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Linear regression with compositional explanatory variables

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  • K. Hron
  • P. Filzmoser
  • K. Thompson

Abstract

Compositional explanatory variables should not be directly used in a linear regression model because any inference statistic can become misleading. While various approaches for this problem were proposed, here an approach based on the isometric logratio (ilr) transformation is used. It turns out that the resulting model is easy to handle, and that parameter estimation can be done in like in usual linear regression. Moreover, it is possible to use the ilr variables for inference statistics in order to obtain an appropriate interpretation of the model.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:5:p:1115-1128
    DOI: 10.1080/02664763.2011.644268
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    References listed on IDEAS

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    1. Hron, K. & Templ, M. & Filzmoser, P., 2010. "Imputation of missing values for compositional data using classical and robust methods," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3095-3107, December.
    2. Billheimer D. & Guttorp P. & Fagan W.F., 2001. "Statistical Interpretation of Species Composition," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1205-1214, December.
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