D-optimal design for the Rasch counts model with multiple binary predictors

In this paper we derive optimal designs for the Rasch Poisson counts model and its extended version of the (generalized) negative binomial counts model incorporating several binary predictors for the difficulty parameter. To efficiently estimate the regression coefficients of the predictors, locally D-optimal designs are developed. After an introduction to the Rasch Poisson counts model and its extension, we will specify these models as particular generalized linear models. Based on this embedding, optimal designs for both models including several binary explanatory variables will be presented. Therefore, we will derive conditions on the effect sizes for certain designs to be locally D-optimal. Finally, it is pointed out that the results derived for the Rasch Poisson models can be applied for more general Poisson regression models which should receive more attention in future psychological research.