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Factor Analysis of Compositional Data with a Total

In: Advances in Compositional Data Analysis

Author

Listed:
  • Carles Barceló-Vidal

    (Campus Montilivi, Edif. P4, University of Girona, Department IMAE)

  • Josep Antoni Martín-Fernández

    (Campus Montilivi, Edif. P4, University of Girona, Department IMAE)

Abstract

The sample space of a manifest random vector is of crucial importance for a latent variable model. Compositional data require an appropriate statistical analysis because they provide the relative importance of the parts of a whole. Any statistical model including variables created using the original parts should be formulated according to the geometry of the simplex. Methods based on log-ratio coordinates give a consistent framework for analyzing this type of data. Here, we introduce an approach that includes both the orthonormal log-ratio coordinates and an auxiliary variable carrying absolute information and illustrate it through the factor analysis of two real datasets.

Suggested Citation

  • Carles Barceló-Vidal & Josep Antoni Martín-Fernández, 2021. "Factor Analysis of Compositional Data with a Total," Springer Books, in: Peter Filzmoser & Karel Hron & Josep Antoni Martín-Fernández & Javier Palarea-Albaladejo (ed.), Advances in Compositional Data Analysis, pages 125-142, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-71175-7_7
    DOI: 10.1007/978-3-030-71175-7_7
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