ABSTRACT
This chapter presents graphical models in which the observed variables are categorical, that is, whose state space consists of a finite number of values. It provides an overview of discrete graphical models focused on chain graph models and, more specifically, on the role played by the class of regression graph models within the existing families of graphical models. The chapter focuses on regression graph models because this family of models allows approaching discrete graphical models with a sufficient degree of generality. It shows that some well-known properties of this parameterization, such as the connection between vanishing terms and independence relationships, the capability of defining context specific independencies, follow directly from the constructing procedure. The chapter also presents the material for the special case of binary data. It describes the use of log-linear parameterizations in graphical modeling, and to models specified by means of regression graph with an emphasis on their connection with other relevant families of graphical models.
