Detail: Parametric & Instantiated Model Types

This page summarizes the main model families currently supported in the Parametric Model and Instantiated Model boxes, and how they interact with estimation and simulation.

Model families

  • Bayes (multinomial)
    Discrete Bayesian networks where each variable has a finite set of states and conditional probability tables (CPTs). Suitable for fully discrete data.

  • SEM (linear SEM)
    Linear Gaussian structural equation models with path coefficients and Gaussian error terms. Often used for continuous data and covariance-structure analysis.

  • Hybrid (conditional Gaussian)
    Conditional Gaussian (CG) models that combine discrete and continuous variables: discrete parents with conditional linear-Gaussian distributions for continuous children. This corresponds to the Hybrid API we introduced in the Tetrad library.

  • Generalized
    A flexible framework in which the functional form and error distribution for each variable are specified by hand (e.g., nonlinear functions, non-Gaussian errors). This is intended for advanced users who need fine-grained control over the data-generating mechanism.

For more details on each family, see:

  • Tetrad Interface → Detail: Bayes (Multinomial) Parametric Model

  • Tetrad Interface → Detail: SEM (Linear) Parametric Model

  • Tetrad Interface → Detail: Hybrid (Conditional Gaussian) Parametric Model

  • Tetrad Interface → Detail: Generalized Parametric Model

  • Tetrad Interface → Detail: Bayes (Multinomial) Instantiated Model

  • Tetrad Interface → Detail: SEM (Linear) Instantiated Model

  • Tetrad Interface → Detail: Hybrid (Conditional Gaussian) Instantiated Model

  • Tetrad Interface → Detail: Generalized Instantiated Model

Interaction with Estimator and Simulation

  • Not all estimators support all model families; SEM models, for example, have specialized covariance-structure estimators with rich fit indices.

  • Simulation from a parametric or instantiated model depends on:

    • The availability of a generative interpretation for that model family.

    • The configuration of error distributions and link functions (especially for Generalized models).

For practical guidance, see the Parametric Model and Instantiated Model box pages and the Simulation box page.