PLS-regression: a basic tool of chemometrics

PLS-regression (PLSR) is the PLS approach in its simplest, and in chemistry and technology, most used form (two-block predictive PLS). PLSR is a metho d for relating two data matrices, X and Y, by a linear multivariate model, but goes beyond traditional regression in that it models also the structure of X and Y. PLSR derives its usefulness from its ability to analyze data w ith many, noisy, collinear, and even incomplete variables in both X and Y. PLSR has the desirable property that the precision of the model parameters improves with the increasing number of relevant variables and observations. This article reviews PLSR as it has developed to become a standard tool in chemometrics and used in chemistry and engineering. The underlying model an d its assumptions are discussed, and commonly used diagnostics are reviewed together with the interpretation of resulting parameters. Two examples are used as illustrations: First, a Quantitative Structure-Act ivity Relationship (QSAR)/Quantitative Structure-Property Relationship (QSP R) data set of peptides is used to outline how to develop, interpret and re fine a PLSR model. Second, a data set from the manufacturing of recycled pa per is analyzed to illustrate time series modelling of process data by mean s of PLSR and time-lagged X-variables. (C) 2001 Elsevier Science B.V. All r ights reserved.