Linear regression with compositional explanatory variables

• Published in: Journal of applied statistics Vol. 39; no. 5; pp. 1115 - 1128
• Main Authors: Hron, K., Filzmoser, P., Thompson, K.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01-05-2012; Taylor and Francis Journals; Taylor & Francis Ltd
• Series: Journal of Applied Statistics
• Subjects: Aitchison geometry on the simplex; Applied statistics; Handles; Inference; isometric logratio transformation; Mathematical models; Mathematical problems; mixtures; orthonormal coordinates; Parameter estimation; Regression; Regression analysis; Statistical inference; Statistics; Studies; Transformations
• ISSN: 0266-4763; 1360-0532
• DOI: 10.1080/02664763.2011.644268

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.