Chapter 3
Association Measures and Matrices
3.1 Objectives
Most methods of multivariate analysis, in particular ordination and clustering techniques, are explicitly or implicitly
1 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
2
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;
• learn or revise some basics of programming functions with the R language.
3.2 The Main Categories of Association Measures (Short
Overview)
It is beyond the scope of this book to explain the various indices in detail, but it is
useful to provide a wrap-up of the main categories of measures. This will facilitate
the choice of an appropriate index in many situations, and improve the
1 The association measure among objects may be implicit. It is the Euclidean distance in principal
component analysis (PCA, Chap. 5) and k-means partitioning (Chap. 4), for example, and the chisquare distance in correspondence analysis (CA, Chap. 5).
2 See footnote 4 in Sect. 3.2.2.
© Springer International Publishing AG, part of Springer Nature 2018
D. Borcard et al., Numerical Ecology with R, Use R!,
https://doi.org/10.1007/978-3-319-71404-2_3
35
Association Measures and Matrices
3.1 Objectives
Most methods of multivariate analysis, in particular ordination and clustering techniques, are explicitly or implicitly
1 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
2
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;
• learn or revise some basics of programming functions with the R language.
3.2 The Main Categories of Association Measures (Short
Overview)
It is beyond the scope of this book to explain the various indices in detail, but it is
useful to provide a wrap-up of the main categories of measures. This will facilitate
the choice of an appropriate index in many situations, and improve the
1 The association measure among objects may be implicit. It is the Euclidean distance in principal
component analysis (PCA, Chap. 5) and k-means partitioning (Chap. 4), for example, and the chisquare distance in correspondence analysis (CA, Chap. 5).
2 See footnote 4 in Sect. 3.2.2.
© Springer International Publishing AG, part of Springer Nature 2018
D. Borcard et al., Numerical Ecology with R, Use R!,
https://doi.org/10.1007/978-3-319-71404-2_3
35