On a likelihood-based goodness-of-fit test of the beta-binomial model

When faced with proportion data that exhibit extra-binomial variation, data analysts often consider the beta-binomial distribution as an alternative m odel to the more common binomial distribution. A typical example occurs in toxicological experiments with laboratory animals, where binary observation s 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 fit of the bet a-binomial model; this effort is complicated, however, when there is large variability among the litter sizes. We investigate a recent goodness-of-fit test proposed by Brooks et al. (1997, Biometrics 53, 1097-1115) but find t hat it lacks the ability to distinguish between the beta-binomial model and some severely non-beta-binomial models. Other tests and models developed i n their article are quite useful and interesting but are not examined herei n.