Performance Evaluation of Custom A-, D-, and I-Optimal Designs for Non-Standard Second-Order Models

The performances of Custom A-, D-, and I-optimal designs on non-standard second-order models are examined using the alphabetic A-, D-, and G-optimality efficiencies, as well as the Average Variance of Prediction. Designs of varying sizes are constructed with the help of JMP Pro 14 software and are customized for specified non-standard models, optimality criteria, prespecified experimental runs, and a specified range of input variables. The results reveal that Custom-A optimal designs perform generally better in terms of G-efficiency. They show high superiority to A-efficiency as the worst G-efficiency value of the created Custom-A optimal designs exceeds the best A-efficiency value of the designs, and also does well in terms of D-efficiency. Custom-D optimal designs perform generally best in terms of G-efficiency, as the worst G-efficiency value exceeds all A- and D-efficiency values. Custom-I optimal designs perform generally best in terms of G-efficiency as the worst G-efficiency value is better than the best A-efficiency value and performs generally better than the corresponding D-efficiency values. For the Average Variance of Prediction, Custom A- and I-optimal designs perform competitively well, with relatively low Average Variances of Prediction. On the contrary, the Average Variance of Prediction is generally larger for Custom-D optimal designs. Hence when seeking designs that minimize the variance of the predicted response, it suffices to construct Custom A-, D-, or I-optimal designs, with a preference for Custom-D optimal designs.