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A Dirichlet Regression Model for Compositional Data with Zeros

Authors
  • Tsagris, Michail1
  • Stewart, Connie2
  • 1 University of Crete, Department of Computer Science, Heraklion Crete, Greece , Heraklion Crete (Greece)
  • 2 University of New Brunswick, Department of Mathematics and Statistics, Saint John, New Brunswick, Canada , Saint John, New Brunswick (Canada)
Type
Published Article
Journal
Lobachevskii Journal of Mathematics
Publisher
Pleiades Publishing
Publication Date
Apr 17, 2018
Volume
39
Issue
3
Pages
398–412
Identifiers
DOI: 10.1134/S1995080218030198
Source
Springer Nature
Keywords
License
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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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