Kernel-Partial Least Squares regression coupled to pseudo-sample trajectories for the analysis of mixture designs of experiments

This article explores the potential of Kernel-Partial Least Squares (K-PLS) regression for the analysis of data proceeding from mixture designs of experiments. Gower's idea of pseudo-sample trajectories is exploited for interpretation purposes. The results show that, when the datasets under study are affected by severe non-linearities and comprise few observations, the proposed approach can represent a feasible alternative to classical methodologies (i.e. Scheffé polynomial fitting by means of Ordinary Least Squares - OLS - and Cox polynomial fitting by means of Partial Least Squares - PLS). Furthermore, a way of recovering the parameters of a Scheffé model (provided that it holds and has the same complexity as the K-PLS one) from the trend of the aforementioned pseudo-sample trajectories is illustrated via a simulated case-study.