A simple rule for the selection of principal components

A vast literature has been devoted to the assessment of the proper number of eigenvalues that have to be retained in Principal Components Analysis. Most of the publications are, based on either distributional assumptions for the underlying populations or on empirical evident. In addition, techniques that are based on bootstrap or cross-validatory techniques have been proposed despite the computational effort implied. In this paper a simple technique based on a control chart approach is proposed for selecting the number of principal components to retain for the analysis. This approach accounts for the sampling variability which can lead to the selection of components that are not in fact statistically significant. The method is compared with other methods and is found to be superior regardless of the underlying distributional properties of the population as well as the existing structure. An illustrative example is provided.