Estimation and testing with overdispersed proportions using the beta-logistic regression model of Heckman and Willis

Methods are presented for modeling dose-related effects in proportion data when extra-binomial variability is a concern. Motivation is taken from expe riments in developmental toxicology, where similarity among conceptuses wit hin a litter leads to intralitter correlations and to overdispersion in the observed proportions. Appeal is made to the well-known beta-binomial distr ibution to represent the overdispersion. From this, an exponential function of the linear predictor is used to model the dose response relationship. T he specification was introduced previously for econometric applications by Heckman and Willis; it induces a form of logistic regression for the mean r esponse, together with a reciprocal biexponential model for the intralitter correlation. Large-sample, likelihood-based methods for estimating and tes ting the joint proportion-correlation response are studied. A developmental toxicity data set illustrates the methods.