Variable Selection in Compositional Data Analysis Using Pairwise Logratios

In the approach to compositional data analysis originated by John Aitchison, a set of linearly independent logratios (i.e., ratios of compositional parts, logarithmically transformed) explains all the variability in a compositional data set. Such a set of ratios can be represented by an acyclic connected graph of all the parts, with edges one less than the number of parts. There are many such candidate sets of ratios, each of which explains 100%...