Random Effects in Log-Linear Models

We conduct a simulation study of a two way layout of Poisson counts whose expectations conform to a log-linear model and whose row effects are sampled from a population. The model can apply to a number of contingency tables exhibiting non-constant relative risk. We evaluate the robustness of a generalization of the mixed model ANOVA F-test (Scheffe [1959]) to the presence of interactions. This test statistic, and its extensions to other log-linear models with random effects, is readily calculated in terms of the output of standard log-linear fitting procedures.