A Comparison of Techniques for Modelling Data with Non-Linear Structure

Abstract

Partial least squares (PLS) is a powerful tool for multivariate linear regression. But what if the data show a non-linear structure? Near infrared spectra from a pharmaceutical process were used as a case study. An ANOVA test revealed that the data are well described by a 2nd order polynomial. This work investigates the application of regression techniques that account for slightly non-linear data. The regression techniques investigated are: linearising data by applying transformations, local PLS, i.e. splitting of data, and quadratic PLS. These models were compared with ordinary PLS and principal component regression (PCR). The predictive ability of the models was tested on an independent data set acquired a year later. Using the knowledge of non-linear pattern and important spectral regions, simpler models with better predictive ability can be obtained.