Cross-Validation for Choosing the Number of Important Components in Principal Component Analysis

A cross-validation method (Krzanowski, 1987) for selecting the significant components from a principal components analysis is described. Some properties of this method are discussed, and parallels are drawn with other related methods in covariance structure modelling. Some comparisons among the methods are effected empirically on two data sets which have been analyzed previously in the literature, and the implications of the analyses for these sets are briefly discussed.