A novel, divergence based, regression for compositional data

Abstract

In compositional data, an observation is a vector with non-negative components which sum to a constant, typically 1. Data of this type arise in many areas, such as geology, archaeology, biology, economics and political science amongst others. The goal of this paper is to propose a new, divergence based, regression modelling technique for compositional data. To do so, a recently proved metric which is a special case of the Jensen-Shannon divergence is employed. A strong advantage of this new regression technique is that zeros are naturally handled. An example with real data and simulation studies are presented and are both compared with the log-ratio based regression suggested by Aitchison in 1986.