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Compositional cubes: a new concept for multi-factorial compositions

Author

Listed:
  • Kamila Fačevicová

    (Palacký University Olomouc)

  • Peter Filzmoser

    (TU Wien)

  • Karel Hron

    (Palacký University Olomouc)

Abstract

Compositional data are commonly known as multivariate observations carrying relative information. Even though the case of vector or even two-factorial compositional data (compositional tables) is already well described in the literature, there is still a need for a comprehensive approach to the analysis of multi-factorial relative-valued data. Therefore, this contribution builds around the current knowledge about compositional data a general theoretical framework for k-factorial compositional data. As a main finding it turns out that, similar to the case of compositional tables, also the multi-factorial structures can be orthogonally decomposed into an independent and several interactive parts and, moreover, a coordinate representation allowing for their separate analysis by standard analytical methods can be constructed. For the sake of simplicity, these features are explained in detail for the case of three-factorial compositions (compositional cubes), followed by an outline covering the general case. The three-dimensional structure is analyzed in depth in two practical examples, dealing with systems of spatial and time dependent compositional cubes. The methodology is implemented in the R package robCompositions.

Suggested Citation

  • Kamila Fačevicová & Peter Filzmoser & Karel Hron, 2023. "Compositional cubes: a new concept for multi-factorial compositions," Statistical Papers, Springer, vol. 64(3), pages 955-985, June.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:3:d:10.1007_s00362-022-01350-8
    DOI: 10.1007/s00362-022-01350-8
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    References listed on IDEAS

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    1. J. de Sousa & K. Hron & K. Fačevicová & P. Filzmoser, 2021. "Robust principal component analysis for compositional tables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(2), pages 214-233, January.
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    Cited by:

    1. Genest, Christian & Hron, Karel & Nešlehová, Johanna G., 2023. "Orthogonal decomposition of multivariate densities in Bayes spaces and relation with their copula-based representation," Journal of Multivariate Analysis, Elsevier, vol. 198(C).

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