Title: Correlation Between Compositional Parts Based on Symmetric Balances
Language: English
Authors: Kynclova, Petra 
Hron, Karel 
Filzmoser, Peter 
Category: Original Research Article
Keywords: Correlation analysis; Compositional data; Sequential binary partitioning; Symmetric balances; Logratio transformations
Issue Date: 2017
Journal: Mathematical Geosciences 
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.
DOI: 10.1007/s11004-016-9669-3
Library ID: AC15187474
URN: urn:nbn:at:at-ubtuw:3-4019
ISSN: 1874-8961
Organisation: E105 - Institut für Stochastik und Wirtschaftsmathematik 
Publication Type: Article
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