D-Optimal Design for the Rasch Counts Model with Multiple Binary Predictors

TL;DR

This paper develops locally D-optimal experimental designs for Rasch Poisson count models with multiple binary predictors, enhancing efficient estimation of regression coefficients in psychological measurement.

Contribution

It introduces new locally D-optimal designs for Rasch Poisson and Rasch Poisson-Gamma models with binary predictors, linking these to generalized linear mixed models.

Findings

Derived conditions for effect sizes to achieve local D-optimality.

Presented optimal designs for models with multiple binary predictors.

Highlighted applicability to broader Poisson regression models.

Abstract

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.