Log-Linear and Marginal Models

Abstract

Log-linear models for the joint distribution of several categorical variables assume that the cell frequencies or probabilities are influenced by multiplicative effects associated with groups of variables. These effects are conditional on the remaining variables in the analysis. Marginal log-linear models provide more flexibility, by allowing some of the effects to depend only on subsets of variables. These models have important applications in social mobility, longitudinal data or causal analysis, and are the basis of doing regression analysis and graphical modeling for categorical variables. This article reviews several of the reasons why log-linear models are considered, discusses the interpretation of such models and of the related parameters, introduces marginal log-linear models, and describes several of the areas of application.