Generalized variance component models for clustered categorical response variables

A generalized variance component model is proposed for the analysis of a categorical response variable with extra-multinomial variation. Categorical data obtained from research designs such as randomized multicenter clinical trials or complex sample surveys with clustering frequently exhibit extra-variation resulting from intracluster correlation. General correlation patterns are accounted for by utilizing a mixed-effects modelling approach, estimating the cluster variance components through the method of moments and modelling functions of the observed proportions through the use of estimating equations. A flexible set of assumptions characterizing the underlying covariance structure for the proportions can be accommodated. The importance of accounting for extra-variation when performing hypothesis tests is highlighted with an application to data from a multi-investigator clinical trial.