Conferences

In this work we discuss a class of models for discrete distributions representable by chain graphs. These models, proposed first by Cox and Wermuth (1993) and recently discussed by Drton (2009), have an interpretation distinct both from the classical (Lauritzen, Wermuth, Frydenberg) and the alternative (Andersson, Madigan, Perlman) interpretation. Under a special block-recursive Markov property, these chain graph models have a multivariate regression interpretation.

We propose a parameterization for discrete distributions which is a recursive version of the multivariate logistic regression models of Glonek and McChullagh (1995). This parameterization satisfies the set of independencies under the block-recursive Markov property by imposing linear constraints. We also
show that these models are equivalent to marginal log-linear models of Bergsma and Rudas (2002) with linear constraints. Moreover we propose an algorithm for fitting multivariate regression chain graph models based and the procedure developed by Lang (2005). The model is illustrated through an example based on a dataset containing joint responses, intermediate and purely explanatory variables taken from the General Social Survey.