  In this paper, we derive optimal designs for the Rasch Poisson counts model
and the Rasch Poisson-Gamma 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 the Rasch Poisson-Gamma
counts model we will specify these models as a particular generalized linear
mixed model. 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 of 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.
