Linear regression with compositional explanatory variables
- 6 January 2012
- journal article
- research article
- Published by Taylor & Francis Ltd in Journal of Applied Statistics
- Vol. 39 (5), 1115-1128
- https://doi.org/10.1080/02664763.2011.644268
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.Keywords
This publication has 15 references indexed in Scilit:
- On the Interpretation of Orthonormal Coordinates for Compositional DataMathematical Geosciences, 2011
- Univariate statistical analysis of environmental (compositional) data: Problems and possibilitiesScience of The Total Environment, 2009
- Reply to “On the Harker Variation Diagrams; …” by J.A. CortésMathematical Geosciences, 2009
- Another Look at the Chemical Relationships in the Dissolved Phase of Complex River SystemsMathematical Geosciences, 2008
- Groups of Parts and Their Balances in Compositional Data AnalysisMathematical Geology, 2005
- Isometric Logratio Transformations for Compositional Data AnalysisMathematical Geology, 2003
- Statistical Interpretation of Species CompositionJournal of the American Statistical Association, 2001
- Logratio Analysis and Compositional DistanceMathematical Geology, 2000
- The Statistical Analysis of Compositional DataPublished by Springer Science and Business Media LLC ,1986
- Log contrast models for experiments with mixturesBiometrika, 1984