ABSTRACT
The log-linear model plays a prominent role in the statistical analysis of categorical data. Log-linear analysis of a contingency table aims at obtaining a parsimonious model for the cell probabilities (or expected frequencies) that provides a statistically acceptable explanation of the association among the observed variables with as few parameters as necessary. In general log-linear analysis is applied to the contingency table that contains the observed frequencies from the joint distribution of all variables involved in the analysis. However, many other substantively interesting questions may be asked that pertain not to the original table, but to subsets of marginal tables that can be derived from it. Some of these questions may be answered by a log-linear analysis on these marginal tables. In longitudinal research, for example, changes in the marginal distribution of some variables may be studied by testing hypotheses of marginal homogeneity. Furthermore, changes in the association among variables over time may be studied by testing hypotheses about equality of corresponding interaction parameters in log-linear models for different marginal tables. Some other questions, however, cannot be reformulated in terms of log-linear models. As an example of this type of research question we consider the question of whether the values of some well-known association coefficients change over time.
