A method for Bayesian regression modelling of composition data

Abstract

Many scientific and industrial processes produce data that is best analysed as vectors of relative values, often called compositions or proportions. The Dirichlet distribution is a natural distribution to use for composition or proportion data. It has the advantage of a low number of parameters, making it the parsimonious choice in many cases. This paper considers the case where the outcome of a process is Dirichlet, dependent on one or more explanatory variables in a regression setting. The paper explores some existing approaches to this problem, and then introduces a new simulation approach to fitting such models, based on the Bayesian framework. The paper illustrates the advantages of the new approach through simulated examples and an application in sport science. These advantages include: increased accuracy of fit, increased power for inference, and the ability to introduce random effects without additional complexity in the analysis.