Analysis of latent structures in linear models

Abstract

AbstractIn chemometrics the emphasis is on latent structure models. The latent structure is the part of the data that the modeling task is based upon. This paper addresses some fundamental issues that arise when latent structures are used. The paper consists of three parts. The first part is concerned with defining the latent structure of a linear model. Here the ‘atomic’ parts of the algorithms that generate the latent structure for linear models are analyzed. It is shown how the PLS algorithm fits within this way of presenting the numerical procedures. The second part concerns graphical illustrations, which are useful when studying latent structures. It is shown how loading weight vectors are generated and how they can be interpreted in analyzing the latent structure. It is shown how the covariance can be used to get useful a priori information on the modeling task. Some simple methods are presented for deciding whether a single or multiple latent structures should be used. The last part is about choosing the variables that should be used in the analysis. The traditional procedures for selecting variables to include in the model are presented and the insufficiencies of such approaches are demonstrated. A case study to illustrate the use of CovProc methods is presented. The CovProc methods are discussed and some of their advantages are presented. Copyright © 2004 John Wiley & Sons, Ltd.