# Detail: Hybrid (Conditional Gaussian) Parametric Model

This page describes the **Hybrid (conditional Gaussian)** model type in the **Parametric Model** and
**Instantiated Model** boxes. These are **conditional Gaussian (CG)** models that combine discrete
and continuous variables.

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

Hybrid Parametric Model
```

## When to use Hybrid models

Use the Hybrid model family when:

- You have a mix of **discrete and continuous variables**, and
- You want a model in which:
  - Discrete variables can act as parents of continuous variables, and
  - Continuous variables have **linear-Gaussian** conditional distributions given their parents,
    with parameters that may depend on discrete parent configurations.

This corresponds to the **Hybrid / CG** API in the Tetrad library.

## Main panel layout

For Hybrid models, the main panel typically shows:

- Variable types (discrete vs continuous).
- For **discrete variables**:
  - State spaces and CPT-style parameters for \( P(X \mid 	ext{Parents}(X)) \) when parents are
    discrete.
- For **continuous variables**:
  - Linear-Gaussian regression parameters conditional on parents, often separated by discrete
    parent configurations (i.e., different regression coefficients and variances per configuration).

The exact layout may be a combination of CPT-like editors and SEM-style parameter tables.

## Typical workflow

1. **Create a Hybrid parametric model**
   - Start from a mixed graph in the *Graph* box where variables have been typed as discrete
     or continuous.
   - In the *Parametric Model* box, choose **New → Hybrid (conditional Gaussian)**.

2. **Specify discrete and continuous parts**
   - For discrete variables, edit their CPT parameters as in the Bayes case.
   - For continuous variables, specify regression coefficients and error variances, potentially
     separately for each configuration of discrete parents.

3. **Estimate from data**
   - Pass the Hybrid model and a mixed dataset to the *Estimator* box.
   - Choose a Hybrid/CG estimator (when available) to fit parameters.

4. **Use with Simulation and Compare**
   - Use the fitted Hybrid model in the *Simulation* box to generate mixed discrete/continuous data.
   - Compare learned graphs or models against the Hybrid generative truth in *Compare*.

## Tips and caveats

- Hybrid models are more complex; keep an eye on:
  - The number of discrete parent configurations (which can grow quickly).
  - Whether the sample size is sufficient to estimate separate regressions for each configuration.
- Ensure that variable types are set correctly **before** creating the Hybrid parametric model.