The methods and models for categorical data analysis cover considerable ground, ranging from regression-type models for binary and binomial data, count data, to ordered and unordered polytomous variables, as well as regression models that mix qualitative and continuous data. This article focuses on methods for binary or binomial data, which are perhaps the most widely applied models in categorical data analysis and may be the most relevant for institutional research where predictions such as program participation, graduation, or dropout are particularly relevant. These particular categorical models are also the most fully developed in the literature on multilevel models. In this article, the author provides a brief overview of two of the most important models for categorical data analysis to show how these models are adapted to the multilevel or mixed modeling framework using the generalized linear mixed model. He then examines a simple model of program placement from both the conventional modeling and then multilevel perspectives. Finally, he considers a more ambitious multilevel analysis of program dropout. (Contains 6 figures and 3 tables.)