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. These may be represented as directed graphs that embody context-specific conditional independence relations. Here, the approach is developed from a statistical perspective. It is shown here that likelihood ratio tests may be constructed using standard contingency table methods, a model selection procedure that minimizes a penalized likelihood criterion is described, and a way to extend the models to incorporate covariates is proposed. The methods are applied to a small-scale dataset. Finally, it is shown that the models generalize certain subclasses of conventional undirected and directed graphical models.