O2‐PLS for qualitative and quantitative analysis in multivariate calibration

Abstract In this paper the O‐PLS method 1 has been modified to further improve its interpretational functionality to give (a) estimates of the pure constituent profiles in X as well as model (b) the Y‐orthogonal variation in X , (c) the X‐orthogonal variation in Y and (d) the joint X–Y covariation. It is also predictive in both ways, X ↔ Y . We call this the O2‐PLS approach. In earlier papers we discussed the improved interpretation using O‐PLS compared to the partial least squares projections to latent structures (PLS) when systematic Y‐orthogonal variation in X exists, i.e. when a PLS model has more components than the number of Y variables. In this paper we show how the parameters in the PLS model are affected and to what degree the interpretational ability of the PLS components changes with the amount of Y‐orthogonal variation. In both real and synthetic examples, the O2‐PLS method provided improved interpretation of the model and gave a good estimate of the pure constituent profiles, and the prediction ability was similar to the standard PLS model. The method is discussed from geometric and algebraic points of view, and a detailed description of this modified O2‐PLS method is given and reviewed. Copyright © 2002 John Wiley & Sons, Ltd.