D-Optimality and D_L-optimality criteria for incomplete block designs

Abstract

The adequacy of an experimental design can be determined from the information matrix. The D-optimality criterion is based on the determinant of the information matrix M(ξ) (ξ is any design measure) of a design, that is it maximizes the determinant of the information matrix M(ξ) or, equivalently, minimizes the determinant of inverse of the information matrix M−1(ξ ) .There are cases where the information matrix M(ξ) of a design degenerates (that is, the determinant is zero). In this situation, we introduce the use of the loss of information matrix designated as L(ξ) matrix. The loss of information matrix L(ξ) is a symmetric positive definite matrix that has exactly the same diagonal elements as those of the information matrix M(ξ) and the off-diagonal elements lying between zero and one. D_L-optimality criterion measures the determinant of the loss of information matrix.In this paper, we consider the correspondence between the D-and D_L-optimality criteria, that is whether a D-optimal design is also D_L-optimal, in a block or more than one block using a regular and irregular experimental region. An optimal design is selected with the aid of the combinatorial algorithm developed by Onukogu and Iwundu (2008). Breaking of ties existing in Doptimality criterion using the DL-optimality criterion is also considered.

KEYWORDS: Loss of information; D_L-optimality criterion; Incomplete block design; Regular and irregular experimental region