Authors / CoAuthors
Hron, K. | Filzmoser, P. | de Caritat, P.
Abstract
Compositional data, commonly used in geochemistry (proportions, percentages, mg/kg), have specific properties that are not compatible with the Euclidean geometry requirement of most standard statistical methods. In order to represent compositional data in the usual Euclidean geometry, they need to be expressed in orthonormal coordinates prior to statistical processing. As it is not possible to construct Cartesian coordinates for compositions that assign a coordinate for each of the parts separately, a choice of interpretable orthonormal coordinates is of particular interest. Although recent experience shows clear advantages of such coordinates where the first coordinate aggregates information from logratios for a particular compositional part of interest, their usefulness is limited if there are distortions like rounding errors or other data "problems" in the involved parts. The purpose of this contribution is to introduce a "weighted" version of these coordinates, where the remaining parts (with respect to the part of interest) in the first coordinate are weighted in a way that is relevant to the aims of the statistical analysis. In a geochemical context, quality assessment analysis and elements of the variation matrix of compositions are proposed to derive possible relevant weights. Theoretical considerations are accompanied by examples using data from the National Geochemical Survey of Australia.
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nonGeographicDataset
eCat Id
83145
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Cnr Jerrabomberra Ave and Hindmarsh Dr GPO Box 378
Canberra
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2601
Australia
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- External Publication
- Australian and New Zealand Standard Research Classification (ANZSRC)
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- Earth Sciences
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- Published_Internal
Publication Date
2015-01-01T00:00:00
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geoscientificInformation
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[-44.0, -10.0, 112.0, 154.0]
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