Optimal designs for beta-binomial logistic regression models

Optimal designs for a logistic regression model with over-dispersion introduced by a beta-binomial distribution are characterized. Designs are defined by a set of design points and design weights as usual but, in addition, the experimenter must also make a choice of a sub-sampling design specifying the distribution of observations on sample sizes. In an earlier work it has been shown that Ds-optimal sampling designs for estimation of the parameters of the beta-binomial distribution are supported on at most two design points. This admits a simplified approach using single sample sizes. Linear predictor values for Ds-optimal designs using a common sample size are tabulated for different levels of over-dispersion and choice of subsets of parameters.