Abstract
OnPLS was recently presented as a general extension of O2PLS to the multiblock case. OnPLS is very similar to O2PLS in the case of two blocks, but generalises symmetrically to cases with more than two blocks, i.e. without giving preference to any one of the blocks. This article presents a straight-forward extension to this method and thereby also introduces the OPLS framework to the field of PLS path modelling. Path modelling links a number of data blocks to each other, thereby establishing a set of paths along which information is considered to flow between blocks, representing for instance a known time sequence, an assumed causality order, or some other chosen organising principle. Compared to existing methods for path analysis, OnPLS extracts a minimum number of predictive components that are maximally covarying with maximised correlation. This is a significant contribution to path modelling, because other methods may yield score vectors with variation that obstructs the interpretation. The method achieves this by extracting a set of "orthogonal" components that capture local phenomena orthogonal to the variation shared with all the connected blocks. Two applications will be used to illustrate the method. The first is based on a simulated dataset that shows how the interpretation is improved by removing orthogonal variation and the second on a real data process for the monitoring of protein structure changes during cheese ripening by analysing infrared data. (C) 2012 Elsevier B.V. All rights reserved.