Optimal Design in Repeated Testing for Count Data

TL;DR

This paper develops optimal experimental designs for count data growth models in educational testing, focusing on the Rasch Poisson-Gamma model to efficiently estimate respondent abilities over time.

Contribution

It introduces locally D-optimal designs for the RPGCM model, accommodating various growth curve structures and analyzing design sensitivity to parameter misspecification.

Findings

Derived explicit optimal designs for different growth models

Analyzed the robustness of designs via D-efficiency measures

Applicable to educational and psychological testing scenarios

Abstract

In this paper, we develop optimal designs for growth curve models with count data based on the Rasch Poisson-Gamma counts (RPGCM) model. This model is often used in educational and psychological testing when test results yield count data. In the RPGCM, the test scores are determined by respondents ability and item difficulty. Locally D-optimal designs are derived for maximum quasi-likelihood estimation to efficiently estimate the mean abilities of the respondents over time. Using the log link, both unstructured, linear and nonlinear growth curves of log mean abilities are taken into account. Finally, the sensitivity of the derived optimal designs due to an imprecise choice of parameter values is analyzed using D-efficiency.