Minimal sufficient confounding information among main effects and two-factor interactions

Abstract

For two-level regular designs, we obtain the structures of Fisher information matrices for estimating main effects and two-factor interactions (2fi’s). Based on these results, we propose the definition of minimal sufficient confounding information among main effects and 2fi’s. As an application, we demonstrate that minimum aberration (MA) designs must be (M,S)-optimal designs for two-level regular designs. In addition, we show that sequentially minimizing M(1,2)1 ,M(2,2)2 and M(2,2)1 , as the core of the minimum M-aberration criterion proposed by Zhu and Zeng (2005), is equivalent to sequentially minimizing word length pattern A3 and A4. In particular, we show that sequentially minimizing A3 and A4 is equivalent to sequentially maximizing the first two components of the maximum estimation capacity, E1(d) and E2(d), defined in Cheng, Steinberg, and Sun (1999).