THE PARSIMONY PRINCIPLE APPLIED TO MULTIVARIATE CALIBRATION

The general principle of parsimonious data modeling states that if two models in some way adequately model a given set of data, the one that is described by a fewer number of parameters will have better predictive ability given new data. This concept is of interest in multivariate calibration since several new non-linear modeling techniques have become available. Three such methods are neural networks, projection pursuit regression (PPR) and multivariate adaptive regression splines (MARS). These methods, while capable of modeling non-linearities, typically have very many parameters that need to be estimated during the model building phase. The biased calibration methods, principal components regression (PCR) and partial least squares (PLS) are linear methods and so may not as efficiently describe some types of non-linearities, however have comparably very few parameters to be estimated. It is therefore of interest to study the parsimony principle formally in order to understand under what circumstances the various methods are appropriate. In this paper, the mathematical theory of parsimonious data modeling is presented. The assumptions made in the theory are shown to hold for multivariate calibration methods. This theory is used to provide a procedure for selecting the most parsimonious model structure for a given calibration application.