Detail: Generalized Parametric Model

This page describes the Generalized model type in the Parametric Model and Instantiated Model boxes. These models offer a flexible framework where you specify functional forms and error distributions by hand.

Generalized Parametric Model

When to use Generalized models

Use the Generalized model family when:

• The predefined families (Bayes, SEM, Hybrid) are too restrictive, and

• You want to define custom relationships, such as:

  • Nonlinear functions of parents.

  • Non-Gaussian error terms.

  • Mixtures or other specialized distributions.

This model family is intended for advanced users who need fine-grained control over the data-generating mechanism.

Main panel layout

For Generalized models, the main panel typically exposes:

• A list of variables and their parents (based on an underlying graph).

• For each variable:

  • A description or editor for the functional form (e.g., symbolic expression, code snippet, or parameterized function).

  • Controls for specifying the error distribution (e.g., Gaussian with parameters, non-Gaussian families, or user-defined errors).

The exact UI may depend on how the Generalized family is implemented in your Tetrad version.

Typical workflow

1. Create a Generalized parametric model

   • Start from a graph in the Graph box capturing the qualitative structure.

   • In the Parametric Model box, choose New → Generalized to create a skeleton model using that structure.

2. Specify functional forms

   • For each variable, define how it depends on its parents:

     • Linear or polynomial functions.

     • Nonlinear functions (e.g., sigmoids, piecewise definitions).

   • Provide any needed parameters or hyperparameters.

3. Specify error distributions

   • Choose an appropriate error family for each variable:

     • Gaussian, heavy-tailed, skewed, etc.

   • Set distribution parameters (variance, scale, shape, etc.).

4. Use with Simulation

   • Generalized models are often used primarily as data-generating models in the Simulation box to create challenging nonlinear or non-Gaussian datasets.

5. Estimation (if supported)

   • In some configurations, the Estimator box may be able to fit subsets of parameters in a Generalized model; in others, the model is used mainly for simulation.

Tips and caveats

• Start simple: begin with modest nonlinearities or deviations from Gaussian errors and build complexity gradually.

• Be mindful of identifiability and overparameterization; extremely flexible models can mimic many different structures.

• Document your functional forms and error choices (for example, using a Note box) so that simulation studies remain reproducible.