Published 2001

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Publication details

Journal : Chemometrics and Intelligent Laboratory Systems , vol. 58 , p. 151–170 , 2001

Publisher : Elsevier

International Standard Numbers :
Printed : 0169-7439
Electronic : 1873-3239

Publication type : Academic article

Contributors : Martens, Harald; Høy, Martin; Westad, Frank Ove; Folkenberg, Ditte; Martens, Magni

Issue : 2

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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]. (C) 2001 Elsevier Science B.V. All rights reserved.