INLR, IMPLICIT NONLINEAR LATENT VARIABLE REGRESSION

A simple way to develop non-linear PLS models is presented, INLR (impl icit non-linear latent variable regression). The paper shows that by s imply added squared x-variables x(a)(2), both the square and cross ter ms of the latent variables are implicitly included in the resulting PL S model. This approach works when X itself is well modelled by a proje ction model TP-T. Hence, if a latent structure is present in X, it is not necessary to include the cross terms of the X-variables in the po lynomial expansion. Analogously, with cubic non-linearities, expanding X with cubic terms x(a)(3) is sufficient. INLR is attractive in that all essential features of PLS are preserved i.e. (a) it can handle man y noisy and collinear variables, (b) it is stable and gives reliable r esults and (c) all PLS plots and diagnostics still apply. The principl es of INLR are outlined and illustrated with three chemical examples w here INLR improved the modelling and predictions compared with ordinar y linear PLS. (C) 1997 by John Wiley & Sons, Ltd.