PLS regression algorithms in the presence of nonlinearity

It has long been emphasized that standard PLS regression algorithms like NIPALS and SIMPLS are not suitable for regressions in which there is a nonlinear relationship between the response and the predictors. We show that this conclusion, while strictly true, fails to recognize that aspects of these algorithms remain serviceable in the presence of nonlinearity. In particular, the dimension reduction step of these standard algorithms is serviceable under linear and nonlinear relationships, while the predictive step is not. Additionally, we propose graphical methods for diagnosing nonlinearity, develop a novel method of nonlinear prediction based on reduced predictors arising from standard PLS regression algorithms and demonstrate the effectiveness of our approach in two case studies.