Methods are presented for modeling dose-related effects in proportion data when extra-binomial variability is a concern. Motivation is taken from experiments in developmental toxicology, where the observed proportions.

Appeal is made to the well-known beta-binomial distribution to represent the overdispersion. From this, an exponential function of the linear predictor is used to model the dose-response relationship. The spesification was introduced previously for econometric applications by Heckman and Willis; it induces a form logistic regression for mean response, together with a reciprocal biexponential model for the intralitter correlation.