A class of context-specific graphical models for discrete longitudinal data

Ron et al (1998) introduced a rich family of models for discrete longitudinal data, called acyclic probabilistic finite automata (APFA). An APFA may be represented as a directed multigraph, and embodies a set of context-specific conditional independence relations that may be read off the graph. So it is a type of context-specific graphical model for discrete longitudinal data. In this paper we develop the methodology from a statistical perspective. We show how likelihood ratio tests may be constructed using standard contingency table methods, and how the algorithm of Ron et al (1998) to select an APFA given a data sample may be modified to minimize a penalized likelihood criterion such as AIC. Finally we show that the models generalize certain subclasses of conventional undirected and directed graphical models.