Analysis of designed experiments by stabilised PLS Regression and jack-knifing

Pragmatical, visually oriented methods for assessing and optimising bi-line ar regression models are described, and applied to PLS Regression (PLSR) an alysis of multi-response data from controlled experiments. The paper outlin es some ways to stabilise the PLSR method to extend its range of applicabil ity to the analysis of effects in designed experiments. Two ways of passify ing unreliable variables are shown. A method for estimating the reliability of the cross-validated prediction error RMSEP is demonstrated. Some recent ly developed jack-knifing extensions are illustrated, for estimating the re liability of the linear and bi-linear model parameter estimates. The paper illustrates how the obtained PLSR "significance" probabilities are similar to those from conventional factorial ANOVA, but the PLSR is shown to give i mportant additional overview plots of the main relevant structures in the m ulti-response data. The study is part of an ongoing effort to establish a cognitively simple an d versatile approach to multivariate data analysis, with reliability assess ment based on the data at hand, and with little need for abstract distribut ion theory [H. Martens, M. Martens, Multivariate Analysis of Quality. An In troduction, Wiley, Chichester, UK, 2001]. (C) 2001 Elsevier Science B.V. Al l rights reserved.