<i>D</i> -optimal designs for beta binomial regression

Optimal designs describe the sampling distributions that achieve most efficient estimation. In this study, we apply optimal design theory to find optimal designs for the beta binomial (BB) regression model, where both location and dispersion are functions of a predictor. A major application of the BB regression model is in psychological test norming, where the location and the dispersion of test scores can be age dependent. Motivated by this context, we derive and characterize locally D -optimal designs for the BB regression model. In a practical example, we consider the designs’ sensitivity to specification of model parameters, model form and optimality criterion. The designs were found to be relatively robust to these effects and thus show promise for practical implementation. However, more research is needed to investigate the suitability of the D -optimality criterion for psychological test norming and to extend the designs to be globally optimal.