Some context-specific graphical models for discrete longitudinal data

TL;DR

This paper develops a statistical methodology for context-specific graphical models for discrete longitudinal data, enabling likelihood-based model selection and generalizing traditional graphical models.

Contribution

It introduces a statistical approach to acyclic probabilistic finite automata, including likelihood ratio tests and model selection techniques.

Findings

Likelihood ratio tests can be constructed using contingency table methods.

Models generalize subclasses of traditional graphical models.

Methodology facilitates model comparison and selection.

Abstract

Ron et al (1998) introduced a rich family of models for discrete longitudinal data, called acyclic probabilistic finite automata. These may be described as context-specific graphical models, since they are represented as directed multigraphs that embody context-specific conditional independence relations. Here we develop the methodology from a statistical modelling perspective. We show how likelihood ratio tests may be constructed using standard contingency table methods, and indicate how these may be used in model selection. We also show that the models generalize certain subclasses of conventional undirected and directed graphical models.