Compositional data: an overview

Abstract

Compositional data are data where the elements of the composition are non-negative and sum to unity. The key question is what is the appropriate analysis for data from this restricted sample space. We start by summarizing more than a century of progress towards answering this question. Aitchison(1986) provides a framework appropriate for data that satisfies sub-compositional coherence, i.e., where conclusions about a sub-composition should be the same based on the full composition or the sub-composition alone. However, not all compositional data satisfies this principle and it is helpful to consider the complete cycle of processes that yield any specific dataset and hence the appropriate analysis for data generated in this manner.