I-optimal versus D-optimal split-plot response surface designsI-optimal versus D-optimal split-plot response surface designs
Faculty of Applied Economics
Antwerp :UA, 2012[*]2012
Research paper / UA, Faculty of Applied Economics ; 2012:002
University of Antwerp
Response surface experiments often involve only quantitative factors, and the re- sponse is ¯t using a full quadratic model in these factors. The term response surface implies that interest in these studies is more on prediction than parameter estima- tion since the points on the ¯tted surface are predicted responses. When computing optimal designs for response surface experiments, it therefore makes sense to focus attention on the predictive capability of the designs. However, the most popular criterion for creating optimal experimental designs is the D-optimality criterion, which aims to minimize the variance of the factor-e®ect estimates in an omnibus sense. Because I-optimal designs minimize the average variance of prediction over the region of experimentation, their focus is clearly on prediction. Therefore, the I-optimality criterion seems to be a more appropriate one than the D-optimality criterion for generating response surface designs. Here, we introduce I-optimal de- sign of split-plot response surface experiments. We show through several examples that I-optimal split-plot designs provide substantial bene¯ts in terms of prediction compared to D-optimal split-plot designs, while also performing very well in terms of the precision of the factor-e®ect estimates.