Optimal designs on the refinement of the $N$-way classification model

Abstract

Under a refined linear model, we establish some methods to construct Φ -optimal n -way classification designs for comparing p test treatments with a standard treatment from Φ -optimal m -way (m<n) classification designs for comparing the same contrasts. Some families of A -optimal and D -optimal designs, which are special cases of Φ -optimal designs, for n≤2 , are given.