Variable Selection for Compositional Data

Abstract

Compositional data consist of vectors of positive percentage values summing up to a unit. In this paper, we propose two variable selection rules for compositional data and two criteria for a recommended solution to select a subset of variables. The proposed rules are based on minor determinants of a variance-covariance matrix or a correlation matrix. They are the same as McCabe's (1984) idea for variable selection rules in principal component analysis. We apply the rules and the criteria to three real datasets and consider their performance. As a conclusion, the performance of the rule based on a minor determinant of a variance-covariance matrix is better than the other one. The rule is useful to apply, but further consideration would be necessary for applying the criteria to any datasets.