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  • 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.
  • 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. (en)
Title
  • Covariance structure of principal components for three-part compositional data
  • Covariance structure of principal components for three-part compositional data (en)
skos:prefLabel
  • Covariance structure of principal components for three-part compositional data
  • Covariance structure of principal components for three-part compositional data (en)
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  • RIV/61989592:15310/13:33144752!RIV14-MSM-15310___
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  • 67225
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  • RIV/61989592:15310/13:33144752
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  • compositional data, covariance structure, principal components, log-contrasts (en)
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  • CZ - Česká republika
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  • [91E49C0E5045]
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  • Acta Universitatis Palackianae Olomucensis, Facultas Rerum Naturalium, Mathematica
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  • 52
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  • Hron, Karel
  • Fišerová, Eva
  • Rypka, Miroslav
  • Hrůzová, Klára
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  • 0231-9721
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  • 15310
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