an:05588628
Zbl 1166.62053
Hijazi, Rafiq H.; Jernigan, Robert W.
Modeling compositional data using Dirichlet regression models
EN
J. Appl. Probab. Stat. 4, No. 1, 77-91 (2009).
00250314
2009
j
62J99 62F12 62J20 62J02 62P12
compositional data; Dirichlet distribution; logratio analysis; maximum likelihood estimation
Summary: 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, or partition a whole measurement into percentage contributions from its various parts. 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.
\textit{J. Aitchison} [The statistical analysis of compositional data. Chapman and Hall (1986; Zbl 0688.62004)] introduced the logratio analysis to model compositional data. \textit{G. Campbell} and \textit{J. Mosimann} [ASA Proc. Sect. Stat. Graphics, 10--17 (1987)] suggested the Dirichlet covariate model as a null model for such data. In this paper, maximum likelihood estimation methods in Dirichlet regression models are developed and the sampling distributions of these 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.
Zbl 0688.62004