Statistical Modelling 15 (4) (2015), 301–325

Context-specific graphical models for discrete longitudinal data

David Edwards
Centre for Quantitative Genetics and Genomics,
Aarhus University,
Denmark
e-mail: David.Edwards@agrsci.dk

Smitha Ankinakatte
Department of Statistics,
Mangalore University,
India


Abstract:

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.

Keywords:

acyclic probabilistic finite automata; Graphical model context-specific; state merging; conditional independence; Markov; chain event graph.
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