Analysis of compositional data using Dirichlet covariate models

Compositional data are non-negative proportions with unit-sum. These types of data arise whenever we classify objects into disjoint categories and record their resulting relative frequencies. Under the unit-sum constraint, the elementary concepts of covariance and correlation are misleading. Therefore, compositional data are rarely analyzed with the usual multivariate statistical methods. Aitchison (1986) introduced the logratio analysis to model compositional data. Campbell and Mosimann (1987) suggested the Dirichlet Covariate Model as a null model for such data. The purpose of this thesis is to investigate the Dirichlet Covariate Model and compare it to the logratio analysis. The estimation methods are introduced and the sampling distributions of the maximum likelihood estimates are investigated. Measures of total variability and goodness of fit are proposed to assess the adequacy of the suggested models in analyzing compositional data.