Regression for Compositional Data by using Distributions Defined on the Hypersphere

Abstract

Summary Compositional data can be transformed to directional data by the square-root transformation and then modelled by using distributions defined on the hypersphere. One advantage of this approach is that zero components are catered for naturally in the models. The Kent distribution for directional data is a good candidate model because it has a sufficiently general covariance structure. We propose a new regression model which models the mean direction of the Kent distribution as a function of a vector of covariates. Our estimators can be regarded as asymptotic maximum likelihood estimators. We show that these estimators perform well and are suitable for typical compositional data sets, including those with some zero components.