A Dirichlet Regression Model for Compositional Data with Zeros
- Authors: Tsagris M.1, Stewart C.2
-
Affiliations:
- Department of Computer Science
- Department of Mathematics and Statistics
- Issue: Vol 39, No 3 (2018)
- Pages: 398-412
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/201853
- DOI: https://doi.org/10.1134/S1995080218030198
- ID: 201853
Cite item
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.
About the authors
Michail Tsagris
Department of Computer Science
Author for correspondence.
Email: mtsagris@yahoo.gr
Greece, Heraklion Crete
Connie Stewart
Department of Mathematics and Statistics
Email: mtsagris@yahoo.gr
Canada, Saint John, New Brunswick