Exploring Compositional Data with the CoDa-Dendrogram

Abstract

Within the special geometry of the simplex, the sample space of compositional
\ndata, compositional orthonormal coordinates allow the application of any multi-
\nvariate statistical approach. The search for meaningful coordinates has suggested
\nbalances (between two groups of parts)|based on a sequential binary partition
\nof a D-part composition|and a representation in form of a CoDa-dendrogram.
\nProjected samples are represented in a dendrogram-like graph showing: (a) the
\nway of grouping parts; (b) the explanatory role of subcompositions generated in
\nthe partition process; (c) the decomposition of the variance; (d) the center and
\nquantiles of each balance. The representation is useful for the interpretation of
\nbalances and to describe the sample in a single diagram despite the number of
\nparts. Also, samples of two or more populations, as well as several samples from
\nthe same population, can be represented in the same graph, as long as they have
\nthe same parts registered. The approach is illustrated by an example of food
\nconsumption in Europe.