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'sZ. It is shown that the rowwise matrix correlation coefficient between two matricesX andY is the partial correlation between the entries ofX andY 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cheverud, J. M., Wagner, G. P., & Dow, M. M. (1989). Methods for the comparative analysis of variation patterns.Systematic Zoology, 38, 201–213.
Daniels, H. E. (1944). The relation between measures of correlation in the universe of sample permutations.Biometrika, 33, 129–135.
de Vries (1992).The object-controlled correlation between two symmetric proximity matrices. Manuscript submitted for publication.
de Waal, F. B. M., & Luttrell, L. M. (1988). Mechanisms of social reciprocity in three primate species: Symmetrical relationship characteristics or cognition?Ethology and Sociobiology, 9, 101–118.
Dietz, E. J. (1983). Permutation tests for association between two distance matrices.Systematic Zoology, 32, 21–26.
Dow, M. M., Cheverud, J. M., & Friedlander, J. S. (1987). Partial correlation of distance matrices in studies of population structure.American Journal of Physiological Anthropology, 72, 343–352.
Dunn, O. J., & Clark, V. A. (1987).Applied statistics: Analysis of variance and regression (2nd ed.). New York: Wiley.
Hemelrijk, C. K. (1990a). Models of, and tests for, reciprocity, unidirectionality and other social interaction patterns at a group level.Animal Behaviour, 39, 1013–1029.
Hemelrijk, C. K. (1990b). A matrix partial correlation test used in investigations of reciprocity and other social interaction patterns at group level.Journal of Theoretical Biology, 143, 405–420.
Hubert, L. J. (1987).Assignment methods in combinatorial data analysis. New York: Academic Press.
Kendall, M. G. (1962).Rank correlation methods (3rd ed.). London: Griffin.
Klauber, M. R. (1971). Two-sample randomization tests for space-time clustering.Biometrics, 27, 129–142.
Krackhardt, D. (1988). Predicting with networks: Nonparametric multiple regression analysis of dyadic data.Social Networks, 10, 359–381.
Maghsoodloo, S. (1975). Estimates of the quantiles of Kendall's partial rank correlation coefficient.Journal of Statistical Computation and Simulation, 4, 155–164.
Mantel, N. (1967). The detection of disease clustering and a generalized regression approach.Cancer Research, pp. 209–220.
Quade, D. (1974). Nonparametric partial correlation. In H. M. Blalock (Ed.),Measurement in the Social Sciences: Theories and strategies (pp. 369–398). London: Macmillan Press.
Schnell, G. D., Watt, D. J., & Douglas, M. (1985). Statistical comparison of proximity matrices: Applications in animal behaviour.Animal Behaviour, 33, 239–253.
Shepard, R. N. (1972). A taxonomy of some principal types of data and of multidimensional methods for their analysis. In R. N. Shepard, A. K. Romney, & S. B. Nerlove (Eds.),Multidimensional scaling: Theory and applications in the behavioral sciences Volume I (pp. 21–47). New York: Seminar Press.
Smouse, P. E., Long, J. C., & Sokal, R. R. (1986). Multiple regression and correlation extensions of the Mantel test of matrix correspondence.Systematic Zoology, 35, 627–632.
Spielman, R. S. (1973). Differences among Yanomama Indian villages: Do the patterns of allele frequencies, anthropometrics and map locations correspond?American Journal of Physiological Anthropology, 39, 461–480.
Author information
Authors and Affiliations
Additional information
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.
Rights and permissions
About this article
Cite this article
de Vries, H. The rowwise correlation between two proximity matrices and the partial rowwise correlation. Psychometrika 58, 53–69 (1993). https://doi.org/10.1007/BF02294470
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02294470