Clustered binary data with random cluster sizes

Abstract

In the analysis of clustered binary data with random cluster sizes, traditional approaches assuming fixed cluster sizes are generally used. Appropriate inference should take account of both intra-cluster correlation and extra-variation arising from the random cluster sizes. We introduce a dual Poisson random effects model for performing appropriate analyses of such data. Our orthodox best linear unbiased predictor approach to this model depends only on the first- and second- moment assumptions of unobserved random effects. This approach is illustrated with analyses of seed germination data and developmental toxicity data.