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The Rowwise Correlation between Two Proximity Matrices and the Partial Rowwise Correlation

Published online by Cambridge University Press:  01 January 2025

Han de Vries
Han de Vries*
Affiliation:
Projectgroup of Ethology & Socio-ecology, State University of Utrecht
*
Requests for reprints should be sent to Han de Vries, Projectgroup of Ethology & Socio-ecology, The University of Utrecht, Postbox 80.086, 3508 TB Utrecht, The Nethedands.
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Abstract

This paper discusses rowwise matrix correlation, based on the weighted sum of correlations between all pairs of corresponding rows of two proximity matrices, which may both be square (symmetric or asymmetric) or rectangular. Using the correlation coefficients usually associated with Pearson, Spearman, and Kendall, three different rowwise test statistics and their normalized coefficients are discussed, and subsequently compared with their nonrowwise alternatives like Mantel's Z. It is shown that the rowwise matrix correlation coefficient between two matrices X and Y is the partial correlation between the entries of X and Y controlled for the nominal variable that has the row objects as categories. Given this fact, partial rowwise correlations (as well as multiple regression extensions in the case of Pearson's approach) can be easily developed.

Keywords

matrix permutation testsrowwise matrix correlationpartial matrix correlationMantel's Z statisticnonparametric statistics
Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 1 , March 1993 , pp. 53 - 69
Copyright
Copyright © 1993 The Psychometric Society

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Footnotes

The author wishes to thank the Editor, two referees, Jan van Hooff, and Ruud Derix for their useful comments, and E. J. Dietz for a copy of the algorithm of the Mantel permutation test.

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