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.

中文翻译：

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具有多个二元预测变量的 Rasch 计数模型的 D 最优设计。

在本文中，我们推导出 Rasch Poisson 计数模型及其扩展版本的（广义）负二项式计数模型的最佳设计，该模型结合了难度参数的几个二元预测变量。为了有效地估计预测变量的回归系数，开发了局部 D 最优设计。在介绍了 Rasch Poisson 计数模型及其扩展之后，我们将把这些模型指定为特定的广义线性模型。基于这种嵌入，将呈现两个模型的最佳设计，包括几个二元解释变量。因此，我们将推导出某些设计的效果大小条件，以使其成为局部 D 最优。最后，