  We discuss a class of chain graph models for categorical variables defined by
what we call a multivariate regression chain graph Markov property. First, the
set of local independencies of these models is shown to be Markov equivalent to
those of a chain graph model recently defined in the literature. Next we
provide a parametrization based on a sequence of generalized linear models with
a multivariate logistic link function that captures all independence
constraints in any chain graph model of this kind.
