.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/latent/plot_b04latent_choice_seq_mc.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_b04latent_choice_seq_mc.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_latent_plot_b04latent_choice_seq_mc.py:


Choice model with a latent variable: sequential estimation (Monte-Carlo)
========================================================================

Mixture of logit, with Monte-Carlo integration
Measurement equation for the indicators.
Sequential estimation.

:author: Michel Bierlaire, EPFL
:date: Thu Apr 13 18:00:05 2023

.. GENERATED FROM PYTHON SOURCE LINES 14-56

.. code-block:: default


    import sys
    import biogeme.biogeme_logging as blog
    import biogeme.biogeme as bio
    import biogeme.exceptions as excep
    from biogeme import models
    from biogeme.results import bioResults
    from biogeme.expressions import (
        Beta,
        bioDraws,
        MonteCarlo,
        exp,
        log,
    )

    from read_or_estimate import read_or_estimate

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

    logger = blog.get_screen_logger(level=blog.INFO)
    logger.info('Example b04latent_choice_seq_mc.py')





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

 .. code-block:: none

    Example b04latent_choice_seq_mc.py 




.. GENERATED FROM PYTHON SOURCE LINES 57-58

Read the estimates from the structural equation estimation.

.. GENERATED FROM PYTHON SOURCE LINES 58-69

.. code-block:: default

    MODELNAME = 'b02one_latent_ordered'
    try:
        struct_results = 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 70-71

Coefficients.

.. GENERATED FROM PYTHON SOURCE LINES 71-81

.. code-block:: default

    coef_intercept = struct_betas['coef_intercept']
    coef_age_65_more = struct_betas['coef_age_65_more']
    coef_haveGA = struct_betas['coef_haveGA']
    coef_moreThanOneCar = struct_betas['coef_moreThanOneCar']
    coef_moreThanOneBike = struct_betas['coef_moreThanOneBike']
    coef_individualHouse = struct_betas['coef_individualHouse']
    coef_male = struct_betas['coef_male']
    coef_haveChildren = struct_betas['coef_haveChildren']
    coef_highEducation = struct_betas['coef_highEducation']








.. GENERATED FROM PYTHON SOURCE LINES 82-83

Latent variable: structural equation.

.. GENERATED FROM PYTHON SOURCE LINES 85-87

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

.. GENERATED FROM PYTHON SOURCE LINES 87-91

.. code-block:: default


    sigma_s = Beta('sigma_s', 1, None, None, 0)
    error_component = sigma_s * bioDraws('EC', 'NORMAL_MLHS')








.. GENERATED FROM PYTHON SOURCE LINES 92-93

Piecewise linear specification for income.

.. GENERATED FROM PYTHON SOURCE LINES 93-121

.. code-block:: default

    thresholds = [None, 4, 6, 8, 10, None]
    formula_income = models.piecewiseFormula(
        variable=ScaledIncome,
        thresholds=thresholds,
        betas=[
            struct_betas['beta_ScaledIncome_minus_inf_4'],
            struct_betas['beta_ScaledIncome_4_6'],
            struct_betas['beta_ScaledIncome_6_8'],
            struct_betas['beta_ScaledIncome_8_10'],
            struct_betas['beta_ScaledIncome_10_inf'],
        ],
    )


    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
        + error_component
    )








.. GENERATED FROM PYTHON SOURCE LINES 122-123

Choice model.

.. GENERATED FROM PYTHON SOURCE LINES 123-133

.. code-block:: default

    ASC_CAR = Beta('ASC_CAR', 0, None, None, 0)
    ASC_PT = Beta('ASC_PT', 0, None, None, 1)
    ASC_SM = Beta('ASC_SM', 0, None, None, 0)
    BETA_COST_HWH = Beta('BETA_COST_HWH', 0, None, None, 0)
    BETA_COST_OTHER = Beta('BETA_COST_OTHER', 0, None, None, 0)
    BETA_DIST = Beta('BETA_DIST', 0, None, None, 0)
    BETA_TIME_CAR_REF = Beta('BETA_TIME_CAR_REF', 0, None, 0, 0)
    BETA_TIME_PT_REF = Beta('BETA_TIME_PT_REF', 0, None, 0, 0)
    BETA_WAITING_TIME = Beta('BETA_WAITING_TIME', 0, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 134-137

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 137-140

.. code-block:: default

    BETA_TIME_PT_CL = Beta('BETA_TIME_PT_CL', -0.01, None, None, 0)
    BETA_TIME_CAR_CL = Beta('BETA_TIME_CAR_CL', -0.01, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 141-142

Definition of utility functions:.

.. GENERATED FROM PYTHON SOURCE LINES 142-163

.. 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 164-165

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 165-167

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 168-169

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

.. GENERATED FROM PYTHON SOURCE LINES 169-171

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 172-173

We integrate over omega using numerical integration

.. GENERATED FROM PYTHON SOURCE LINES 173-183

.. code-block:: default

    loglike = log(MonteCarlo(condprob))

    #
    # Create the Biogeme object. As the objective is to illustrate the
    # syntax, we calculate the Monte-Carlo approximation with a small
    # number of draws. To achieve that, we provide a parameter file
    # different from the default one: `few_draws.toml<few_draws.toml>`_
    the_biogeme = bio.BIOGEME(database, loglike, parameter_file='few_draws.toml')
    the_biogeme.modelName = 'b04latent_choice_seq_mc'





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

 .. code-block:: none

    File few_draws.toml has been parsed. 




.. GENERATED FROM PYTHON SOURCE LINES 184-186

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 186-188

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 189-195

.. 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: 11
    Final log likelihood: -1154.746
    Output file: b04latent_choice_seq_mc.html
    Results saved in file b04latent_choice_seq_mc.tex 
    LaTeX file: b04latent_choice_seq_mc.tex




.. GENERATED FROM PYTHON SOURCE LINES 196-197

.. 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>0.676777</td>
          <td>0.118907</td>
          <td>5.691674</td>
          <td>1.258000e-08</td>
        </tr>
        <tr>
          <th>ASC_SM</th>
          <td>0.407741</td>
          <td>0.423455</td>
          <td>0.962890</td>
          <td>3.356028e-01</td>
        </tr>
        <tr>
          <th>BETA_COST_HWH</th>
          <td>-1.710818</td>
          <td>0.566357</td>
          <td>-3.020738</td>
          <td>2.521593e-03</td>
        </tr>
        <tr>
          <th>BETA_COST_OTHER</th>
          <td>-0.651766</td>
          <td>0.233699</td>
          <td>-2.788905</td>
          <td>5.288661e-03</td>
        </tr>
        <tr>
          <th>BETA_DIST</th>
          <td>-1.922239</td>
          <td>0.710063</td>
          <td>-2.707140</td>
          <td>6.786558e-03</td>
        </tr>
        <tr>
          <th>BETA_TIME_CAR_CL</th>
          <td>-1.220522</td>
          <td>0.144733</td>
          <td>-8.432899</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>BETA_TIME_CAR_REF</th>
          <td>-13.335400</td>
          <td>2.789259</td>
          <td>-4.780984</td>
          <td>1.744396e-06</td>
        </tr>
        <tr>
          <th>BETA_TIME_PT_CL</th>
          <td>-0.713205</td>
          <td>0.140085</td>
          <td>-5.091230</td>
          <td>3.557473e-07</td>
        </tr>
        <tr>
          <th>BETA_TIME_PT_REF</th>
          <td>-4.560173</td>
          <td>1.196052</td>
          <td>-3.812688</td>
          <td>1.374634e-04</td>
        </tr>
        <tr>
          <th>BETA_WAITING_TIME</th>
          <td>-0.029117</td>
          <td>0.013123</td>
          <td>-2.218809</td>
          <td>2.649969e-02</td>
        </tr>
        <tr>
          <th>sigma_s</th>
          <td>-0.770324</td>
          <td>0.192815</td>
          <td>-3.995151</td>
          <td>6.465292e-05</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** (0 minutes 0.541 seconds)


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