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Lobachevskii Journal of Mathematics

, Volume 39, Issue 3, pp 398–412 | Cite as

A Dirichlet Regression Model for Compositional Data with Zeros

  • Michail Tsagris
  • Connie Stewart
Article
  • 62 Downloads

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.

Keywords

Compositional data regression Dirichlet distribution zero values 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of CreteHeraklion CreteGreece
  2. 2.Department of Mathematics and StatisticsUniversity of New BrunswickSaint John, New BrunswickCanada

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