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Analysing Pairwise Logratios Revisited

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Abstract

Even though the logratio methodology provides a range of both generic, mostly exploratory, and purpose-built coordinate representations of compositional data, simple pairwise logratios are preferred by many for multivariate analysis in the geochemical practice, principally because of their simpler interpretation. However, the logratio coordinate systems that incorporate them are predominantly oblique, resulting in both conceptual and practical problems. We propose a new approach, called backwards pivot coordinates, where each pairwise logratio is linked to one orthogonal coordinate system, and these systems are then used together to produce a concise output. In this work, principal component analysis and regression with compositional explanatory variables are used as primary methods to demonstrate the methodological and interpretative advantages of the proposal. In the applied part of this study, sediment compositions from the Jizera River, Czech Republic, were analysed using these techniques through backwards pivot coordinates. This allowed us to discuss grain size control of the element composition of sediments and clearly distinguish anthropogenically contaminated and uncontaminated strata in sediment depth profiles.

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Acknowledgements

The authors thank to Štěpánka Tůmová (IIC Řež) for providing the digital terrain model of the sampling site. KH, PF, MF and TMG gratefully acknowledge the support of the Czech Science Foundation GA19-01768S. GC and JPA were supported by the Spanish Ministry of Science, Innovation and Universities under the project CODAMET (RTI2018-095518-B-C21, 2019-2021).

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Authors and Affiliations

  1. Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Karel Hron

  2. Department of Economics, Faculty of Economics and Business, University of Girona, c. Universitat de Girona 10, 17003, Girona, Spain

    Germá Coenders

  3. Institute of Inorganic Chemistry of the Czech Academy of Sciences, 250 68, Husinec-Řež, Czech Republic

    Martin Faměra & Tomáš Matys Grygar

  4. Department of Geology, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Martin Faměra

  5. Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria

    Peter Filzmoser

  6. Biomathematics and Statistics Scotland, JCMB, The King’s Buildings, Peter Guthrie Tait Road, Edinburgh, Scotland, EH9 3FD, UK

    Javier Palarea-Albaladejo

Authors
  1. Karel Hron
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  2. Germá Coenders
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  3. Peter Filzmoser
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  4. Javier Palarea-Albaladejo
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  5. Martin Faměra
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  6. Tomáš Matys Grygar
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Contributions

KH, GC and TMG conceived this research and designed the experiments; TMG provided the geochemical dataset and interpretations; GC and PF performed the experiments and analysis; KH and GC wrote the first draft of the paper and KH, GC, TMG, PF and JPA all participated in the revisions of it; MF planned and performed sediment sampling, which represented the studied floodplain, and supervised sediment analyses.

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Correspondence to Karel Hron.

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Hron, K., Coenders, G., Filzmoser, P. et al. Analysing Pairwise Logratios Revisited. Math Geosci 53, 1643–1666 (2021). https://doi.org/10.1007/s11004-021-09938-w

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  • DOI: https://doi.org/10.1007/s11004-021-09938-w

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