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Log-contrast and Orthonormal Log-ratio Coordinates for Compositional Data with a Total

In: Advances in Contemporary Statistics and Econometrics

Author

Listed:
  • Josep Antoni Martín-Fernández

    (University of Girona, Department of IMAE)

  • Carles Barceló-Vidal

    (University of Girona, Department of IMAE)

Abstract

Compositional data require an appropriate statistical analysis because they provide the relative importance of the parts of a whole. Methods based on log-ratio coordinates give a consistent framework for analyzing this type of data. Any statistical model including variables created using the original parts should be formulated according to the geometry of the simplex. This geometry includes the log-contrast: a simple way to express a set of log-ratios in a linear form. Basic concepts and properties of log-ratios, log-contrasts, and orthonormal coordinates are revisited. In addition, we introduce an approach that includes both the log-ratio orthonormal coordinates and an auxiliary variable carrying absolute information. We illustrate the approach through the principal component analysis and discriminant analysis of real data sets.

Suggested Citation

  • Josep Antoni Martín-Fernández & Carles Barceló-Vidal, 2021. "Log-contrast and Orthonormal Log-ratio Coordinates for Compositional Data with a Total," Springer Books, in: Abdelaati Daouia & Anne Ruiz-Gazen (ed.), Advances in Contemporary Statistics and Econometrics, pages 509-524, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-73249-3_26
    DOI: 10.1007/978-3-030-73249-3_26
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