A Dirichlet Regression Model for Compositional Data with Zeros

Lobachevskii Journal of Mathematics volume 39, pages398–412(2018)Cite this article

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.

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Author information

Affiliations

  1. Department of Computer Science, University of Crete, Heraklion Crete, Greece

    Michail Tsagris

  2. Department of Mathematics and Statistics, University of New Brunswick, Saint John, New Brunswick, Canada

    Connie Stewart

Authors
  1. Michail Tsagris
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  2. Connie Stewart
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Correspondence to Michail Tsagris.

Additional information

(Submitted by A. I. Volodin)

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Tsagris, M., Stewart, C. A Dirichlet Regression Model for Compositional Data with Zeros. Lobachevskii J Math 39, 398–412 (2018). https://doi.org/10.1134/S1995080218030198

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Keywords

  • Compositional data
  • regression
  • Dirichlet distribution
  • zero values