Bootstrap Goodness-of-Fit Test for the Beta-Binomial Model

A common question in the analysis of binary data is how to deal with overdispersion. One widely advocated sampling distribution for overdispersed binary data is the beta-binomial model. For example, this distribution often is used to model litter effects in toxicological experiments. Therein, testing the null hypothesis of a beta-binomial distribution against all other distributions is difficult due to the large variability in litter sizes. We investigate a recent test proposed by Brooks et al. (1997, Biometrics) but find it to have low power in comparison with a Pearson test. Therefore, we generalize the Pearson test statistic by combining Pearson statistics from individual litter sizes, and estimate the p-value using bootstrap techniques. A Monte Carlo study confirms the accuracy and power of our omnibus test against a beta-binomial distribution contaminated with a few outliers. The method also is applied to data from environmental toxicity studies. Key words: Beta-binomial; Bootstr..