Matrix comparison, Part 2: Measuring the resemblance between proximity measures or ordination results by use of the mantel and procrustes statistics

Abstract

The present two-part article introduces matrix comparison as a formal means for evaluation purposes in informetric studies such as cocitation analysis. In the first part, the motivation behind introducing matrix comparison to informetric studies, as well as two important issues influencing such comparisons, matrix generation, and the composition of proximity measures, are introduced and discussed. In this second part, the authors introduce and thoroughly demonstrate two related matrix comparison techniques the Mantel test and Procrustes analysis, respectively. These techniques can compare and evaluate the degree of monotonicity between different proximity measures or their ordination results. In common with these techniques is the application of permutation procedures to test hypotheses about matrix resemblances. The choice of technique is related to the validation at hand. In the case of the Mantel test, the degree of resemblance between two measures forecast their potentially different affect upon ordination and clustering results. In principle, two proximity measures with a very strong resemblance most likely produce identical results, thus, choice of measure between the two becomes less important. Alternatively, or as a supplement, Procrustes analysis compares the actual ordination results without investigating the underlying proximity measures, by matching two configurations of the same objects in a multidimensional space. An advantage of the Procrustes analysis though, is the graphical solution provided by the superimposition plot and the resulting decomposition of variance components. Accordingly, the Procrustes analysis provides not only a measure of general fit between configurations, but also values for individual objects enabling more elaborate validations. As such, the Mantel test and Procrustes analysis can be used as statistical validation tools in informetric studies and thus help choosing suitable proximity measures.

Quantifying Brain Connectivity: A Comparative Tractography Study

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“…We used the standardized Mantel statistic (r M ), calculated using Eq. (2) from Schneider and Borlund (2007), to determine if there was a linear correlation between genetic and discrete trait proximity matrices. This correlation coefficient is easily interpretable and informative as a descriptive measure, because the coefficient is bounded between 21 and 11.…”

Concept mapping—An effective method for identifying diversity and congruity in cognitive style

“…The Procrustes analysis is an improvement of the Mantel test (Mantel, 1967), which is becoming a popular measure of the association between distance matrices. It has been found that the Procrustes analysis is more sensitive to type I error rates and to power of significance tests compared to the Mantel test (Peres-Neto & Jackson, 2001;Schneider & Borlund, 2007). There are two additional features of the Procrustes analysis that make it more appropriate for the case study considered in this paper.…”