Variable selection and covariance structure identification using sparse principal loading analysis

We provide sparse principal loading analysis which is a new concept that reduces dimensionality of cross sectional data and identifies the underlying covariance structure. Sparse principal loading analysis selects a subset of the existing variables for dimensionality reduction while variables that have a small distorting effect on the covariance matrix are discarded. Therefore, we show how to detect those variables and provide methods to assess their magnitude of distortion. Sparse principal loading analysis is twofold and can also identify the underlying block diagonal covariance structure. In this context, we provide required criteria to evaluate if the found block-structure fits the sample. The method is based on sparse loadings rather than eigenvectors which can result in a large loss of information if the loadings of choice are too sparse. However, we show that this is no concern in our new concept because we control sparseness by the aforementioned evaluation criteria. Further, we show the advantages of sparse principal loading analysis in contrast to principal loading analysis and illustrate the performance of the method on simulated data and on real datasets. Supplementary materials for this article are available online.