Modeling Joint and Marginal Distributions in the Analysis of Categorical Panel Data

Abstract

This article presents a unifying approach to the analysis of repeated univariate categorical (ordered) responses based on the application of the generalized log-linear modeling framework proposed by Lang and Agresti. It is shown that three important research questions in longitudinal studies can be addressed simultaneously. These questions are the following: What is the overall dependence structure of the repeated responses? What is the structure of the change between consecutive time points? and What is the structure of the change in the marginal distributions? Each of these questions involves specifying log-linear models for different marginal distributions of the multiway cross classification of the responses. The proposed approach is illustrated by means of two real data examples.