.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/latent/plot_b01one_latent_regression.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_b01one_latent_regression.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_latent_plot_b01one_latent_regression.py:


Measurement equations: continuous indicators
============================================

It is actually a simle linear regression.

:author: Michel Bierlaire, EPFL
:date: Thu Apr 13 16:42:02 2023

.. GENERATED FROM PYTHON SOURCE LINES 11-40

.. code-block:: default


    import biogeme.biogeme_logging as blog
    import biogeme.biogeme as bio
    from biogeme.models import piecewiseFormula
    import biogeme.loglikelihood as ll
    from biogeme.expressions import Beta, Elem, bioMultSum
    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 b01one_latent_regression.py')





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

 .. code-block:: none

    Example b01one_latent_regression.py 




.. GENERATED FROM PYTHON SOURCE LINES 41-42

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 42-55

.. 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 56-57

Latent variable: structural equation.

.. GENERATED FROM PYTHON SOURCE LINES 57-71

.. 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 72-73

Measurement equations.

.. GENERATED FROM PYTHON SOURCE LINES 75-76

Intercepts.

.. GENERATED FROM PYTHON SOURCE LINES 76-84

.. 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 85-86

Coefficients.

.. GENERATED FROM PYTHON SOURCE LINES 86-94

.. 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 95-96

Linear models.

.. GENERATED FROM PYTHON SOURCE LINES 96-104

.. 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 105-106

Scale parameters.

.. GENERATED FROM PYTHON SOURCE LINES 106-114

.. code-block:: default

    SIGMA_STAR_Envir01 = Beta('SIGMA_STAR_Envir01', 1, None, None, 0)
    SIGMA_STAR_Envir02 = Beta('SIGMA_STAR_Envir02', 1, None, None, 0)
    SIGMA_STAR_Envir03 = Beta('SIGMA_STAR_Envir03', 1, None, None, 0)
    SIGMA_STAR_Mobil11 = Beta('SIGMA_STAR_Mobil11', 1, None, None, 0)
    SIGMA_STAR_Mobil14 = Beta('SIGMA_STAR_Mobil14', 1, None, None, 0)
    SIGMA_STAR_Mobil16 = Beta('SIGMA_STAR_Mobil16', 1, None, None, 0)
    SIGMA_STAR_Mobil17 = Beta('SIGMA_STAR_Mobil17', 1, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 115-117

We build a dict with each contribution to the loglikelihood if
(var > 0) and (var < 6). If not, 0 is returned.

.. GENERATED FROM PYTHON SOURCE LINES 117-168

.. code-block:: default

    F = {}
    F['Envir01'] = Elem(
        {
            0: 0,
            1: ll.loglikelihoodregression(Envir01, MODEL_Envir01, SIGMA_STAR_Envir01),
        },
        (Envir01 > 0) * (Envir01 < 6),
    )
    F['Envir02'] = Elem(
        {
            0: 0,
            1: ll.loglikelihoodregression(Envir02, MODEL_Envir02, SIGMA_STAR_Envir02),
        },
        (Envir02 > 0) * (Envir02 < 6),
    )
    F['Envir03'] = Elem(
        {
            0: 0,
            1: ll.loglikelihoodregression(Envir03, MODEL_Envir03, SIGMA_STAR_Envir03),
        },
        (Envir03 > 0) * (Envir03 < 6),
    )
    F['Mobil11'] = Elem(
        {
            0: 0,
            1: ll.loglikelihoodregression(Mobil11, MODEL_Mobil11, SIGMA_STAR_Mobil11),
        },
        (Mobil11 > 0) * (Mobil11 < 6),
    )
    F['Mobil14'] = Elem(
        {
            0: 0,
            1: ll.loglikelihoodregression(Mobil14, MODEL_Mobil14, SIGMA_STAR_Mobil14),
        },
        (Mobil14 > 0) * (Mobil14 < 6),
    )
    F['Mobil16'] = Elem(
        {
            0: 0,
            1: ll.loglikelihoodregression(Mobil16, MODEL_Mobil16, SIGMA_STAR_Mobil16),
        },
        (Mobil16 > 0) * (Mobil16 < 6),
    )
    F['Mobil17'] = Elem(
        {
            0: 0,
            1: ll.loglikelihoodregression(Mobil17, MODEL_Mobil17, SIGMA_STAR_Mobil17),
        },
        (Mobil17 > 0) * (Mobil17 < 6),
    )








.. GENERATED FROM PYTHON SOURCE LINES 169-170

The log likelihood is the sum of the elements of the above dict

.. GENERATED FROM PYTHON SOURCE LINES 170-172

.. code-block:: default

    loglike = bioMultSum(F)








.. GENERATED FROM PYTHON SOURCE LINES 173-174

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 174-177

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, loglike)
    the_biogeme.modelName = 'b01one_latent_regression'





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

 .. code-block:: none

    File biogeme.toml has been created 




.. GENERATED FROM PYTHON SOURCE LINES 178-179

Estimate the parameters

.. GENERATED FROM PYTHON SOURCE LINES 179-181

.. 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 __b01one_latent_regression.iter 
    Cannot read file __b01one_latent_regression.iter. Statement is ignored. 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Iter.     Function    Relgrad   Radius      Rho      
        0      3.4e+04        0.3       10     0.91   ++ 
        1      3.4e+04        0.3        5 -3.7e+03    - 
        2      3.4e+04        0.3      2.5 -1.9e+03    - 
        3      3.4e+04        0.3      1.2      -51    - 
        4      3.4e+04        0.3     0.62     -1.6    - 
        5      2.6e+04       0.15      6.2     0.95   ++ 
        6      2.6e+04       0.15      3.1 -1.1e+02    - 
        7      2.6e+04       0.15      1.6 -3.7e+05    - 
        8      2.6e+04       0.15     0.78    -0.19    - 
        9      2.3e+04       0.13      7.8        1   ++ 
       10      2.3e+04       0.13      3.9 -1.9e+02    - 
       11      2.3e+04       0.13        2     -8.4    - 
       12      2.3e+04       0.13     0.98     -6.5    - 
       13      2.1e+04      0.088     0.98     0.89    + 
       14      2.1e+04      0.017     0.98     0.57    + 
       15      2.1e+04      0.017     0.49       -4    - 
       16      2.1e+04       0.14     0.49     0.61    + 
       17      2.1e+04     0.0076      4.9     0.95   ++ 
       18      2.1e+04     0.0076      2.4 -3.1e+02    - 
       19      2.1e+04     0.0076      1.2      -40    - 
       20      2.1e+04     0.0076     0.61     -3.5    - 
       21      2.1e+04       0.13     0.61      0.2    + 
       22        2e+04      0.017      6.1      1.2   ++ 
       23        2e+04      0.017      3.1      -35    - 
       24        2e+04      0.017      1.5     -6.9    - 
       25        2e+04       0.11      1.5     0.28    + 
       26        2e+04       0.15      1.5     0.85    + 
       27        2e+04       0.22       15        1   ++ 
       28        2e+04       0.22      7.6 -2.6e+02    - 
       29        2e+04       0.22      3.8      -16    - 
       30        2e+04       0.22      1.9     -1.9    - 
       31      1.9e+04       0.17      1.9     0.67    + 
       32      1.9e+04       0.17     0.95      -10    - 
       33      1.9e+04       0.17     0.48    -0.47    - 
       34      1.9e+04      0.072     0.48     0.78    + 
       35      1.9e+04       0.13     0.48     0.85    + 
       36      1.9e+04     0.0094      4.8        1   ++ 
       37      1.9e+04     0.0094      2.4     -4.1    - 
       38      1.9e+04     0.0094      1.2    -0.02    - 
       39      1.9e+04     0.0046       12      1.1   ++ 
       40      1.9e+04     0.0046        6      -53    - 
       41      1.9e+04     0.0046        3       -8    - 
       42      1.9e+04     0.0046      1.5    -0.77    - 
       43      1.9e+04      0.013      1.5     0.75    + 
       44      1.9e+04     0.0047      1.5     0.52    + 
       45      1.9e+04     0.0065      1.5     0.58    + 
       46      1.9e+04     0.0011      1.5     0.22    + 
       47      1.9e+04     0.0012      1.5     0.13    + 
       48      1.9e+04     0.0012     0.51  0.00076    - 
       49      1.9e+04    0.00062      5.1     0.91   ++ 
       50      1.9e+04    9.1e-05       51     0.95   ++ 
       51      1.9e+04      9e-07       51        1   ++ 




.. GENERATED FROM PYTHON SOURCE LINES 182-188

.. 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: 33
    final log likelihood: -18658.152
    Output file: None
    Results saved in file b01one_latent_regression.tex 
    LaTeX file: b01one_latent_regression.tex




.. GENERATED FROM PYTHON SOURCE LINES 189-190

.. 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>-0.496160</td>
          <td>0.057780</td>
          <td>-8.587026</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_Envir03_F1</th>
          <td>0.670919</td>
          <td>0.060137</td>
          <td>11.156562</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_Mobil11_F1</th>
          <td>0.562862</td>
          <td>0.058911</td>
          <td>9.554380</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_Mobil14_F1</th>
          <td>0.705344</td>
          <td>0.059649</td>
          <td>11.824941</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_Mobil16_F1</th>
          <td>0.539936</td>
          <td>0.061248</td>
          <td>8.815632</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_Mobil17_F1</th>
          <td>0.431749</td>
          <td>0.059963</td>
          <td>7.200288</td>
          <td>6.008527e-13</td>
        </tr>
        <tr>
          <th>INTER_Envir02</th>
          <td>2.008185</td>
          <td>0.153261</td>
          <td>13.103062</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>INTER_Envir03</th>
          <td>4.565455</td>
          <td>0.158304</td>
          <td>28.839845</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>INTER_Mobil11</th>
          <td>5.143851</td>
          <td>0.151171</td>
          <td>34.026714</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>INTER_Mobil14</th>
          <td>4.914890</td>
          <td>0.157521</td>
          <td>31.201469</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>INTER_Mobil16</th>
          <td>4.797498</td>
          <td>0.158486</td>
          <td>30.270822</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>INTER_Mobil17</th>
          <td>4.500423</td>
          <td>0.157149</td>
          <td>28.637908</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>SIGMA_STAR_Envir01</th>
          <td>1.248310</td>
          <td>0.016139</td>
          <td>77.345225</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>SIGMA_STAR_Envir02</th>
          <td>1.120135</td>
          <td>0.014927</td>
          <td>75.043199</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>SIGMA_STAR_Envir03</th>
          <td>1.069487</td>
          <td>0.015518</td>
          <td>68.919604</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>SIGMA_STAR_Mobil11</th>
          <td>1.082910</td>
          <td>0.016309</td>
          <td>66.398524</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>SIGMA_STAR_Mobil14</th>
          <td>1.050687</td>
          <td>0.014081</td>
          <td>74.618994</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>SIGMA_STAR_Mobil16</th>
          <td>1.096088</td>
          <td>0.015107</td>
          <td>72.555763</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>SIGMA_STAR_Mobil17</th>
          <td>1.109030</td>
          <td>0.015460</td>
          <td>71.737716</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>beta_ScaledIncome_10_inf</th>
          <td>0.102971</td>
          <td>0.036009</td>
          <td>2.859596</td>
          <td>4.241810e-03</td>
        </tr>
        <tr>
          <th>beta_ScaledIncome_4_6</th>
          <td>-0.252093</td>
          <td>0.108158</td>
          <td>-2.330778</td>
          <td>1.976509e-02</td>
        </tr>
        <tr>
          <th>beta_ScaledIncome_6_8</th>
          <td>0.299881</td>
          <td>0.129823</td>
          <td>2.309914</td>
          <td>2.089290e-02</td>
        </tr>
        <tr>
          <th>beta_ScaledIncome_8_10</th>
          <td>-0.620844</td>
          <td>0.150375</td>
          <td>-4.128652</td>
          <td>3.648969e-05</td>
        </tr>
        <tr>
          <th>beta_ScaledIncome_minus_inf_4</th>
          <td>0.103050</td>
          <td>0.063320</td>
          <td>1.627460</td>
          <td>1.036394e-01</td>
        </tr>
        <tr>
          <th>coef_age_65_more</th>
          <td>0.103132</td>
          <td>0.073161</td>
          <td>1.409656</td>
          <td>1.586413e-01</td>
        </tr>
        <tr>
          <th>coef_haveChildren</th>
          <td>-0.045353</td>
          <td>0.054154</td>
          <td>-0.837491</td>
          <td>4.023168e-01</td>
        </tr>
        <tr>
          <th>coef_haveGA</th>
          <td>-0.688798</td>
          <td>0.086095</td>
          <td>-8.000392</td>
          <td>1.332268e-15</td>
        </tr>
        <tr>
          <th>coef_highEducation</th>
          <td>-0.298037</td>
          <td>0.061203</td>
          <td>-4.869668</td>
          <td>1.117861e-06</td>
        </tr>
        <tr>
          <th>coef_individualHouse</th>
          <td>-0.109935</td>
          <td>0.053967</td>
          <td>-2.037088</td>
          <td>4.164118e-02</td>
        </tr>
        <tr>
          <th>coef_intercept</th>
          <td>-2.497252</td>
          <td>0.182810</td>
          <td>-13.660364</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>coef_male</th>
          <td>0.071602</td>
          <td>0.050626</td>
          <td>1.414346</td>
          <td>1.572603e-01</td>
        </tr>
        <tr>
          <th>coef_moreThanOneBike</th>
          <td>-0.327629</td>
          <td>0.062047</td>
          <td>-5.280314</td>
          <td>1.289627e-07</td>
        </tr>
        <tr>
          <th>coef_moreThanOneCar</th>
          <td>0.624407</td>
          <td>0.058136</td>
          <td>10.740379</td>
          <td>0.000000e+00</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** (0 minutes 6.524 seconds)


.. _sphx_glr_download_auto_examples_latent_plot_b01one_latent_regression.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_b01one_latent_regression.py <plot_b01one_latent_regression.py>`

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

      :download:`Download Jupyter notebook: plot_b01one_latent_regression.ipynb <plot_b01one_latent_regression.ipynb>`


.. only:: html

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