Precision of full polynomial response surface designs on models with missing coefficients

The precision of using full polynomial response surface designs on models with missing coefficients (reduced models) is studied using efficiency measures. The loss in D- and G-efficiency of constructed first-order exact designs is minimized for the model with missing interaction coefficient. However, higher losses in D- and G-efficiency are recorded when constructed second-order exact designs are used on the model with missing interaction coefficient with few exceptions showing preferences for using the designs on the reduced model. Lower condition numbers are observed for the designs under the first-order reduced models thus indicating that the N-point exact designs are closer to being orthogonal for the reduced model than for the full model. Perfect orthoganality is achieved at design sizes 4 and 8. In fact, N-point exact designs of multiples of N=4 show perfect orthoganality when defined either for the full or reduced first-order models. In comparison to a design with perfect orthoganality, the second-order designs are far from being orthogonal.