Compositional Data

Compositional data are vectors of proportions describing the relative contributions of each of D categories to the whole. This structure is an essential feature of data in many disciplines: in geology as oxide composition of rocks, in ecology as the relative abundance of plants or animals, in air pollution monitoring as the relative concentrations of different chemical species (among others). Statistical approaches for modeling compositional data exhibiting temporal or spatial correlation structure are described in this article. Because methods for compositions are not widely included in statistics education, a brief introduction is given to data characteristics and analysis techniques for independent observations. The focus is observations with three or more categories (D ≥ 3). With only two categories, compositional data are (essentially) univariate, and can be addressed by means of standard statistical techniques (e.g. logit transform). Since the compositional structure is present in a wide variety of problems, many of the methods summarized in this article have been developed outside the environmental context. The approach is to present methods in a general form, and note when there is special development for an environmental application.