Covariance-Based Variable Selection for Compositional Data
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Omitting variables in compositional data analysis may lead to a substantial change in results from that of multivariate statistical analysis. In particular, this is the case for principal component analysis and the compositional biplot, where both the interpretation of loadings and scores of the remaining subcomposition are affected. A stepwise procedure is introduced that allows for a reduction of the original composition to a subcomposition by avoiding a substantial change of the information, like those carried by the compositional biplot. The subcomposition is easier to handle and interpret. Numerical results give evidence of the usefulness of the procedure.
KeywordsAitchison geometry on the simplex Centered log-ratio transformation Isometric log-ratio transformation Variable selection
The authors are grateful to the referee for helpful comments and suggestions. The authors also gratefully acknowledge the support by the Operational Program Education for Competitiveness—European Social Fund (project CZ.1.07/2.3.00/20.0170 of the Ministry of Education, Youth, and Sports of the Czech Republic) and the Grant No. PrF-2012-017 of the Internal Grant Agency of the Palacký University in Olomouc.
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