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.
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