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Compositional data analysis — linear algebra, visualization and interpretation

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Abstract

Compositional data analysis is concerned with multivariate data that have a constant sum, usually 1 or 100%. These are data often found in biochemistry and geochemistry, but also in the social sciences, when relative values are of interest rather than the raw values. Recent applications are in the area of very high-dimensional "omics" data. Logratios are frequently used for this type of data, i.e. the logarithms of ratios of the components of the data vectors. These ratios raise interesting issues in matrix-vector representation, computation and interpretation, which will be dealt with in this chapter.

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  • Michael Greenacre, 2021. "Compositional data analysis — linear algebra, visualization and interpretation," Economics Working Papers 1805, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1805
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    References listed on IDEAS

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    1. Michael Greenacre, 2003. "Singular value decomposition of matched matrices," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(10), pages 1101-1113.
    2. John Aitchison & Michael Greenacre, 2002. "Biplots of compositional data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(4), pages 375-392, October.
    3. Michael Greenacre & Paul Lewi, 2009. "Distributional Equivalence and Subcompositional Coherence in the Analysis of Compositional Data, Contingency Tables and Ratio-Scale Measurements," Journal of Classification, Springer;The Classification Society, vol. 26(1), pages 29-54, April.
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    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software

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