Loglinear Marginal Models

Abstract

Loglinear models provide the most flexible tools for analyzing relationships among categorical variables in complex tables. It will be shown in this chapter how to apply these models in the context of marginal modeling. First, in Section 2.1, the basics of ordinary loglinear modeling will be explained. The main purpose of this section is to introduce terminology and notation and those aspects of loglinear modeling that will be used most in the remainder of this book. It will be assumed that the reader already has some familiarity with loglinear modeling and, therefore, the discussion will be concise. An advanced overview of loglinear models is provided by Agresti (2002); an intermediate one by Hagenaars (1990) and an introduction is given by Knoke and Burke (1980) among many others. In Section 2.2, several motivating examples will be presented showing what types of research questions can be answered by means of loglinear marginal modeling. Finally, in Section 2.3, a general ML estimation procedure will be discussed for testing and estimating loglinear marginal models.