Effect of Response Scaling on the Detection of Singularities in Multiresponse Estimation

摘要

Box and Draper (1965) introduced a criterion for the estimation of parameters from a multiresponse model. This criterion can lead to misleading results in the presence of linear relationships among the responses. Box et al. (1973) proposed a procedure for detecting the existence of such relationships when the multiresponse data are subject to round-off errors. The procedure, however, can be adversely affected by large differences in the orders of magnitude of the responses as well as in the units of measurement on which the responses are expressed. It is, therefore, necessary to scale the responses prior to the application of that procedure. This document discusses the effect of scaling on the implementation of the eigenvalue analysis by Box et al. (1973). Two numerical examples are given for illustration.