Optimal Design for Estimating the Mean Ability over Time in Repeated Item Response Testing

TL;DR

This paper develops methods for designing optimal repeated measures studies to accurately estimate mean ability over time, including novel theoretical tools and computational approaches for nonlinear growth models.

Contribution

It introduces a new equivalence theorem for design optimality and applies computational methods to determine D-optimal designs for nonlinear growth curve models.

Findings

Derived a novel equivalence theorem for design optimality.

Determined D-optimal designs for nonlinear growth models.

Validated designs through computational methods.

Abstract

We present general results on D-optimal designs for estimating the mean response in repeated measures growth curve models with metric outcomes. For this situation, we derive a novel equivalence theorem for checking design optimality. The motivation of this work originates from designing a study in psychological item response testing with multiple retests to measure the improvement in ability. Besides introductory linear growth curves for which analytical results can be obtained, we consider two non-linear growth curve models incorporating an increasing mean ability and a saturation effect. For these models, D-optimal designs are determined by computational methods and are validated by means of the equivalence theorem.