Post-transformation of PLS2 (ptPLS2) by orthogonal matrix: a new approach for generating predictive and orthogonal latent variables

Partial Least Squares (PLS) is a wide class of regression methods aiming at modelling relationships between sets of observed variables by means of latent variables. Specifically, PLS2 was developed to correlate two blocks of data, the X-block representing the independent or explanatory variables and the Y-block representing the dependent or response variables. Lately, OPLS was introduced to further reduce model complexity by removing Y-orthogonal sources of variation from X in the latent space, thus improving data interpretation through the generated predictive latent variables. Nevertheless, relationships between PLS2 and OPLS in case of multiple Y-response have not yet been fully explored. With this perspective and taking inspiration from some basic mathematical properties of PLS2, we here present a novel and general approach consisting in a post-transformation of PLS2 (ptPLS2), which results in a decomposition of the latent space into orthogonal and predictive components, while preserving the same goodness of fit and predictive ability of PLS2. Additionally, we discuss the application of ptPLS2 approach to two metabolomic data sets extracted from earlier published studies and its advantages in model interpretation as compared with the 'standard' PLS approach. Copyright (C) 2016 John Wiley & Sons, Ltd.