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

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

.. _sphx_glr_auto_examples_latent_measurement_equations_continuous.py:


Specification of the continuous measurement equations
=====================================================

Measurement equations for the (latent) indicators associated with the Likert scale,
as functions of the latent variables.

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

.. GENERATED FROM PYTHON SOURCE LINES 12-27

.. code-block:: Python


    from itertools import chain
    from typing import NamedTuple

    from structural_equations import LatentVariable

    from biogeme.expressions import Beta, Expression, MultipleSum, Numeric


    class MeasurementEquation(NamedTuple):
        intercept: Expression
        linear_terms: Expression
        scale_parameter: Expression



.. GENERATED FROM PYTHON SOURCE LINES 28-29

Measurement equations

.. GENERATED FROM PYTHON SOURCE LINES 29-72

.. code-block:: Python

    def generate_continuous_measurement_equations(
        latent_variables: list[LatentVariable],
        latent_variables_indicators: dict[str, list[str]],
        normalized: dict[str, float],
    ) -> dict[str, MeasurementEquation]:
        all_indicators = set(chain.from_iterable(latent_variables_indicators.values()))
        result_dict = {}
        for indicator in all_indicators:
            # Intercept
            intercept = Beta(f'meas_intercept_{indicator}', 0, None, None, 0)

            # Coefficients for each latent_old variables
            list_of_terms = list()
            for latent_variable in latent_variables:
                list_of_indicators = latent_variables_indicators[latent_variable.name]
                if indicator in list_of_indicators:
                    coefficient = (
                        normalized[indicator]
                        if indicator in normalized
                        else Beta(
                            f'meas_{latent_variable.name}_coeff_{indicator}',
                            0,
                            None,
                            None,
                            0,
                        )
                    )
                    term = coefficient * latent_variable.expression
                    list_of_terms.append(term)

            # Scale parameters of the error terms.
            scale_parameter = (
                Numeric(1)
                if indicator in normalized.keys()
                else Beta(f'meas_scale_{indicator}', 1, 1.0e-4, None, 0)
            )
            the_equation = MeasurementEquation(
                intercept=intercept,
                linear_terms=MultipleSum(list_of_terms) if list_of_terms else Numeric(0),
                scale_parameter=scale_parameter,
            )
            result_dict[indicator] = the_equation
        return result_dict


.. _sphx_glr_download_auto_examples_latent_measurement_equations_continuous.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

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


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_