  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.
