A-optimal design measures for one-way layouts with additive regression

Abstract

Abstract For linear models with one discrete factor and additive general regression term the problem of characterizing A-optimal design measures for inference on (i) treatment effects, (ii) the regression parameters and (iii) all parameters will be considered. In any of these problems product designs can be found which are optimal among all designs, and equal weigth 1/J may be given to each of the J levels of the discrete factor. For problem (i) and (ii) the allocation of the continuous factors for the regression term should follow a suitable optimal design for the corresponding pure regression model, whereas for problem (iii) this would not give an A-optimal product design. For this problem an equivalence theorem for A-optimal product designs will be given. An example will illustrate these results. Finally, by analyzing a model with two discrete factors it will be shown that for enlarged models the best product designs may not be A-optimal.