This chapter describes a family of models for mixed discrete and continuous variables that combine and generalize the models of the previous two chapters. Graphical models for mixed discrete and continuous variables were introduced by Lauritzen and Wermuth (1989), and both undirected and directed types of models were described. The undirected models (graphical interaction models) were extended to a broader class, the hierarchical interaction models, in Edwards (1990). The latter are constructed by combining loglinear models for discrete variables with graphical Gaussian models for continuous variables, as we now describe.
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