Principles of compositional data analysis

Compositional data consisting of vectors of positive components subject to a unit-sum constraint arise in many disciplines, for example in geology as majoroxide compositions of rocks, in economics as budget share patterns of household expenditures, in medicine as compositions of renal calculi, in psychology as activity patterns of subjects. 'Standard' multivariate techniques, designed for unconstrained data, are wholly inappropriate and uninterpretable for such data and yet are still being commonly misapplied. Recognition that the study of compositions must satisfy simple principles has led recently to the advocacy of new forms of analysis of compositional data. The nature of the absurdities arising from applying traditional multivariate techniques to compositions is briefly highlighted and a description of the essential aspects and the advantages of the new methodology is provided.