  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.
