Comparison of Simplex Designs for Quadratic Mixture Models

TLDR: In this paper, the authors considered quadratic regression with mixtures of nonnegative components and compared the designs that are optimum with respect to the D-, A-, and E-optimality criteria in their performance relative to these and other criteria.

Abstract: Designs for quadratic regression are considered when the possible values of the controlable variable are mixtures x = (x 1, x 2, …, x q + 1) of nonnegative components x i with Σ q + 1 1 x i = 1. The designs that are optimum with respect to the D-, A-, and E-optimality criteria are compared in their performance relative to these and other criteria. Computational routines for obtaining these designs are developed, and the geometry of optimum structures is discussed. Except when q = 2, the A-optimum design is supported by the vertices and midpoints of edges of the simplex, as is the case for the previously known D-optimum design. Although the E-optimum design requires more observation points, it is more robust in its efficiency, under variation of criterion: but all three designs perform reasonably well in this sense.