# 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**.

```{figure} ../../_static/images/tetrad-interface/box-by-box/generalized-pm.png
:name: tetrad-beneralized-pm-screenshot
:alt: Generalized Parametric Model

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.