Log-Linear Models: Interpretation

Abstract

This chapter starts with the specification and handling of regression type problems for categorical data. The log-linear parameters can be transformed into multiplicative parameters, and these are useful in dealing with the regression problem for categorical variables, where this approach provides a clear and testable concept of separate effects versus joint effect of the explanatory variables. Further topics related to the use of log-linear models in data analysis are also considered. First, the selection and interpretation of log-linear models are illustrated in regression type and non-regression type problems, using real data sets. Two special classes of log-linear models, decomposable and graphical log-linear models, are presented next. Decomposable log-linear models may be seen as direct generalizations of conditional independence. Graphical log-linear models, which are the basis of many current applications of log-linear models, may also be interpreted using generalized conditional independence statements, called Markov properties. Further, these models admit a representation using graphs, where the nodes are the variables in the model. Next, a representation of every log-linear model as the intersection of several log-linear models is discussed, where all of the latter models belong to one of two classes of simple log-linear models. One is the model of conditional joint independence of a group of variables, given all other variables (and graphical log-linear models) may be represented as intersections of such models only and (in the case of non-graphical models) no highest-order conditional interaction among a group of variables.