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Covariance structure of principal components for three-part compositional data. (English) Zbl 1292.62092

Summary: Statistical analysis of compositional data, multivariate observations carrying only relative information (proportions, percentages), should be performed only in orthonormal coordinates with respect to the Aitchison geometry on the simplex. In case of three-part compositions it is possible to decompose the covariance structure of the well-known principal components using variances of log-ratios of the original parts. They seem to be helpful for the interpretation of these special orthonormal coordinates. Theoretical results are applied to real-world data containing relative structure of landscape use in German regions.

MSC:

62H25 Factor analysis and principal components; correspondence analysis
15A18 Eigenvalues, singular values, and eigenvectors
62H99 Multivariate analysis
62J10 Analysis of variance and covariance (ANOVA)
62P12 Applications of statistics to environmental and related topics

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References:

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