Parameterizations and fitting of bi-directed graph models to categorical data

TL;DR

This paper explores two parameterizations of bi-directed graph models for categorical data, introducing a maximum likelihood fitting algorithm and discussing their utility in data analysis.

Contribution

It presents a new parameterization approach for bi-directed graph models and an algorithm for maximum likelihood fitting, enhancing their applicability in categorical data analysis.

Findings

Two parameterizations of bi-directed graph models are proposed.

An algorithm for maximum likelihood fitting is developed.

The models facilitate analysis of marginal independencies in categorical data.

Abstract

We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bi-directed graph models, under the global Markov property. Such models are useful data analytic tools especially if used in combination with other graphical models. The first parameterization, in the saturated case, is also known as the multivariate logistic transformation, the second is a variant that allows, in some (but not all) cases, variation independent parameters. An algorithm for maximum likelihood fitting is proposed, based on an extension of the Aitchison and Silvey method.