Robust Methods for Compositional Data

Abstract

Many practical data sets in environmental sciences, official statistics and various other disciplines are in fact compositional data because only the ratios between the variables are informative. Compositional data are represented in the Aitchison geometry on the simplex, and for applying statistical methods designed for the Euclidean geometry they need to be transformed first. The isometric logratio (ilr) transformation has the best geometrical properties, and it avoids the singularity problem introduced by the centered logratio (clr) transformation. Robust multivariate methods which are based on a robust covariance estimation can thus only be used with ilr transformed data. However, usually the results are difficult to interpret because the ilr coordinates are formed by non-linear combinations of the original variables. We show for different multivariate methods how robustness can be managed for compositional data, and provide algorithms for the computation.