In Chapters 1-4 we developed a variety of probability models for analyzing different types of categorical data. In each case we started with a fixed set of explanatory variables and explored techniques of model fitting and inference assuming that the model and the chosen variables were correct. However, each of these probability models is an assumption that may or may not be satisfied by the data from a particular problem. Also, in practice there is often uncertainty regarding which explanatory variables are needed in a model. Indeed, the goal of many categorical regression analyses is to identify which variables from a large number of candidates are associated with a response or with one another, and which are not.