.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/latent/plot_b07problem.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_latent_plot_b07problem.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_latent_plot_b07problem.py:


Illustration of a common estimation problem
===========================================

 This file is the same as b02one_latent_ordered.py, where the starting
 values for the sigma have been changed in order to illustrate a common
 issue with the estimation of such models.

 We set the starting value of a scale parameter (SIGMA_STAR_Envir02)
 to a small value: 0.01. The resulting likelihood is so close to zero
 that taking the log generates a numerical issue.

 Make sure to set large initial values for scale parameters.

:author: Michel Bierlaire, EPFL
:date: Thu Apr 13 18:19:27 2023

.. GENERATED FROM PYTHON SOURCE LINES 20-49

.. code-block:: default


    import biogeme.biogeme_logging as blog
    from biogeme.models import piecewiseFormula
    import biogeme.biogeme as bio
    from biogeme.expressions import Beta, log, Elem, bioNormalCdf

    from optima import (
        database,
        age_65_more,
        ScaledIncome,
        moreThanOneCar,
        moreThanOneBike,
        individualHouse,
        male,
        haveChildren,
        haveGA,
        highEducation,
        Envir01,
        Envir02,
        Envir03,
        Mobil11,
        Mobil14,
        Mobil16,
        Mobil17,
    )

    logger = blog.get_screen_logger(level=blog.INFO)
    logger.info('Example b07problem.py')





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

 .. code-block:: none

    Example b07problem.py 




.. GENERATED FROM PYTHON SOURCE LINES 50-51

Parameters to be estimated

.. GENERATED FROM PYTHON SOURCE LINES 51-64

.. code-block:: default

    coef_intercept = Beta('coef_intercept', 0.0, None, None, 0)
    coef_age_65_more = Beta('coef_age_65_more', 0.0, None, None, 0)
    coef_haveGA = Beta('coef_haveGA', 0.0, None, None, 0)
    coef_moreThanOneCar = Beta('coef_moreThanOneCar', 0.0, None, None, 0)
    coef_moreThanOneBike = Beta('coef_moreThanOneBike', 0.0, None, None, 0)
    coef_individualHouse = Beta('coef_individualHouse', 0.0, None, None, 0)
    coef_male = Beta('coef_male', 0.0, None, None, 0)
    coef_haveChildren = Beta('coef_haveChildren', 0.0, None, None, 0)
    coef_highEducation = Beta('coef_highEducation', 0.0, None, None, 0)

    thresholds = [None, 4, 6, 8, 10, None]
    formula_income = piecewiseFormula(variable=ScaledIncome, thresholds=thresholds)








.. GENERATED FROM PYTHON SOURCE LINES 65-66

Latent variable: structural equation.

.. GENERATED FROM PYTHON SOURCE LINES 66-79

.. code-block:: default

    CARLOVERS = (
        coef_intercept
        + coef_age_65_more * age_65_more
        + formula_income
        + coef_moreThanOneCar * moreThanOneCar
        + coef_moreThanOneBike * moreThanOneBike
        + coef_individualHouse * individualHouse
        + coef_male * male
        + coef_haveChildren * haveChildren
        + coef_haveGA * haveGA
        + coef_highEducation * highEducation
    )








.. GENERATED FROM PYTHON SOURCE LINES 80-81

Measurement equations

.. GENERATED FROM PYTHON SOURCE LINES 83-84

Intercepts.

.. GENERATED FROM PYTHON SOURCE LINES 84-92

.. code-block:: default

    INTER_Envir01 = Beta('INTER_Envir01', 0, None, None, 1)
    INTER_Envir02 = Beta('INTER_Envir02', 0, None, None, 0)
    INTER_Envir03 = Beta('INTER_Envir03', 0, None, None, 0)
    INTER_Mobil11 = Beta('INTER_Mobil11', 0, None, None, 0)
    INTER_Mobil14 = Beta('INTER_Mobil14', 0, None, None, 0)
    INTER_Mobil16 = Beta('INTER_Mobil16', 0, None, None, 0)
    INTER_Mobil17 = Beta('INTER_Mobil17', 0, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 93-94

Coefficients.

.. GENERATED FROM PYTHON SOURCE LINES 94-102

.. code-block:: default

    B_Envir01_F1 = Beta('B_Envir01_F1', -1, None, None, 1)
    B_Envir02_F1 = Beta('B_Envir02_F1', -1, None, None, 0)
    B_Envir03_F1 = Beta('B_Envir03_F1', 1, None, None, 0)
    B_Mobil11_F1 = Beta('B_Mobil11_F1', 1, None, None, 0)
    B_Mobil14_F1 = Beta('B_Mobil14_F1', 1, None, None, 0)
    B_Mobil16_F1 = Beta('B_Mobil16_F1', 1, None, None, 0)
    B_Mobil17_F1 = Beta('B_Mobil17_F1', 1, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 103-104

Linear models.

.. GENERATED FROM PYTHON SOURCE LINES 104-112

.. code-block:: default

    MODEL_Envir01 = INTER_Envir01 + B_Envir01_F1 * CARLOVERS
    MODEL_Envir02 = INTER_Envir02 + B_Envir02_F1 * CARLOVERS
    MODEL_Envir03 = INTER_Envir03 + B_Envir03_F1 * CARLOVERS
    MODEL_Mobil11 = INTER_Mobil11 + B_Mobil11_F1 * CARLOVERS
    MODEL_Mobil14 = INTER_Mobil14 + B_Mobil14_F1 * CARLOVERS
    MODEL_Mobil16 = INTER_Mobil16 + B_Mobil16_F1 * CARLOVERS
    MODEL_Mobil17 = INTER_Mobil17 + B_Mobil17_F1 * CARLOVERS








.. GENERATED FROM PYTHON SOURCE LINES 113-114

Scale parameters.

.. GENERATED FROM PYTHON SOURCE LINES 114-122

.. code-block:: default

    SIGMA_STAR_Envir01 = Beta('SIGMA_STAR_Envir01', 1, 1.0e-5, None, 1)
    SIGMA_STAR_Envir02 = Beta('SIGMA_STAR_Envir02', 0.01, 1.0e-5, None, 0)
    SIGMA_STAR_Envir03 = Beta('SIGMA_STAR_Envir03', 1, 1.0e-5, None, 0)
    SIGMA_STAR_Mobil11 = Beta('SIGMA_STAR_Mobil11', 1, 1.0e-5, None, 0)
    SIGMA_STAR_Mobil14 = Beta('SIGMA_STAR_Mobil14', 1, 1.0e-5, None, 0)
    SIGMA_STAR_Mobil16 = Beta('SIGMA_STAR_Mobil16', 1, 1.0e-5, None, 0)
    SIGMA_STAR_Mobil17 = Beta('SIGMA_STAR_Mobil17', 1, 1.0e-5, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 123-124

Symmetric thresholds.

.. GENERATED FROM PYTHON SOURCE LINES 124-131

.. code-block:: default

    delta_1 = Beta('delta_1', 0.1, 1.0e-5, None, 0)
    delta_2 = Beta('delta_2', 0.2, 1.0e-5, None, 0)
    tau_1 = -delta_1 - delta_2
    tau_2 = -delta_1
    tau_3 = delta_1
    tau_4 = delta_1 + delta_2








.. GENERATED FROM PYTHON SOURCE LINES 132-133

Ordered probit models.

.. GENERATED FROM PYTHON SOURCE LINES 133-263

.. code-block:: default

    Envir01_tau_1 = (tau_1 - MODEL_Envir01) / SIGMA_STAR_Envir01
    Envir01_tau_2 = (tau_2 - MODEL_Envir01) / SIGMA_STAR_Envir01
    Envir01_tau_3 = (tau_3 - MODEL_Envir01) / SIGMA_STAR_Envir01
    Envir01_tau_4 = (tau_4 - MODEL_Envir01) / SIGMA_STAR_Envir01
    IndEnvir01 = {
        1: bioNormalCdf(Envir01_tau_1),
        2: bioNormalCdf(Envir01_tau_2) - bioNormalCdf(Envir01_tau_1),
        3: bioNormalCdf(Envir01_tau_3) - bioNormalCdf(Envir01_tau_2),
        4: bioNormalCdf(Envir01_tau_4) - bioNormalCdf(Envir01_tau_3),
        5: 1 - bioNormalCdf(Envir01_tau_4),
        6: 1.0,
        -1: 1.0,
        -2: 1.0,
    }

    P_Envir01 = Elem(IndEnvir01, Envir01)

    Envir02_tau_1 = (tau_1 - MODEL_Envir02) / SIGMA_STAR_Envir02
    Envir02_tau_2 = (tau_2 - MODEL_Envir02) / SIGMA_STAR_Envir02
    Envir02_tau_3 = (tau_3 - MODEL_Envir02) / SIGMA_STAR_Envir02
    Envir02_tau_4 = (tau_4 - MODEL_Envir02) / SIGMA_STAR_Envir02
    IndEnvir02 = {
        1: bioNormalCdf(Envir02_tau_1),
        2: bioNormalCdf(Envir02_tau_2) - bioNormalCdf(Envir02_tau_1),
        3: bioNormalCdf(Envir02_tau_3) - bioNormalCdf(Envir02_tau_2),
        4: bioNormalCdf(Envir02_tau_4) - bioNormalCdf(Envir02_tau_3),
        5: 1 - bioNormalCdf(Envir02_tau_4),
        6: 1.0,
        -1: 1.0,
        -2: 1.0,
    }

    P_Envir02 = Elem(IndEnvir02, Envir02)

    Envir03_tau_1 = (tau_1 - MODEL_Envir03) / SIGMA_STAR_Envir03
    Envir03_tau_2 = (tau_2 - MODEL_Envir03) / SIGMA_STAR_Envir03
    Envir03_tau_3 = (tau_3 - MODEL_Envir03) / SIGMA_STAR_Envir03
    Envir03_tau_4 = (tau_4 - MODEL_Envir03) / SIGMA_STAR_Envir03
    IndEnvir03 = {
        1: bioNormalCdf(Envir03_tau_1),
        2: bioNormalCdf(Envir03_tau_2) - bioNormalCdf(Envir03_tau_1),
        3: bioNormalCdf(Envir03_tau_3) - bioNormalCdf(Envir03_tau_2),
        4: bioNormalCdf(Envir03_tau_4) - bioNormalCdf(Envir03_tau_3),
        5: 1 - bioNormalCdf(Envir03_tau_4),
        6: 1.0,
        -1: 1.0,
        -2: 1.0,
    }

    P_Envir03 = Elem(IndEnvir03, Envir03)

    Mobil11_tau_1 = (tau_1 - MODEL_Mobil11) / SIGMA_STAR_Mobil11
    Mobil11_tau_2 = (tau_2 - MODEL_Mobil11) / SIGMA_STAR_Mobil11
    Mobil11_tau_3 = (tau_3 - MODEL_Mobil11) / SIGMA_STAR_Mobil11
    Mobil11_tau_4 = (tau_4 - MODEL_Mobil11) / SIGMA_STAR_Mobil11
    IndMobil11 = {
        1: bioNormalCdf(Mobil11_tau_1),
        2: bioNormalCdf(Mobil11_tau_2) - bioNormalCdf(Mobil11_tau_1),
        3: bioNormalCdf(Mobil11_tau_3) - bioNormalCdf(Mobil11_tau_2),
        4: bioNormalCdf(Mobil11_tau_4) - bioNormalCdf(Mobil11_tau_3),
        5: 1 - bioNormalCdf(Mobil11_tau_4),
        6: 1.0,
        -1: 1.0,
        -2: 1.0,
    }

    P_Mobil11 = Elem(IndMobil11, Mobil11)

    Mobil14_tau_1 = (tau_1 - MODEL_Mobil14) / SIGMA_STAR_Mobil14
    Mobil14_tau_2 = (tau_2 - MODEL_Mobil14) / SIGMA_STAR_Mobil14
    Mobil14_tau_3 = (tau_3 - MODEL_Mobil14) / SIGMA_STAR_Mobil14
    Mobil14_tau_4 = (tau_4 - MODEL_Mobil14) / SIGMA_STAR_Mobil14
    IndMobil14 = {
        1: bioNormalCdf(Mobil14_tau_1),
        2: bioNormalCdf(Mobil14_tau_2) - bioNormalCdf(Mobil14_tau_1),
        3: bioNormalCdf(Mobil14_tau_3) - bioNormalCdf(Mobil14_tau_2),
        4: bioNormalCdf(Mobil14_tau_4) - bioNormalCdf(Mobil14_tau_3),
        5: 1 - bioNormalCdf(Mobil14_tau_4),
        6: 1.0,
        -1: 1.0,
        -2: 1.0,
    }

    P_Mobil14 = Elem(IndMobil14, Mobil14)

    Mobil16_tau_1 = (tau_1 - MODEL_Mobil16) / SIGMA_STAR_Mobil16
    Mobil16_tau_2 = (tau_2 - MODEL_Mobil16) / SIGMA_STAR_Mobil16
    Mobil16_tau_3 = (tau_3 - MODEL_Mobil16) / SIGMA_STAR_Mobil16
    Mobil16_tau_4 = (tau_4 - MODEL_Mobil16) / SIGMA_STAR_Mobil16
    IndMobil16 = {
        1: bioNormalCdf(Mobil16_tau_1),
        2: bioNormalCdf(Mobil16_tau_2) - bioNormalCdf(Mobil16_tau_1),
        3: bioNormalCdf(Mobil16_tau_3) - bioNormalCdf(Mobil16_tau_2),
        4: bioNormalCdf(Mobil16_tau_4) - bioNormalCdf(Mobil16_tau_3),
        5: 1 - bioNormalCdf(Mobil16_tau_4),
        6: 1.0,
        -1: 1.0,
        -2: 1.0,
    }

    P_Mobil16 = Elem(IndMobil16, Mobil16)

    Mobil17_tau_1 = (tau_1 - MODEL_Mobil17) / SIGMA_STAR_Mobil17
    Mobil17_tau_2 = (tau_2 - MODEL_Mobil17) / SIGMA_STAR_Mobil17
    Mobil17_tau_3 = (tau_3 - MODEL_Mobil17) / SIGMA_STAR_Mobil17
    Mobil17_tau_4 = (tau_4 - MODEL_Mobil17) / SIGMA_STAR_Mobil17
    IndMobil17 = {
        1: bioNormalCdf(Mobil17_tau_1),
        2: bioNormalCdf(Mobil17_tau_2) - bioNormalCdf(Mobil17_tau_1),
        3: bioNormalCdf(Mobil17_tau_3) - bioNormalCdf(Mobil17_tau_2),
        4: bioNormalCdf(Mobil17_tau_4) - bioNormalCdf(Mobil17_tau_3),
        5: 1 - bioNormalCdf(Mobil17_tau_4),
        6: 1.0,
        -1: 1.0,
        -2: 1.0,
    }

    P_Mobil17 = Elem(IndMobil17, Mobil17)


    loglike = (
        log(P_Envir01)
        + log(P_Envir02)
        + log(P_Envir03)
        + log(P_Mobil11)
        + log(P_Mobil14)
        + log(P_Mobil16)
        + log(P_Mobil17)
    )








.. GENERATED FROM PYTHON SOURCE LINES 264-265

Create the Biogeme object

.. GENERATED FROM PYTHON SOURCE LINES 265-268

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, loglike)
    the_biogeme.modelName = 'b07problem'





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

 .. code-block:: none

    File biogeme.toml has been parsed. 




.. GENERATED FROM PYTHON SOURCE LINES 269-270

Estimate the parameters

.. GENERATED FROM PYTHON SOURCE LINES 270-272

.. code-block:: default

    results = the_biogeme.estimate()





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

 .. code-block:: none

    *** Initial values of the parameters are obtained from the file __b07problem.iter 
    Cannot read file __b07problem.iter. Statement is ignored. 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    The norm of the gradient at B_Envir02_F1=-1, B_Envir03_F1=1, B_Mobil11_F1=1, B_Mobil14_F1=1, B_Mobil16_F1=1, B_Mobil17_F1=1, INTER_Envir02=0, INTER_Envir03=0, INTER_Mobil11=0, INTER_Mobil14=0, INTER_Mobil16=0, INTER_Mobil17=0, SIGMA_STAR_Envir02=0.01, SIGMA_STAR_Envir03=1, SIGMA_STAR_Mobil11=1 is inf: g=-1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308 
    The norm of the gradient at B_Envir02_F1=-1, B_Envir03_F1=1, B_Mobil11_F1=1, B_Mobil14_F1=1, B_Mobil16_F1=1, B_Mobil17_F1=1, INTER_Envir02=0, INTER_Envir03=0, INTER_Mobil11=0, INTER_Mobil14=0, INTER_Mobil16=0, INTER_Mobil17=0, SIGMA_STAR_Envir02=0.01, SIGMA_STAR_Envir03=1, SIGMA_STAR_Mobil11=1 is inf: g=-1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308, -1.8e+308 




.. GENERATED FROM PYTHON SOURCE LINES 273-279

.. code-block:: default

    print(f'Estimated betas: {len(results.data.betaValues)}')
    print(f'final log likelihood: {results.data.logLike:.3f}')
    print(f'Output file: {results.data.htmlFileName}')
    results.writeLaTeX()
    print(f'LaTeX file: {results.data.latexFileName}')





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

 .. code-block:: none

    Estimated betas: 34
    final log likelihood: -179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368.000
    Output file: None
    Results saved in file b07problem.tex 
    LaTeX file: b07problem.tex




.. GENERATED FROM PYTHON SOURCE LINES 280-281

.. 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>B_Envir02_F1</th>
          <td>-1.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>B_Envir03_F1</th>
          <td>1.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>B_Mobil11_F1</th>
          <td>1.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>B_Mobil14_F1</th>
          <td>1.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>B_Mobil16_F1</th>
          <td>1.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>B_Mobil17_F1</th>
          <td>1.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>INTER_Envir02</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>INTER_Envir03</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>INTER_Mobil11</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>INTER_Mobil14</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>INTER_Mobil16</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>INTER_Mobil17</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>SIGMA_STAR_Envir02</th>
          <td>0.01</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>SIGMA_STAR_Envir03</th>
          <td>1.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>SIGMA_STAR_Mobil11</th>
          <td>1.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>SIGMA_STAR_Mobil14</th>
          <td>1.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>SIGMA_STAR_Mobil16</th>
          <td>1.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>SIGMA_STAR_Mobil17</th>
          <td>1.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta_ScaledIncome_10_inf</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta_ScaledIncome_4_6</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta_ScaledIncome_6_8</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta_ScaledIncome_8_10</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta_ScaledIncome_minus_inf_4</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>coef_age_65_more</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>coef_haveChildren</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>coef_haveGA</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>coef_highEducation</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>coef_individualHouse</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>coef_intercept</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>coef_male</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>coef_moreThanOneBike</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>coef_moreThanOneCar</th>
          <td>0.00</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>delta_1</th>
          <td>0.10</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>delta_2</th>
          <td>0.20</td>
          <td>0.0</td>
          <td>1.797693e+308</td>
          <td>0.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** (0 minutes 0.571 seconds)


.. _sphx_glr_download_auto_examples_latent_plot_b07problem.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_b07problem.py <plot_b07problem.py>`

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

      :download:`Download Jupyter notebook: plot_b07problem.ipynb <plot_b07problem.ipynb>`


.. only:: html

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

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