Compositional data (CoDa) are typically defined as vectors of positive components and constant sum, usually 100% or 1. These conditions render most classical statistical techniques incoherent on compositions, as they were devised for unbounded real vectors. However, there are many more types of data exhibiting the same limitations: as soon as the variables of a data set show the relative importance of some parts of a whole, data should be considered compositional. Examples of disguised compositions are data presented in ppm, ppb, molarities, or any other concentration units. Aitchison introduced the log-ratio approach for analysing CoDa back in the eighties. His solution was based on mapping the data vector with some log-ratio transformations, and applying classical techniques to the scores thus obtained. This would become the foundation of modern CoDa analysis. Sometimes CoDA is used as an acronym for CoDa analysis, whereas CoDa refers to Compositional Data. Nowadays, CoDA is based on an own geometric structure for the simplex; an appropriate representation of the sample space of CoDa. The validity of these considerations is not restricted to CoDa as there are many more data sets where sample space does not obey the rules of real numbers, or whcih can be given an own, alternative, meaningful geometric structure. Examples abound in natural and social sciences, such as vectors of positive amounts, functional data, spherical data, ordered variables, etc. CoDa analysis insights may be of good use to scientists working with these data sets, and vice versa.
Practitioners interested in CoDA can find on the www.compositionaldata.com website, a forum where information, material and ideas are exchanged. Also a free software can be found there, the Compositional Data Package (CoDaPack), which currently employs the most elementary the compositional statistical methods. It can be downloaded from: http://ima.udg.edu/codapack. This software has been developed and is maintained by the University of Girona reseach group on compositional data analysis, and is oriented towards users from an applied sciences background, with no extensive experience in using various computer packages.
On www.compositionaldata.com the R Packages compositions, robCompositions and zCompositions can also be obtained.