Comparison of design optimality criteria of reduced models for response surface designs in a spherical design region

Abstract

In this dissertation, the major objective is to compare 3 and 4 factor response surface designs in a spherical design region by studying design optimality criteria (D, A, G, and IV-criteria) over sets of reduced models. Hence, theoretical and computational details of evaluating optimality criteria for reduced models for response surface designs in a spherical design region have been described. Specifically, robustness results of the spherical response surface designs and the comparison of design optimality criteria of the response surface designs across the full second-order model and sets of reduced models for 3 and 4 design variables based on the four optimality criteria (D, A, G, and IV-criteria) are presented. Also, new types of D, A, G, and IV optimality criteria for response surface designs in a spherical design region are developed by using prior probability assignment to model effects (for some specified values of pl, pq, p 1, and p2). The four new D, A, G , and IV optimality criteria will be referred to as weighted design optimality criteria. The weighted design optimality criteria of the response surface designs across the weak heredity and strong heredity reduced models for 3 and 4 design variables are evaluated.