A marginal model for binomial data where the experimental units involving one or two random factors is presented. Two variance-covariance models are derived based on the multiplicative error formulation. The parameters of mean and variance components are estimated using quasi-likelihood and method of moments, respectively. The model is applied to analyzing multivariate overdispersed binomial data from a developmental toxicity experiment.

Key Words
Extra-binomial variation; Mixed effects model; Nested design; Random effects model; Two-way layout.

James J. Chen is Mathematical Statistician, Division of Biometry and Risk Assessment, National Center for Toxicological Research, Food and Drug Administration, Jefferson, Arkansas 72079 (E-mail: jchen@nctr.fda.gov). Hongshik Ahn is Assistant Professor, Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, New York 11794-3600.