Modelling compositional data. The sample space approach

Abstract

Compositions describe parts of a whole and carry relative information. Compositional data appear in all fields of science, and their analysis requires paying attention to the appropriate sample space. The log-ratio approach proposes the simplex, endowed with the Aitchison geometry, as an appropriate representation of the sample space. The main characteristics of the Aitchison geometry are presented, which open the door to statistical analysis addressed to extract the relative, not absolute, information. As a consequence, compositions can be represented in Cartesian coordinates by using an isometric log-ratio transformation. Standard statistical techniques can be used with these coordinates.