Association Measures and Matrices

  • Daniel Borcard
  • François Gillet
  • Pierre Legendre
Part of the Use R! book series (USE R)


Most methods of multivariate analysis, in particular ordination and clustering techniques, are explicitly or implicitly based on the comparison of all possible pairs of objects or descriptors. The comparisons take the form of association measures (often called coefficients or indices), which are assembled in a square and symmetric association matrix, of dimensions n × n when objects are compared, or p × p when variables are compared. Since the subsequent analyses are done on association matrices, the choice of an appropriate measure is crucial. In this Chapter you will quickly revise the main categories of association coefficients, learn how to compute, examine and visually compare dissimilarity matrices (Q mode) and dependence matrices (R mode), apply these techniques to a classical dataset and learn or revise some basics of programming functions with the R language.


  1. Jaccard, P.: Étude comparative de la distribution florale dans une portion des Alpes et du Jura. Bulletin de la Société Vaudoise des Sciences Naturelles. 37, 547–579 (1901)Google Scholar
  2. Legendre, P.: Species associations: the Kendall coefficient of concordance revisited. J. Agric. Biol. Environ. Stat. 10, 226–245 (2005)CrossRefGoogle Scholar
  3. Legendre, P., De Cáceres, M.: Beta diversity as the variance of community data: dissimilarity coefficients and partitioning. Ecol. Lett. 16, 951–963 (2013)CrossRefGoogle Scholar
  4. Legendre, P., Gallagher, E.D.: Ecologically meaningful transformations for ordination of species data. Oecologia. 129, 271–280 (2001)CrossRefGoogle Scholar
  5. Legendre, P., Legendre, L.: Numerical Ecology, 3rd English edn. Elsevier, Amsterdam (2012)Google Scholar
  6. Legendre, P., Borcard, D.: Box-Cox-chord transformations for community composition data prior to beta diversity analysis. Ecography (2018, in press)Google Scholar
  7. Podani, J.: Extending Gower's general coefficient of similarity to ordinal characters. Taxon. 48, 331–340 (1999)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Daniel Borcard
    • 1
  • François Gillet
    • 2
  • Pierre Legendre
    • 1
  1. 1.Département de sciences biologiquesUniversité de MontréalMontréalCanada
  2. 2.UMR Chrono-environnementUniversité Bourgogne Franche-ComtéBesançonFrance

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