I-optimal mixture designs
Faculty of Applied Economics
Antwerp :Universiteit Antwerpen, Faculty of Applied Economics, 2013
Research paper / University of Antwerp, Faculty of Applied Economics ; 2013:033
University of Antwerp
In mixture experiments, the factors under study are proportions of the ingredients of a mixture. The special nature of the factors in a mixture experiment necessitates specific types of regression models, and specific types of experimental designs. Al- though mixture experiments usually are intended to predict the response(s) for all possible formulations of the mixture and to identify optimal proportions for each of the ingredients, little research has been done concerning their I-optimal design. This is surprising given that I-optimal designs minimize the average variance of prediction and, therefore, seem more appropriate for mixture experiments than the commonly used D-optimal designs, which focus on a precise model estimation rather than precise predictions. In this paper, we provide the first detailed overview of the literature on the I-optimal design of mixture experiments and identify several con- tradictions. For the second-order, special cubic and qth degree models, we present I-optimal continuous designs and contrast them with the published results. We also study exact I-optimal designs, and compare them in detail to continuous I-optimal designs and to D-optimal designs. One striking result of our work is that the per- formance of D-optimal designs in terms of the I-optimality criterion very strongly depends on which of the D-optimal design points are replicated.