A Dirichlet Regression Model for Compositional Data with Zeros

TL;DR

This paper introduces a zero-adjusted Dirichlet regression model that handles compositional data with zeros without data substitution, improving analysis in various fields.

Contribution

It proposes a novel adjustment to the Dirichlet distribution's log-likelihood to accommodate zeros directly in regression models.

Findings

The model effectively handles zero values in compositional data.

Simulation studies demonstrate improved performance over existing methods.

Examples show practical applicability across different disciplines.

Abstract

Compositional data are met in many different fields, such as economics, archaeometry, ecology, geology and political sciences. Regression where the dependent variable is a composition is usually carried out via a log-ratio transformation of the composition or via the Dirichlet distribution. However, when there are zero values in the data these two ways are not readily applicable. Suggestions for this problem exist, but most of them rely on substituting the zero values. In this paper we adjust the Dirichlet distribution when covariates are present, in order to allow for zero values to be present in the data, without modifying any values. To do so, we modify the log-likelihood of the Dirichlet distribution to account for zero values. Examples and simulation studies exhibit the performance of the zero adjusted Dirichlet regression.