Psychometrika

, Volume 58, Issue 1, pp 53–69 | Cite as

The rowwise correlation between two proximity matrices and the partial rowwise correlation

  • Han de Vries
Article

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.

Key words

matrix permutation tests rowwise matrix correlation partial matrix correlation Mantel'sZ statistic nonparametric statistics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Cheverud, J. M., Wagner, G. P., & Dow, M. M. (1989). Methods for the comparative analysis of variation patterns.Systematic Zoology, 38, 201–213.Google Scholar
  2. Daniels, H. E. (1944). The relation between measures of correlation in the universe of sample permutations.Biometrika, 33, 129–135.Google Scholar
  3. de Vries (1992).The object-controlled correlation between two symmetric proximity matrices. Manuscript submitted for publication.Google Scholar
  4. 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.Google Scholar
  5. Dietz, E. J. (1983). Permutation tests for association between two distance matrices.Systematic Zoology, 32, 21–26.Google Scholar
  6. 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.Google Scholar
  7. Dunn, O. J., & Clark, V. A. (1987).Applied statistics: Analysis of variance and regression (2nd ed.). New York: Wiley.Google Scholar
  8. 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.Google Scholar
  9. 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.Google Scholar
  10. Hubert, L. J. (1987).Assignment methods in combinatorial data analysis. New York: Academic Press.Google Scholar
  11. Kendall, M. G. (1962).Rank correlation methods (3rd ed.). London: Griffin.Google Scholar
  12. Klauber, M. R. (1971). Two-sample randomization tests for space-time clustering.Biometrics, 27, 129–142.Google Scholar
  13. Krackhardt, D. (1988). Predicting with networks: Nonparametric multiple regression analysis of dyadic data.Social Networks, 10, 359–381.Google Scholar
  14. Maghsoodloo, S. (1975). Estimates of the quantiles of Kendall's partial rank correlation coefficient.Journal of Statistical Computation and Simulation, 4, 155–164.Google Scholar
  15. Mantel, N. (1967). The detection of disease clustering and a generalized regression approach.Cancer Research, pp. 209–220.Google Scholar
  16. 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.Google Scholar
  17. Schnell, G. D., Watt, D. J., & Douglas, M. (1985). Statistical comparison of proximity matrices: Applications in animal behaviour.Animal Behaviour, 33, 239–253.Google Scholar
  18. 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.Google Scholar
  19. 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.Google Scholar
  20. 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.Google Scholar

Copyright information

© The Psychometric Society 1993

Authors and Affiliations

  • Han de Vries
    • 1
  1. 1.Projectgroup of Ethology & Socio-ecologyThe University of UtrechtUtrechtThe Netherlands

Personalised recommendations