.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/latent/plot_b03choice_only.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_b03choice_only.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_latent_plot_b03choice_only.py:


Mixture of logit
================

Choice model with latent variable. No measurement equation for the indicators.

:author: Michel Bierlaire, EPFL
:date: Thu Apr 13 16:58:21 2023

.. GENERATED FROM PYTHON SOURCE LINES 12-53

.. code-block:: default


    import biogeme.biogeme_logging as blog
    import biogeme.biogeme as bio
    from biogeme import models
    import biogeme.distributions as dist
    from biogeme.expressions import (
        Beta,
        RandomVariable,
        Integrate,
        exp,
        log,
    )

    from read_or_estimate import read_or_estimate

    from optima import (
        database,
        age_65_more,
        ScaledIncome,
        moreThanOneCar,
        moreThanOneBike,
        individualHouse,
        male,
        haveChildren,
        haveGA,
        highEducation,
        WaitingTimePT,
        Choice,
        TimePT_scaled,
        TimeCar_scaled,
        MarginalCostPT_scaled,
        CostCarCHF_scaled,
        distance_km_scaled,
        PurpHWH,
        PurpOther,
    )


    logger = blog.get_screen_logger(level=blog.INFO)
    logger.info('Example b03choice_only.py')





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

 .. code-block:: none

    Example b03choice_only.py 




.. GENERATED FROM PYTHON SOURCE LINES 54-55

Parameters to be estimated

.. GENERATED FROM PYTHON SOURCE LINES 55-65

.. code-block:: default

    coef_intercept = Beta('coef_intercept', 0.0, None, None, 1)
    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)








.. GENERATED FROM PYTHON SOURCE LINES 66-67

Latent variable: structural equation.

.. GENERATED FROM PYTHON SOURCE LINES 69-72

Define a random parameter, normally distributed)
designed to be used
for numerical integration.

.. GENERATED FROM PYTHON SOURCE LINES 72-93

.. code-block:: default

    omega = RandomVariable('omega')
    density = dist.normalpdf(omega)
    sigma_s = Beta('sigma_s', 1, None, None, 0)

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

    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
        + sigma_s * omega
    )








.. GENERATED FROM PYTHON SOURCE LINES 94-95

Choice model: parameters.

.. GENERATED FROM PYTHON SOURCE LINES 95-107

.. code-block:: default

    ASC_CAR = Beta('ASC_CAR', 0.0, None, None, 0)
    ASC_PT = Beta('ASC_PT', 0.0, None, None, 1)
    ASC_SM = Beta('ASC_SM', 0.0, None, None, 0)
    BETA_COST_HWH = Beta('BETA_COST_HWH', 0.0, None, None, 0)
    BETA_COST_OTHER = Beta('BETA_COST_OTHER', 0.0, None, None, 0)
    BETA_DIST = Beta('BETA_DIST', 0.0, None, None, 0)
    BETA_TIME_CAR_REF = Beta('BETA_TIME_CAR_REF', -0.0001, None, 0, 0)
    BETA_TIME_CAR_CL = Beta('BETA_TIME_CAR_CL', -1.0, -3, 3, 0)
    BETA_TIME_PT_REF = Beta('BETA_TIME_PT_REF', -0.0001, None, 0, 0)
    BETA_TIME_PT_CL = Beta('BETA_TIME_PT_CL', -1.0, -3, 3, 0)
    BETA_WAITING_TIME = Beta('BETA_WAITING_TIME', 0.0, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 108-109

Definition of utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 109-130

.. code-block:: default

    BETA_TIME_PT = BETA_TIME_PT_REF * exp(BETA_TIME_PT_CL * CARLOVERS)

    V0 = (
        ASC_PT
        + BETA_TIME_PT * TimePT_scaled
        + BETA_WAITING_TIME * WaitingTimePT
        + BETA_COST_HWH * MarginalCostPT_scaled * PurpHWH
        + BETA_COST_OTHER * MarginalCostPT_scaled * PurpOther
    )

    BETA_TIME_CAR = BETA_TIME_CAR_REF * exp(BETA_TIME_CAR_CL * CARLOVERS)

    V1 = (
        ASC_CAR
        + BETA_TIME_CAR * TimeCar_scaled
        + BETA_COST_HWH * CostCarCHF_scaled * PurpHWH
        + BETA_COST_OTHER * CostCarCHF_scaled * PurpOther
    )

    V2 = ASC_SM + BETA_DIST * distance_km_scaled








.. GENERATED FROM PYTHON SOURCE LINES 131-132

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 132-134

.. code-block:: default

    V = {0: V0, 1: V1, 2: V2}








.. GENERATED FROM PYTHON SOURCE LINES 135-136

Conditional on  omega, we have a logit model (called the kernel).

.. GENERATED FROM PYTHON SOURCE LINES 136-138

.. code-block:: default

    condprob = models.logit(V, None, Choice)








.. GENERATED FROM PYTHON SOURCE LINES 139-140

We integrate over omega using numerical integration.

.. GENERATED FROM PYTHON SOURCE LINES 140-143

.. code-block:: default

    loglike = log(Integrate(condprob * density, 'omega'))









.. GENERATED FROM PYTHON SOURCE LINES 144-145

Create the Biogeme object.

.. GENERATED FROM PYTHON SOURCE LINES 145-148

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, loglike)
    the_biogeme.modelName = 'b03choice_only'





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

 .. code-block:: none

    File biogeme.toml has been parsed. 




.. GENERATED FROM PYTHON SOURCE LINES 149-151

If estimation results are saved on file, we read them to speed up the process.
If not, we estimate the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 151-153

.. code-block:: default

    results = read_or_estimate(the_biogeme=the_biogeme, directory='saved_results')








.. GENERATED FROM PYTHON SOURCE LINES 154-158

.. 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}')





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

 .. code-block:: none

    Estimated betas: 24
    Final log likelihood: -1075.485
    Output file: b03choice_only.html




.. GENERATED FROM PYTHON SOURCE LINES 159-160

.. code-block:: default

    results.getEstimatedParameters()





.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>Value</th>
          <th>Rob. Std err</th>
          <th>Rob. t-test</th>
          <th>Rob. p-value</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>ASC_CAR</th>
          <td>0.933907</td>
          <td>0.181626</td>
          <td>5.141910</td>
          <td>2.719592e-07</td>
        </tr>
        <tr>
          <th>ASC_SM</th>
          <td>1.870388</td>
          <td>0.764420</td>
          <td>2.446808</td>
          <td>1.441278e-02</td>
        </tr>
        <tr>
          <th>BETA_COST_HWH</th>
          <td>-1.463999</td>
          <td>0.553502</td>
          <td>-2.644977</td>
          <td>8.169639e-03</td>
        </tr>
        <tr>
          <th>BETA_COST_OTHER</th>
          <td>-0.719213</td>
          <td>0.261093</td>
          <td>-2.754627</td>
          <td>5.875901e-03</td>
        </tr>
        <tr>
          <th>BETA_DIST</th>
          <td>-5.184167</td>
          <td>2.772885</td>
          <td>-1.869593</td>
          <td>6.154032e-02</td>
        </tr>
        <tr>
          <th>BETA_TIME_CAR_CL</th>
          <td>-2.038191</td>
          <td>0.711591</td>
          <td>-2.864274</td>
          <td>4.179663e-03</td>
        </tr>
        <tr>
          <th>BETA_TIME_CAR_REF</th>
          <td>-5.160340</td>
          <td>1.895779</td>
          <td>-2.722015</td>
          <td>6.488523e-03</td>
        </tr>
        <tr>
          <th>BETA_TIME_PT_CL</th>
          <td>-1.424666</td>
          <td>0.128401</td>
          <td>-11.095451</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>BETA_TIME_PT_REF</th>
          <td>-2.411777</td>
          <td>0.612787</td>
          <td>-3.935747</td>
          <td>8.293822e-05</td>
        </tr>
        <tr>
          <th>BETA_WAITING_TIME</th>
          <td>-0.039506</td>
          <td>0.016827</td>
          <td>-2.347735</td>
          <td>1.888797e-02</td>
        </tr>
        <tr>
          <th>beta_ScaledIncome_10_inf</th>
          <td>-0.009327</td>
          <td>0.061969</td>
          <td>-0.150511</td>
          <td>8.803611e-01</td>
        </tr>
        <tr>
          <th>beta_ScaledIncome_4_6</th>
          <td>0.181499</td>
          <td>0.283421</td>
          <td>0.640386</td>
          <td>5.219218e-01</td>
        </tr>
        <tr>
          <th>beta_ScaledIncome_6_8</th>
          <td>-0.294790</td>
          <td>0.257292</td>
          <td>-1.145739</td>
          <td>2.519032e-01</td>
        </tr>
        <tr>
          <th>beta_ScaledIncome_8_10</th>
          <td>0.128598</td>
          <td>0.222033</td>
          <td>0.579184</td>
          <td>5.624648e-01</td>
        </tr>
        <tr>
          <th>beta_ScaledIncome_minus_inf_4</th>
          <td>-0.089157</td>
          <td>0.095093</td>
          <td>-0.937574</td>
          <td>3.484632e-01</td>
        </tr>
        <tr>
          <th>coef_age_65_more</th>
          <td>-0.054803</td>
          <td>0.094912</td>
          <td>-0.577413</td>
          <td>5.636607e-01</td>
        </tr>
        <tr>
          <th>coef_haveChildren</th>
          <td>-0.032954</td>
          <td>0.235116</td>
          <td>-0.140161</td>
          <td>8.885329e-01</td>
        </tr>
        <tr>
          <th>coef_haveGA</th>
          <td>-0.657874</td>
          <td>0.204498</td>
          <td>-3.217024</td>
          <td>1.295279e-03</td>
        </tr>
        <tr>
          <th>coef_highEducation</th>
          <td>0.001339</td>
          <td>0.136040</td>
          <td>0.009840</td>
          <td>9.921489e-01</td>
        </tr>
        <tr>
          <th>coef_individualHouse</th>
          <td>-0.112264</td>
          <td>0.371466</td>
          <td>-0.302220</td>
          <td>7.624846e-01</td>
        </tr>
        <tr>
          <th>coef_male</th>
          <td>0.105574</td>
          <td>0.234527</td>
          <td>0.450155</td>
          <td>6.525990e-01</td>
        </tr>
        <tr>
          <th>coef_moreThanOneBike</th>
          <td>-0.306580</td>
          <td>0.155313</td>
          <td>-1.973949</td>
          <td>4.838753e-02</td>
        </tr>
        <tr>
          <th>coef_moreThanOneCar</th>
          <td>0.783374</td>
          <td>0.088790</td>
          <td>8.822745</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>sigma_s</th>
          <td>0.687676</td>
          <td>0.068003</td>
          <td>10.112384</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 0.109 seconds)


.. _sphx_glr_download_auto_examples_latent_plot_b03choice_only.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_b03choice_only.py <plot_b03choice_only.py>`

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

      :download:`Download Jupyter notebook: plot_b03choice_only.ipynb <plot_b03choice_only.ipynb>`


.. only:: html

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