Comparison of linear and nonlinear multivariate calibration methods

This work is a comparative study of multivariate calibration methods that have been adapted to chemical systems exhibiting nonlinear responses from multicomponent spectroscopic assays. Nonlinear spectroscopic responses have been a subject of much interest in recent years and a variety of methods have been developed to address the problem of modeling such data. These range from polynomial extensions of principal component regression (PCR) and partial least squares regression (PLSR) to more elaborate strategies such as locally weighted regression (LWR) and artificial neural networks (ANN). Comparison of such methods has been made difficult by a shortage of experimental systems for which nonlinear behavior has been well-characterized. This is due to the fact that, although many systems may be expected to exhibit nonlinearities, the extent to which this is true is difficult to assess in a multidimensional context. In this work, development of a well-designed and well-characterized data set that allows a comparison of nonlinear multivariate methods was achieved. The system studied was a mixture of three isomers of dimethylbenzene, whose UV absorbance spectra exhibit characteristics well-suited for examining nonlinear response characteristics. A multilayered mixture design consisting of 49 points for both calibration and prediction sets, each with replicate runs was used, resulting in a total of 343 spectra. A four-level three-factor factorial design was also employed to generate another data set with 192 spectra including replicates. On the basis of these experiments, the nonlinearities in the data sets were characterized and a variety of calibration methods were compared. It was found that nonparametric methods slightly outperformed polynomial extensions of latent variable methods but none of these achieved their full potential in capturing and modeling nonlinearity in the data as well as constrained nonlinear classical least squares (NLCLS) which was used as the benchmark.