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

Abstract

Pragmatical, visually oriented methods for assessing and optimising bi-linear regression models are described, and applied to PLS Regression (PLSR) analysis of multi-response data from controlled experiments. The paper outlines some ways to stabilise the PLSR method to extend its range of applicability to the analysis of effects in designed experiments. Two ways of passifying unreliable variables are shown. A method for estimating the reliability of the cross-validated prediction error RMSEP is demonstrated. Some recently developed jack-knifing extensions are illustrated, for estimating the reliability 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 important additional overview plots of the main relevant structures in the multi-response data. The study is part of an ongoing effort to establish a cognitively simple and versatile approach to multivariate data analysis, with reliability assessment based on the data at hand, and with little need for abstract distribution theory [H. Martens, M. Martens, Multivariate Analysis of Quality. An Introduction, Wiley, Chichester, UK, 2001].