Abstract

The behaviour of D-optimal exact designs for first order polynomial models under changing regression polynomials is considered. The polynomials, some of which are with or without intercept or with or without interactive term, are defined on design regions that are supported by the points of the Circumscribed Central Composite Design. The best N-point D-optimal exact design for the intercept model (model 1), is the same as the best N-point D-optimal design for the no-intercept model (model 3). Similarly, the best N-point D-optimal design for the intercept model (model 2) is the same as the best N-point D-optimal design for the no-intercept model (model 4), as measured by the determinant values, D-efficiencies, G-efficiencies and Condition numbers. Other N-point designs constructed using the no-intercept models had better determinant values than their corresponding intercept models. The condition numbers indicate that for model 1, the 4-point D-optimal design is orthogonal. For model 2, the 2-point D-optimal exact design and the 4-point D-optimal exact designs are orthogonal. For model 3, the 4-point D-optimal exact design is orthogonal and for model 4, the 4-point D-optimal exact design is orthogonal. Other N-sized designs show less orthogonality. The Equivalence of D-optimality and G-optimality criteria is established for the 4-point design under model 1, for the 2-point and 4-point designs under model 2, for the 4-point design under model 3 and for the 4-point design under model 4.

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