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Title
Error propagation in isometric log-ratio coordinates for compositional data: theoretical and practical considerations
AuthorMert, Mehmet Can ; Filzmoser, Peter In der Gemeinsamen Normdatei der DNB nachschlagen ; Hron, Karel In der Gemeinsamen Normdatei der DNB nachschlagen
Published in
Mathematical Geosciences, Berlin ; Heidelberg, 2016, Vol. 48, Issue 8, page 941-961
PublishedSpringer, 2016
Edition
Published version
LanguageEnglish
Document typeJournal Article
Keywords (EN)Aitchison geometry / Orthonormal coordinates / Taylor approximation / Compositional differential calculus / Detection limit
ISSN1874-8953
URNurn:nbn:at:at-ubtuw:3-1895 Persistent Identifier (URN)
DOI10.1007/s11004-016-9646-x 
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 The work is publicly available
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Error propagation in isometric log-ratio coordinates for compositional data: theoretical and practical considerations [1.08 mb]
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Abstract (English)

Compositional data, as they typically appear in geochemistry in terms of concentrations of chemical elements in soil samples, need to be expressed in log-ratio coordinates before applying the traditional statistical tools if the relative structure of the data is of primary interest. There are different possibilities for this purpose, like centered log-ratio coefficients, or isometric log-ratio coordinates. In both the approaches, geometric means of the compositional parts are involved, and it is unclear how measurement errors or detection limit problems affect their presentation in coordinates. This problem is investigated theoretically by making use of the theory of error propagation. Due to certain limitations of this approach, the effect of error propagation is also studied by means of simulations. This allows to provide recommendations for practitioners on the amount of error and on the expected distortion of the results, depending on the purpose of the analysis.

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CC-BY-License (4.0)Creative Commons Attribution 4.0 International License