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Correlation Between Compositional Parts Based on Symmetric Balances
Verfasser / Verfasserin Kynčlová, Petra ; Hron, Karel ; Filzmoser, Peter
Erschienen in
Mathematical Geosciences, 2017, Jg. 49, H. 6, S. 777-796
ErschienenSpringer Nature, 2017
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)Correlation analysis / Compositional data / Sequential binary partitioning / Symmetric balances / Logratio transformations
Projekt-/ReportnummerGrant COST Action CRoNoS: IC1408
ISSN1874-8953
URNurn:nbn:at:at-ubtuw:3-4019 Persistent Identifier (URN)
DOI10.1007/s11004-016-9669-3 
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Correlation Between Compositional Parts Based on Symmetric Balances [1.13 mb]
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Correlation coefficients are most popular in statistical practice for measuring pairwise variable associations. Compositional data, carrying only relative information, require a different treatment in correlation analysis. For identifying the association between two compositional parts in terms of their dominance with respect to the other parts in the composition, symmetric balances are constructed, which capture all relative information in the form of aggregated logratios of both compositional parts of interest. The resulting coordinates have the form of logratios of individual parts to a (weighted) “average representative” of the other parts, and thus, they clearly indicate how the respective parts dominate in the composition on average. The balances form orthonormal coordinates, and thus, the standard correlation measures relying on the Euclidean geometry can be used to measure the association. Simulation studies provide deeper insight into the proposed approach, and allow for comparisons with alternative measures. An application from geochemistry (Kola moss) indicates that correlations based on symmetric balances serve as a sensitive tool to reveal underlying geochemical processes.

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