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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/latent/measurement_equations_likert.py"
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        :ref:`Go to the end <sphx_glr_download_auto_examples_latent_measurement_equations_likert.py>`
        to download the full example code.

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.. _sphx_glr_auto_examples_latent_measurement_equations_likert.py:


Specification of the discrete measurement equations
===================================================

Measurement equations for the Likert indicators as functions of the latent variables.

Michel Bierlaire
Wed Sept 03 2025, 08:15:52

.. GENERATED FROM PYTHON SOURCE LINES 11-23

.. code-block:: Python


    import numpy as np
    from likelihood_discrete import likelihood_discrete_mimic
    from measurement_equations_continuous import generate_continuous_measurement_equations
    from relevant_data import (
        latent_variables_indicators,
        normalized,
    )
    from structural_equations import LatentVariable

    from biogeme.expressions import Beta, Expression, exp


.. GENERATED FROM PYTHON SOURCE LINES 24-25

Measurement equations.

.. GENERATED FROM PYTHON SOURCE LINES 25-57

.. code-block:: Python



    def generate_likert_measurement_equations(
        car_centric_attitude: LatentVariable, urban_preference_attitude: LatentVariable
    ) -> Expression:
        """

        :param car_centric_attitude: expression for the latent_old variable.
        :param urban_preference_attitude: expression for the latent_old variable.
        :return: the likelihood contribution of the likert indicators
        """
        models = generate_continuous_measurement_equations(
            latent_variables=[car_centric_attitude, urban_preference_attitude],
            latent_variables_indicators=latent_variables_indicators,
            normalized=normalized,
        )

        # Symmetric threshold.
        delta_1 = exp(Beta('log_delta_1', np.log(0.3), None, None, 0))
        delta_2 = exp(Beta('log_delta_2', np.log(0.8), None, None, 0))
        tau_1 = -delta_1 - delta_2
        tau_2 = -delta_1
        tau_3 = delta_1
        tau_4 = delta_1 + delta_2

        likert_likelihood = likelihood_discrete_mimic(
            measurement_equations=models,
            threshold_parameters=[tau_1, tau_2, tau_3, tau_4],
            discrete_values=[1, 2, 3, 4, 5],
            missing_values=[6, -1, -2],
        )
        return likert_likelihood


.. _sphx_glr_download_auto_examples_latent_measurement_equations_likert.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

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      :download:`Download Python source code: measurement_equations_likert.py <measurement_equations_likert.py>`

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      :download:`Download zipped: measurement_equations_likert.zip <measurement_equations_likert.zip>`


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