Compositional Data

Compositional data are vectors of quantities for which only the relative proportions carry information. In the standard positive case, they are normalized to a fixed sum, such as 1 or 100, and therefore lie in a simplex. Because an increase in one component necessarily changes at least one other normalized component, ordinary Euclidean operations on the raw coordinates can be misleading. Quantities such as , and more generally log contrasts, are invariant under rescaling of the whole vector and are basic tools of Aitchison geometry.