Correlation analysis of dissimilarity matrices |
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Authors: | Sarah C Goslee |
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Institution: | (1) USDA-ARS PSWMRU, University Park, PA 16801, USA |
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Abstract: | Distance-based methods have been a valuable tool for ecologists for decades. Indirectly, distance-based ordination and cluster
analysis, in particular, have been widely practiced as they allow the visualization of a multivariate data set in a few dimensions.
The explicitly distance-based Mantel test and multiple regression on distance matrices (MRM) add hypothesis testing to the
toolbox. One concern for ecologists wishing to use these methods lies in deciding whether to combine data vectors into a compound
multivariate dissimilarity to analyze them individually. For Euclidean distances on scaled data, the correlation of a pair
of multivariate distance matrices can be calculated from the correlations between the two sets of individual distance matrices
if one set is orthogonal, demonstrating a clear link between individual and compound distances. The choice between Mantel
and MRM should be driven by ecological hypotheses rather than mathematical concerns. The relationship between individual and
compound distance matrices also provides a means for calculating the maximum possible value of the Mantel statistic, which
can be considerably less than 1 for a given analysis. These relationships are demonstrated with simulated data. Although these
mathematical relationships are only strictly true for Euclidean distances when one set of variables is orthogonal, simulations
show that they are approximately true for weakly correlated variables and Bray–Curtis dissimilarities. |
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