The effect of mean centering on prediction in multivariate calibration

Abstract

Abstract Traditionally, one form of preprocessing in multivariate calibration methods such as principal component regression and partial least squares is mean centering the independent variables (responses) and the dependent variables (concentrations). However, upon examination of the statistical issue of error propagation in multivariate calibration, it was found that mean centering is not advised for some data structures. In this paper it is shown that for response data which (i) vary linearly with concentration, (ii) have no baseline (when there is a component with a non‐zero response that does not change in concentration) and (iii) have no closure in the concentrations (for each sample the concentrations of all components add to a constant, e.g. 100%) it is better not to mean center the calibration data. That is, the prediction errors as evaluated by a root mean square error statistic will be smaller for a model made with the raw data than a model made with mean‐centered data. With simulated data relative improvements ranging from 1% to 13% were observed depending on the amount of error in the calibration concentrations and responses.