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Towards a pragmatic approach to compositional data analysis

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Abstract
Compositional data are nonnegative data with the property of closure: that is, each set of values on their components, or so-called parts, has a fixed sum, usually 1 or 100%. The approach to compositional data analysis originated by John Aitchison uses ratios of parts as the fundamental starting point for description and modeling. I show that a compositional data set can be effectively replaced by a set of ratios, one less than the number of parts, and that these ratios describe an acyclic connected graph of all the parts. Contrary to recent literature, I show that the additive log-ratio transformation can be an excellent substitute for the original data set, as shown in an archaeological data set as well as in three other examples. I propose further that a smaller set of ratios of parts can be determined, either by expert choice or by automatic selection, which explains as much variance as required for all practical purposes. These part ratios can then be validly summarized and analyzed by conventional univariate methods, as well as multivariate methods, where the ratios are preferably log-transformed.

Suggested Citation

  • Michael Greenacre, 2017. "Towards a pragmatic approach to compositional data analysis," Economics Working Papers 1554, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1554
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    References listed on IDEAS

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    1. Arnold Wollenberg, 1977. "Redundancy analysis an alternative for canonical correlation analysis," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 207-219, June.
    2. Luc Wouters & Hinrich W. Göhlmann & Luc Bijnens & Stefan U. Kass & Geert Molenberghs & Paul J. Lewi, 2003. "Graphical Exploration of Gene Expression Data: A Comparative Study of Three Multivariate Methods," Biometrics, The International Biometric Society, vol. 59(4), pages 1131-1139, December.
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    More about this item

    Keywords

    compositional data; log-ratio transformation; log-ratio analysis; log-ratio distance; multivariate analysis; ratios; subcompositional coherence; univariate statistics.;
    All these keywords.

    JEL classification:

    • Z32 - Other Special Topics - - Tourism Economics - - - Tourism and Development
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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