Partial Least Squares Regression on Smooth Factors

Abstract

In this article we present a modification of partial least squares regression to account for inherent nonexchangeabilities of the columns of the design matrix. In chemometrics applications it is common to write the matrix as a bilinear form of latent variables and loadings. These loadings are often interpreted as sampled values of functions; hence they should exhibit a degree of smoothness. Our method forces the partial least squares factors to be smooth, by using a roughness penalty motivated by nonparametric regression. We present a computational method to determine the loadings that guarantees a desired orthogonality at successive steps. We propose a cross-validatory choice of the smoothing parameter and the number of loadings. We illustrate the algorithm by an example and describe our experience with real data.

Key Words:

• Calibration
• Chemometrics
• Cross-validation
• Latent factors
• Roughness penalty
• Spectroscopy