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A novel, divergence based, regression for compositional data

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  • Tsagris, Michail

Abstract

In compositional data, an observation is a vector with non-negative components which sum to a constant, typically 1. Data of this type arise in many areas, such as geology, archaeology, biology, economics and political science among others. The goal of this paper is to propose a new, divergence based, regression modelling technique for compositional data. To do so, a recently proved metric which is a special case of the Jensen-Shannon divergence is employed. A strong advantage of this new regression technique is that zeros are naturally handled. An example with real data and simulation studies are presented and are both compared with the log-ratio based regression suggested by Aitchison in 1986.

Suggested Citation

  • Tsagris, Michail, 2015. "A novel, divergence based, regression for compositional data," MPRA Paper 72769, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:72769
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    References listed on IDEAS

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    1. Kateri, Maria & Agresti, Alan, 2010. "A generalized regression model for a binary response," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 89-95, January.
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    3. J. L. Scealy & A. H. Welsh, 2011. "Regression for compositional data by using distributions defined on the hypersphere," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 351-375, June.
    4. Gueorguieva, Ralitza & Rosenheck, Robert & Zelterman, Daniel, 2008. "Dirichlet component regression and its applications to psychiatric data," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5344-5355, August.
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    More about this item

    Keywords

    compositional data; Jensen-Shannon divergence; regression; zero values; φ-divergence;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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