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

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

.. _sphx_glr_auto_examples_latent_structural_equations.py:


Specification of the structural equations
=========================================

Structural equations as functions of the latent variables.

Michel Bierlaire
Wed Sept 03 2025, 08:13:37

.. GENERATED FROM PYTHON SOURCE LINES 11-36

.. code-block:: Python


    from typing import NamedTuple

    from relevant_data import (
        car_centric_name,
        car_explanatory_variables,
        urban_explanatory_variables,
        urban_preference_name,
    )

    from biogeme.expressions import (
        Beta,
        Draws,
        Expression,
        LinearTermTuple,
        LinearUtility,
        Variable,
    )


    class LatentVariable(NamedTuple):
        name: str
        expression: Expression



.. GENERATED FROM PYTHON SOURCE LINES 37-38

Structural equation: car centric attitude

.. GENERATED FROM PYTHON SOURCE LINES 38-74

.. code-block:: Python

    def build_car_centric_attitude(
        estimated_parameters: dict[str, float] | None = None,
    ) -> LatentVariable:
        """Builds the expression for the structural equation of the car centric attitude

        :param estimated_parameters: if not None, provides the value of the parameters for
            the direct calculation.
        :return: the expression for the structural equation
        """
        prefix = 'struct_car'
        if estimated_parameters is None:
            car_struct_coefficients = {
                variable_name: Beta(f'{prefix}_{variable_name}', 0.0, None, None, 0)
                for variable_name in car_explanatory_variables
            }
            sigma_car_centric = Beta(f'{prefix}_sigma', 1.0, None, None, 0)

        else:
            car_struct_coefficients = {
                variable_name: estimated_parameters[f'{prefix}_{variable_name}']
                for variable_name in car_explanatory_variables
            }
            sigma_car_centric = estimated_parameters[f'{prefix}_sigma']

        car_centric_attitude = LinearUtility(
            [
                LinearTermTuple(
                    beta=car_struct_coefficients[variable_name], x=Variable(variable_name)
                )
                for variable_name in car_explanatory_variables
            ]
        ) + sigma_car_centric * Draws(f'{prefix}_error_term', 'NORMAL_MLHS_ANTI')

        return LatentVariable(name=car_centric_name, expression=car_centric_attitude)



.. GENERATED FROM PYTHON SOURCE LINES 75-77

Latent variable for the urban preference attitude
Structural equation

.. GENERATED FROM PYTHON SOURCE LINES 77-113

.. code-block:: Python

    def build_urban_preference_attitude(
        estimated_parameters: dict[str, float] | None = None,
    ) -> LatentVariable:
        """Builds the expression for the structural equation of the urban preference
            attitude

        :param estimated_parameters: if not None, provides the value of the parameters for
            the direct calculation
        :return: the expression for the structural equation
        """
        prefix = 'struct_urban'

        if estimated_parameters is None:
            urban_struct_coefficients = {
                variable_name: Beta(f'{prefix}_{variable_name}', 0.0, None, None, 0)
                for variable_name in urban_explanatory_variables
            }
            sigma_urban_preference = Beta(f'{prefix}_sigma', 1.0, None, None, 0)
        else:
            urban_struct_coefficients = {
                variable_name: estimated_parameters[f'{prefix}_{variable_name}']
                for variable_name in urban_explanatory_variables
            }
            sigma_urban_preference = estimated_parameters[f'{prefix}_sigma']

        urban_preference_attitude = LinearUtility(
            [
                LinearTermTuple(
                    beta=urban_struct_coefficients[variable_name], x=Variable(variable_name)
                )
                for variable_name in urban_explanatory_variables
            ]
        ) + sigma_urban_preference * Draws(f'{prefix}_error_term', 'NORMAL_MLHS_ANTI')
        return LatentVariable(
            name=urban_preference_name, expression=urban_preference_attitude
        )


.. _sphx_glr_download_auto_examples_latent_structural_equations.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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