Optimal design for estimating the mean ability over time in repeated item response testing

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 nonlinear 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.
Keywords: D-optimal design; Growth curve; Repeated measures model; Mixed effect model