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Chain graph models of multivariate regression type for categorical data. (English) Zbl 1221.62108

Summary: 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.

MSC:

62J12 Generalized linear models (logistic models)
05C90 Applications of graph theory
62H12 Estimation in multivariate analysis
60J99 Markov processes
62H10 Multivariate distribution of statistics
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