.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/latentbis/plot_m02_sequential_estimation.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_latentbis_plot_m02_sequential_estimation.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_latentbis_plot_m02_sequential_estimation.py:


Choice model with latent variable: sequential estimation
========================================================

Mixture of logit.
Measurement equation for the indicators.
Sequential estimation.

:author: Michel Bierlaire, EPFL
:date: Fri Apr 14 09:47:53 2023

.. GENERATED FROM PYTHON SOURCE LINES 14-55

.. code-block:: default


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

    from read_or_estimate import read_or_estimate

    from optima import (
        database,
        male,
        age,
        haveChildren,
        highEducation,
        childCenter,
        childSuburb,
        SocioProfCat,
        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 m02_sequential_estimation.py')





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

 .. code-block:: none

    Example m02_sequential_estimation.py 




.. GENERATED FROM PYTHON SOURCE LINES 56-57

Read the estimates from the structural equation estimation.

.. GENERATED FROM PYTHON SOURCE LINES 57-68

.. code-block:: default

    MODELNAME = 'm01_latent_variable'
    try:
        struct_results = res.bioResults(pickleFile=f'saved_results/{MODELNAME}.pickle')
    except excep.BiogemeError:
        print(
            f'Run first the script {MODELNAME}.py in order to generate the '
            f'file {MODELNAME}.pickle, and move it to the directory saved_results'
        )
        sys.exit()
    struct_betas = struct_results.getBetaValues()








.. GENERATED FROM PYTHON SOURCE LINES 69-70

Coefficients

.. GENERATED FROM PYTHON SOURCE LINES 70-80

.. code-block:: default

    coef_intercept = struct_betas['coef_intercept']
    coef_age_30_less = struct_betas['coef_age_30_less']
    coef_male = struct_betas['coef_male']
    coef_haveChildren = struct_betas['coef_haveChildren']
    coef_highEducation = struct_betas['coef_highEducation']
    coef_artisans = struct_betas['coef_artisans']
    coef_employees = struct_betas['coef_employees']
    coef_child_center = struct_betas['coef_child_center']
    coef_child_suburb = struct_betas['coef_child_suburb']








.. GENERATED FROM PYTHON SOURCE LINES 81-82

Latent variable: structural equation

.. GENERATED FROM PYTHON SOURCE LINES 84-86

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

.. GENERATED FROM PYTHON SOURCE LINES 86-90

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 91-104

.. code-block:: default

    ACTIVELIFE = (
        coef_intercept
        + coef_child_center * childCenter
        + coef_child_suburb * childSuburb
        + coef_highEducation * highEducation
        + coef_artisans * (SocioProfCat == 5)
        + coef_employees * (SocioProfCat == 6)
        + coef_age_30_less * (age <= 30)
        + coef_male * male
        + coef_haveChildren * haveChildren
        + sigma_s * omega
    )








.. GENERATED FROM PYTHON SOURCE LINES 105-106

Choice model

.. GENERATED FROM PYTHON SOURCE LINES 106-116

.. code-block:: default

    ASC_CAR = Beta('ASC_CAR', 0.94, None, None, 0)
    ASC_PT = Beta('ASC_PT', 0, None, None, 1)
    ASC_SM = Beta('ASC_SM', 0.35, None, None, 0)
    BETA_COST_HWH = Beta('BETA_COST_HWH', -2.3, None, None, 0)
    BETA_COST_OTHER = Beta('BETA_COST_OTHER', -1.9, None, None, 0)
    BETA_DIST = Beta('BETA_DIST', -1.3, None, None, 0)
    BETA_TIME_CAR_REF = Beta('BETA_TIME_CAR_REF', -6.1, None, 0, 0)
    BETA_TIME_PT_REF = Beta('BETA_TIME_PT_REF', 0, None, 0, 0)
    BETA_WAITING_TIME = Beta('BETA_WAITING_TIME', -0.075, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 117-120

The coefficient of the latent variable should be initialized to
something different from zero. If not, the algorithm may be trapped
in a local optimum, and never change the value.

.. GENERATED FROM PYTHON SOURCE LINES 120-125

.. code-block:: default

    BETA_TIME_PT_AL = Beta('BETA_TIME_PT_AL', 1.5, None, None, 0)
    BETA_TIME_PT = BETA_TIME_PT_REF * exp(BETA_TIME_PT_AL * ACTIVELIFE)
    BETA_TIME_CAR_AL = Beta('BETA_TIME_CAR_AL', -0.11, None, None, 0)
    BETA_TIME_CAR = BETA_TIME_CAR_REF * exp(BETA_TIME_CAR_AL * ACTIVELIFE)








.. GENERATED FROM PYTHON SOURCE LINES 126-127

Definition of utility functions:

.. GENERATED FROM PYTHON SOURCE LINES 127-144

.. code-block:: default

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

    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 145-146

Associate utility functions with the numbering of alternatives

.. GENERATED FROM PYTHON SOURCE LINES 146-148

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 149-150

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

.. GENERATED FROM PYTHON SOURCE LINES 150-152

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 153-154

We integrate over omega using numerical integration

.. GENERATED FROM PYTHON SOURCE LINES 154-156

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 157-158

Create the Biogeme object

.. GENERATED FROM PYTHON SOURCE LINES 158-162

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, loglike)
    the_biogeme.modelName = 'm02_sequential_estimation'
    the_biogeme.maxiter = 1000





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

 .. code-block:: none

    File biogeme.toml has been parsed. 




.. GENERATED FROM PYTHON SOURCE LINES 163-165

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 165-167

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 168-170

.. code-block:: default

    print(results.short_summary())





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

 .. code-block:: none

    Results for model m02_sequential_estimation
    Nbr of parameters:              11
    Sample size:                    1906
    Excluded data:                  359
    Final log likelihood:           -1121.273
    Akaike Information Criterion:   2264.546
    Bayesian Information Criterion: 2325.626





.. GENERATED FROM PYTHON SOURCE LINES 171-174

.. code-block:: default

    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

    Final log likelihood: -1121.273
    Output file: m02_sequential_estimation.html




.. GENERATED FROM PYTHON SOURCE LINES 175-176

.. 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>0.622583</td>
          <td>0.116322</td>
          <td>5.352241</td>
          <td>8.687180e-08</td>
        </tr>
        <tr>
          <th>ASC_SM</th>
          <td>1.654831</td>
          <td>0.225762</td>
          <td>7.329973</td>
          <td>2.302603e-13</td>
        </tr>
        <tr>
          <th>BETA_COST_HWH</th>
          <td>-1.822974</td>
          <td>0.386925</td>
          <td>-4.711438</td>
          <td>2.459747e-06</td>
        </tr>
        <tr>
          <th>BETA_COST_OTHER</th>
          <td>-0.929877</td>
          <td>0.213730</td>
          <td>-4.350703</td>
          <td>1.357015e-05</td>
        </tr>
        <tr>
          <th>BETA_DIST</th>
          <td>-4.920546</td>
          <td>0.532287</td>
          <td>-9.244152</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>BETA_TIME_CAR_AL</th>
          <td>-0.038697</td>
          <td>0.022999</td>
          <td>-1.682579</td>
          <td>9.245669e-02</td>
        </tr>
        <tr>
          <th>BETA_TIME_CAR_REF</th>
          <td>-9.057901</td>
          <td>1.304489</td>
          <td>-6.943639</td>
          <td>3.821166e-12</td>
        </tr>
        <tr>
          <th>BETA_TIME_PT_AL</th>
          <td>-0.036915</td>
          <td>0.021627</td>
          <td>-1.706888</td>
          <td>8.784284e-02</td>
        </tr>
        <tr>
          <th>BETA_TIME_PT_REF</th>
          <td>-3.054210</td>
          <td>0.517935</td>
          <td>-5.896901</td>
          <td>3.703930e-09</td>
        </tr>
        <tr>
          <th>BETA_WAITING_TIME</th>
          <td>-0.027764</td>
          <td>0.011142</td>
          <td>-2.491826</td>
          <td>1.270885e-02</td>
        </tr>
        <tr>
          <th>sigma_s</th>
          <td>33.539526</td>
          <td>20.078869</td>
          <td>1.670389</td>
          <td>9.484239e-02</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


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    .. container:: sphx-glr-download sphx-glr-download-python

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      :download:`Download Jupyter notebook: plot_m02_sequential_estimation.ipynb <plot_m02_sequential_estimation.ipynb>`


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