A new Bootstrap-Based stopping criterion in PLS components construction

Abstract

We develop a new universal stopping criterion in components construction, in the sense that it is suitable both for Partial Least Squares Regressions (PLSR) and its extension to Generalized Linear Regressions (PLSGLR). This criterion is based on a bootstrap method and has to be computed algorithmically. It allows to test each successive components on a significant level α. In order to assess its performances and robustness with respect to different noise levels, we perform intensive datasets simulations, with a preset and known number of components to extract, both in the case N > P (N being the number of subjects and P the number of original predictors), and for datasets with N < P. We then use t-tests to compare the predictive performance of our approach to some others classical criteria. Our conclusion is that our criterion presents better performances, both in PLSR and PLS-Logistic Regressions (PLS-LR) frameworks.