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Size and shape in the measurement of multivariate proximity

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Abstract

Most methods of multivariate analysis rely on a measure of proximity between individual cases or samples to quantify inter-sample differences. The choice of this measure is fundamental to the method and its subsequent results. For example, when data are abundance counts of a set of species at several sampling locations, some approaches rely on the Bray-Curtis dissimilarity measure between samples, while other approaches rely on the chi-square distance. A set of observed species abundances at a location has both size, in the form of the overall levels of the species counts, and shape, in the form of the relative values of the counts. The aim of this report is to clarify how much the chosen proximity measure is capturing differences in size between samples as opposed to differences in shape. After motivating the idea using physical morphometric data, the study is extended to nonnegative data in general, with special focus on abundance counts and biomass estimates, which are ubiquitous in ecological research.

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  • Michael Greenacre, 2014. "Size and shape in the measurement of multivariate proximity," Economics Working Papers 1444, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1444
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    References listed on IDEAS

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    1. Michael Greenacre, 2008. "Correspondence analysis of raw data," Economics Working Papers 1112, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2009.
    2. Michael Greenacre, 2012. "Fuzzy coding in constrained ordinations," Economics Working Papers 1325, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Greenacre Michael, 2010. "Biplots in Practice," Books, Fundacion BBVA / BBVA Foundation, number 2011113, October.
    4. J. Gower & P. Legendre, 1986. "Metric and Euclidean properties of dissimilarity coefficients," Journal of Classification, Springer;The Classification Society, vol. 3(1), pages 5-48, March.
    5. Zerrin Asan & Michael Greenacre, 2008. "Biplots of fuzzy coded data," Economics Working Papers 1077, Department of Economics and Business, Universitat Pompeu Fabra.
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    More about this item

    Keywords

    Bray-Curtis dissimilarity; chi-square distance; cluster analysis; correspondence analysis; multivariate analysis; ordination; visualization.;
    All these keywords.

    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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