Revisiting some design criteria

Abstract

We address the problem that the A (trace) design criterion is not scale invariant and often is in disagreement with the D (determinant) design criterion. We consider the canonical moment matrix CM and use the trace of its inverse as the canonical trace CA design criterion and use the determinant of its inverse as the canonical determinant CD design criterion. For designs which contain higher order terms, we note that the determinant of the canonical moment matrix gives a measure of the collinearity between the lower order terms and the higher order terms.