Random effects in log—linear models

Abstract

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.

Keywords:

• Random effects
• mixed model
• Poisson
• contingency table
• relative risk
• log—linear models
• Monte Carlo method