Sequential and orthogonalized PLS (SO-PLS) regression for path analysis: Order of blocks and relations between effects

This paper is about the use of the multiblock regression method sequential and orthogonalized partial least squares (SO-PLS) for path modeling. The paper is a follow up of previously published papers on the same topic and presents a number of new results for the method. First of all, the paper discusses more thoroughly the aspect of how to incorporate blocks in the models and relates this to standard concepts in the area of graphical modeling. Second, the paper defines the concept of direct and indirect effects more precisely in terms of population parameters and shows how they are related to the additional effect in SO-PLS modeling. The paper illustrates the theory by simple graphs, simulations, and a real example from process monitoring.