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.
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