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.
"Chain graph models of multivariate regression type for categorical data." Bernoulli 17 (3) 827 - 844, August 2011. https://doi.org/10.3150/10-BEJ300