No Interactions

Abstract

In many practically relevant experimental situations no interactions occur between the factors of influence. Also in these cases there are many design problems in which product designs are optimum and, again, the associated marginal designs are optimum in the corresponding marginal models. In particular, D-optimality is included if there is a constant term in the model under consideration. Such additive models with an explicit constant term will be treated in the first subsection. The second subsection deals with the case that for all or, at least, for all but one factors the regression functions are centered with respect to the optimum designs in the marginal models and the product of them results in orthogonal estimators of the parameters associated with the effects of the single factors in the whole model.