Chain graph models of multivariate regression type for categorical data

TL;DR

This paper introduces a class of chain graph models for categorical data, establishing their independence properties and providing a parametrization using generalized linear models with multivariate logistic links.

Contribution

It defines a new multivariate regression chain graph model for categorical variables, linking local independencies to existing models and offering a comprehensive parametrization method.

Findings

Models are Markov equivalent to existing chain graph models.

A parametrization using generalized linear models captures all independence constraints.

Provides a framework for analyzing categorical data with chain graph structures.

Abstract

We discuss a class of chain graph models for categorical variables defined by what we call a multivariate regression chain graph Markov property. First, the set of local independencies of these models is shown to be Markov equivalent to those of a chain graph model recently defined in the literature. Next we provide a parametrization based on a sequence of generalized linear models with a multivariate logistic link function that captures all independence constraints in any chain graph model of this kind.