ABSTRACT
It is common for data to be collected with a multivariate structure, for example, from a sample survey in which each individual is asked several questions or an experiment in which several outcomes are measured on each unit. In Sections 3.5 and 3.6, we introduced the most commonly used and useful models for multivariate data: the multinomial and multivariate normal models for categorical and continuous data, respectively. Why, then, have a separate chapter for multivariate models? Because, when combined with hierarchical models, or regression models, the standard distributions require additional work in specifying prior distributions and in computation. In this chapter, we discuss how to graft multivariate distributions onto the hierarchical and regression models that have been our focus in most of this book. Our basic approach, in modeling and computation, is to use normal distributions at the hierarchical level, while paying attention to the additional difficulties required in specifying distributions and computing with mean vectors and covariance matrices. We illustrate the resulting procedures with several examples.
