Linear regression with compositional explanatory variables |
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| Authors: | K Hron P Filzmoser K Thompson |
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| Institution: | 1. Faculty of Science , Palacky University , 17. listopadu 12, CZ-77146 , Czech Republic;2. Institute of Statistics and Probability Theory, Vienna University of Technology , Wiedner Hauptstrasse 8-10, A-1040 , Vienna , Austria;3. Institute for Discrete Mathematics and Geometry, Vienna University of Technology , Wiedner Hauptstrasse 8-10, A-1040 , Vienna , Austria |
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| 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. |
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| Keywords: | mixtures Aitchison geometry on the simplex isometric logratio transformation orthonormal coordinates |
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