REACTIONOn a Likelihood - Based Goodness - of - Fit Test of theBeta - Binomial

SUMMARY When faced with proportion data that exhibit extra-binomial variation, data analysts often consider the beta-binomial distribution as an alternative model to the more common bino-mial distribution. A typical example occurs in toxicological experiments with laboratory animals, where binary observations on fetuses within a litter are often correlated with each other. In such instances, it may be of interest to test for the goodness-of-t of the beta-binomial model; this eeort is complicated, however, when there is large variability among the litter sizes. We investigate a recent goodness-of-t test proposed by Brooks, Morgan, Ridout, and Pack (1997, Biometrics 53, 1097{1115) but nd that it lacks the ability to distinguish between the beta-binomial model and some severely non-beta-binomial models. Other tests and models developed in their article are quite useful and interesting, but are not examined herein.