PCR eigenvector selection based on correlation relative standard deviations

While principal component regression (PCR) is often performed with eigenvectors ordered by decreasing singular values, PCR models have been formed using other eigenvector arrangements. A common criterion for organizing eigenvectors involves absolute correlations between respective eigenvectors and the prediction property being modeled. However, correlation cut-off values for eigenvector selection are inconsistent between data sets, and additional criteria are needed such as the root mean square error of cross-validation (RMSECV). Furthermore, correlations for some selected eigenvectors are often extremely low (e.g. values of 0.1 have been considered acceptable) and it is difficult to justify inclusion of these eigenvectors. Relative standard deviations (RSDs) of correlations are evaluated in this paper as an alternative method of eigenvector selection. This paper reveals distinct advantages for using eigenvectors ordered by RSDs of correlations compared to eigenvectors ordered by absolute correlations. In particular, RSDs can be used to determine significant eigenvectors without resorting to additional criteria such as the RMSECV. Additionally, inspection of RSD values explains why different correlation cut-off values are obtained for different data sets as well as why correlations can be small. Copyright (C) 2001 John Wiley & Sons, Ltd.