A-optimal versus D-optimal design of screening experiments

Abstract

The purpose of this article is to persuade experimenters to choose A-optimal designs rather than D-optimal designs for screening experiments. The primary reason for this advice is that the A-optimality criterion is more consistent with the screening objective than the D-optimality criterion. The goal of screening experiments is to identify an active subset of the factors. An A-optimal design minimizes the average variance of the parameter estimates, which is directly related to that goal. While there are many cases where A- and D-optimal designs coincide, the A-optimal designs tend to have better statistical properties when the A- and D-optimal designs differ. In such cases, A-optimal designs generally have more uncorrelated columns in their model matrices than D-optimal designs. Also, even though A-optimal designs minimize the average variance of the parameter estimates, various cases exist where they outperform D-optimal designs in terms of the variances of all individual parameter estimates. Finally, A-optimal designs can also substantially reduce the worst prediction variance compared with D-optimal designs.