O2-PLS for qualitative and quantitative analysis in multivariate calibration

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 (C) 2002 John Wiley Sons, Ltd.