Partial Interactions

Abstract

In the previous Sections 4 and 5 we have treated experimental situations either with complete product-type interactions or with no interactions and discovered that the same product designs are D-optimum in both cases. This result can be extended to the intermediate interaction structure of complete M-factor interactions which will be shown in Subsection 6.1. In the second subsection we treat the frequently occuring situation that the model associated with one of the factors is invariant with respect to a group of transformations which acts transitively on the marginal design region. In this case the restriction to product designs is possible due to the invariance structure. However, in contrast to the previous results the marginals of the optimum designs are not necessarily optimum in the marginal models.