The Sequential and Orthogonalized PLS Regression for Multiblock Regression: Theory, Examples, and Extensions

Abstract In this chapter, the sequentially orthogonalized-PLS (SO-PLS) method and some of its main extensions are described and illustrated. Both theoretical aspects and applications on real data are discussed. SO-PLS is a multiblock regression method in which the information is extracted sequentially from the predictor blocks and there is no limitation in the number of predictors that can be handled. Moreover, the significance of the addition of any predictor block can be tested. An extension of the method for handling multiway arrays is also described and illustrated. SO-PLS and its extensions are versatile methods for both regression and classification; in both cases, they are particularly suitable from an interpretation point of view.