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Regression analysis with compositional data containing zero values

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  • Tsagris, Michail

Abstract

Regression analysis, for prediction purposes, with compositional data is the subject of this paper. We examine both cases when compositional data are either response or predictor variables. A parametric model is assumed but the interest lies in the accuracy of the predicted values. For this reason, a data based power transformation is employed in both cases and the results are compared with the standard log-ratio approach. There are some interesting results and one advantage of the methods proposed here is the handling of the zero values.

Suggested Citation

  • Tsagris, Michail, 2015. "Regression analysis with compositional data containing zero values," MPRA Paper 67868, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:67868
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    File URL: https://mpra.ub.uni-muenchen.de/67868/1/MPRA_paper_67868.pdf
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    References listed on IDEAS

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    1. Martín-Fernández, J.A. & Hron, K. & Templ, M. & Filzmoser, P. & Palarea-Albaladejo, J., 2012. "Model-based replacement of rounded zeros in compositional data: Classical and robust approaches," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2688-2704.
    2. T. Tsagris, Michail & Preston, Simon & T.A. Wood, Andrew, 2011. "A data-based power transformation for compositional data," MPRA Paper 53068, University Library of Munich, Germany.
    3. K. Hron & P. Filzmoser & K. Thompson, 2012. "Linear regression with compositional explanatory variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1115-1128, November.
    4. 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.
    5. 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.
    6. J. Aitchison & I. J. Lauder, 1985. "Kernel Density Estimation for Compositional Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(2), pages 129-137, June.
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    Cited by:

    1. Jacob Fiksel & Scott Zeger & Abhirup Datta, 2022. "A transformation‐free linear regression for compositional outcomes and predictors," Biometrics, The International Biometric Society, vol. 78(3), pages 974-987, September.
    2. Matt Kammer-Kerwick & Kara Takasaki & J. Bruce Kellison & Jeff Sternberg, 2022. "Asset-Based, Sustainable Local Economic Development: Using Community Participation to Improve Quality of Life Across Rural, Small-Town, and Urban Communities," Applied Research in Quality of Life, Springer;International Society for Quality-of-Life Studies, vol. 17(5), pages 3023-3047, October.

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    More about this item

    Keywords

    Compositional data; regression; prediction; α-transformation; principal component regression;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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