Covariance-based variable selection for compositional data

Abstract

Omitting variables in compositional data analysis may lead to a substantial change in results from that of multivariate statistical analysis. In particular, this is the case for principal component analysis and the compositional biplot, where both the interpretation of loadings and scores of the remaining subcomposition are affected. A stepwise procedure is introduced that allows for a reduction of the original composition to a subcomposition by avoiding a substantial change of the information, like those carried by the compositional biplot. The subcomposition is easier to handle and interpret. Numerical results give evidence of the usefulness of the procedure.