This chapter covers multivariate categorical distributions. In the simplest case, the data can be presented as a two-way contingency table (also called a cross tabulation or cross tab) of frequency counts. The contingency table contains expected cell probabilities and counts formed from products of marginal probabilities and counts. The chi-square test again is used for the contingency table and is the same as testing multiple categorical responses for independence.

Correspondence analysis is shown as a graphical technique useful when the response and factors have many levels or values.

Also, a more general categorical response model is used to introduce nominal and ordinal logistic regression, which allows multiple continuous or categorical factors.