Simultaneous optimization of incomplete multi-response experiments

Abstract

This article attempts to develop a simultaneous optimization procedure of several response variables from incomplete multi-response experiments. In incomplete multi-response experiments all the responses (p) are not recorded from all the experimental units (n). Two situations of multi-response experiments considered are (i) on n1 units all the responses are recorded while on n2=n-n1 units a subset of p2 < p responses is recorded and (ii) on n2 units all the responses (p) are recorded, on n1 units a subset of p1 < p responses is recorded and on n3(n-n1-n2) units the remaining subset of p2 (=p-p1) responses is recorded. The procedure of estimation of parameters from linear multi-response models for incomplete multi-response experiments has been developed for both the situations. It has been shown that the parameter estimates are consistent and asymptotically unbiased. Using these parameter estimates, simultaneous optimization of incomplete multi-response experiments is attempted following the generalized distance criterion. For the implementation of these procedures, SAS codes have been developed for both complete (k ≤ 5, p = 5) and incomplete (k ≤ 5, p1 = 2, 3 and p2 = 2, 3, where k is the number of factors) multi-response experiments. The procedure developed is illustrated with the help of a real data set.