In the previous chapter we developed models with one categorical predictor. In this chapter we expand our consideration to models with two or more categorical predictor variables. Our reasons for wanting to include more than one categorical variable as a predictor in our model are the same as those that motivated us to expand from simple regression models with one predictor to multiple regression models with two or more predictors in Chapter 6. Models in which predictions are conditional on two or more categorical variables may be required by our data and, more importantly, by the underlying process that generates the data. Just as in multiple regression, controlling for one categorical variable by including it in the model often allows us to have a better look at the eﬀects of other categorical variables. Also, as in multiple regression, we are often interested in modeling the joint eﬀect of two or more categorical variables. With categorical variables we will be especially interested in whether the eﬀect of a given categorical variable depends on the levels of the other categorical variables; that is, we are interested in whether or not there is an interaction between the categorical variables analogous to the interactions of continuous variables in multiple regression considered in Chapter 7.