</td>
          <td>0.000811</td>
          <td>1.0</td>
          <td>55.597975</td>
          <td>0.0</td>
          <td>0.000531</td>
          <td>0.999983</td>
          <td>68.644336</td>
          <td>0.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 106-107

Obtain the values of the parameters

.. GENERATED FROM PYTHON SOURCE LINES 107-109

.. code-block:: Python

    read_results.get_beta_values()





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

 .. code-block:: none


    {'beta1': np.float64(-1.2732639874991436), 'beta2': np.float64(1.2487688117902658)}



.. GENERATED FROM PYTHON SOURCE LINES 110-111

Obtain the value of one or several specific parameters

.. GENERATED FROM PYTHON SOURCE LINES 111-113

.. code-block:: Python

    read_results.get_beta_values(my_betas=['beta2'])





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

 .. code-block:: none


    {'beta2': np.float64(1.2487688117902658)}



.. GENERATED FROM PYTHON SOURCE LINES 114-115

Variance-covariance matrix (Rao-Cramer)

.. GENERATED FROM PYTHON SOURCE LINES 115-117

.. code-block:: Python

    read_results.get_var_covar()






.. 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 118-119

Variance-covariance matrix (robust)

.. GENERATED FROM PYTHON SOURCE LINES 119-121

.. code-block:: Python

    read_results.get_robust_var_covar()






.. 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 122-123

Variance-covaraince matrix (bootstrap)

.. GENERATED FROM PYTHON SOURCE LINES 123-125

.. code-block:: Python

    read_results.get_bootstrap_var_covar()






.. 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 126-129

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 investigated.

.. GENERATED FROM PYTHON SOURCE LINES 129-131

.. code-block:: Python

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





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

 .. code-block:: none


    [{'beta1': np.float64(-1.2873325336200956), 'beta2': np.float64(1.1875198317199467)}, {'beta1': np.float64(-1.2823937362836413), 'beta2': np.float64(1.209195603860152)}, {'beta1': np.float64(-1.2690260405244642), 'beta2': np.float64(1.2669668838392414)}, {'beta1': np.float64(-1.2823937362836415), 'beta2': np.float64(1.209195603860152)}, {'beta1': np.float64(-1.257397879951302), 'beta2': np.float64(1.31651208100832)}, {'beta1': np.float64(-1.2873325336200956), 'beta2': np.float64(1.1875198317199467)}, {'beta1': np.float64(-1.2690260405244642), 'beta2': np.float64(1.2669668838392414)}, {'beta1': np.float64(-1.2777126116342759), 'beta2': np.float64(1.229556814073192)}, {'beta1': np.float64(-1.257397879951302), 'beta2': np.float64(1.31651208100832)}, {'beta1': np.float64(-1.2732639874991436), 'beta2': np.float64(1.2487688117902658)}]



.. GENERATED FROM PYTHON SOURCE LINES 132-133

Results can be produced in the ALOGIT F12 format

.. GENERATED FROM PYTHON SOURCE LINES 133-135

.. code-block:: Python

    print(read_results.get_f12())





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

 .. code-block:: none

                                                                     simple_example
    From biogeme 3.2.14                                     2024-08-05 20:01:27  
    END
       0      beta1 F  -1.273263987499e+00 +1.372396830767e-02
       0      beta2 F  +1.248768811790e+00 +5.908592227624e-02
      -1
           5                  0                   0 -6.706549047946e+01
       0   0  2024-08-05 20:01:27
     100000





.. GENERATED FROM PYTHON SOURCE LINES 136-137

Miscellaneous functions

.. GENERATED FROM PYTHON SOURCE LINES 139-140

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

.. GENERATED FROM PYTHON SOURCE LINES 142-153

.. code-block:: Python

    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 154-155

We can now perform a likelihood ratio test.

.. GENERATED FROM PYTHON SOURCE LINES 155-160

.. code-block:: Python

    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: 95.40936413216042
    Threshold: 0.003932140000019531




.. GENERATED FROM PYTHON SOURCE LINES 161-162

Calculation of the :math:`p`-value

.. GENERATED FROM PYTHON SOURCE LINES 162-164

.. code-block:: Python

    res.calc_p_value(1.96)





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

 .. code-block:: none


    np.float64(0.04999579029644097)



.. GENERATED FROM PYTHON SOURCE LINES 165-166

Compilation of results

.. GENERATED FROM PYTHON SOURCE LINES 166-168

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 169-171

.. code-block:: Python

    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 0.066 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-jupyter

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

    .. 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-zip

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


.. only:: html

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

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