Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-07T18:56:01.071Z Has data issue: false hasContentIssue false

Generalized Concordance

Published online by Cambridge University Press:  01 January 2025

Lawrence J. Hubert*
Affiliation:
The University of California, Santa Barbara
*
Requests for reprints should be sent to Lawrence Hubert, Graduate School of Education, University of California, Santa Barbara, California, 93106.

Abstract

Based on a simple nonparametric procedure for comparing two proximity matrices, a measure of concordance is introduced that is appropriate when K independent proximity matrices are available. In addition to the development of a general concept of concordance and specific techniques for its evaluation within and between the subsets of a partition of the K matrices, several methods are also suggested for comparing and/or for fitting a particular structure to the given data. Finally, brief indications are provided as to how the well-known notion of concordance for K rank orders can be included within the more general framework.

Type
Original Paper
Copyright
Copyright © 1979 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Partial support for this research was supplied by the National Science Foundation through SOC-77-28227.

References

Baker, F. B. & Hubert, L. J. Applications of combinatorial programming to data analysis: Seriation using asymmetric proximity measures. British Journal of Mathematical and Statistical Psychology, 1977, 30, 154164.CrossRefGoogle Scholar
Besag, J. & Diggle, P. J. Simple Monte Carlo tests for spatial pattern. Applied Statistics, 1977, 26, 327333.CrossRefGoogle Scholar
Carroll, J. D. & Chang, J. J. Analysis of individual differences in multidimensional scaling via an N-way generalization of Eckart-Young decomposition. Psychometrika, 1970, 35, 283319.CrossRefGoogle Scholar
Cliff, A. D. & Ord, J. K. Spatial autocorrelation, 1973, London: Pion.Google Scholar
Dywer, P. S. The mean and standard deviation of the distribution of group assembly sums. Psychometrika, 1964, 29, 397408.CrossRefGoogle Scholar
Edgington, E. S. Statistical inference: The distribution-free approach, 1969, New York: McGraw-Hill.Google Scholar
Ehrenberg, A. S. C. On sampling from a population of rankers. Biometrika, 1952, 39, 8287.CrossRefGoogle Scholar
Hays, W. L. A note on average tau as a measure of concordance. Journal of the American Statistical Association, 1960, 55, 331341.CrossRefGoogle Scholar
Hope, A. C. A. A simplified Monte Carlo significance test procedure. Journal of the Royal Statistical Society, Series B, 1968, 30, 582598.CrossRefGoogle Scholar
Hubert, L. J. Seriation using asymmetric proximity measures. British Journal of Mathematical and Statistical Psychology, 1976, 29, 3252.CrossRefGoogle Scholar
Hubert, L. J. Generalized proximity function comparisons. British Journal of Mathematical and Statistical Psychology, 1978, 31, 179192.CrossRefGoogle Scholar
Hubert, L. J. Matching models in the analysis of cross-classifications. Psychometrika, 1979, 44, in press.CrossRefGoogle Scholar
Hubert, L. J.The comparison of sequences. Psychological Bulletin, 1980, in press.Google Scholar
Hubert, L. J. Baker, F. B. Analyzing distinctive features. Journal of Educational Statistics, 1977, 2, 7998.CrossRefGoogle Scholar
Hubert, L. J. & Baker, F. B. Evaluating the conformity of sociometric measurements. Psychometrika, 1978, 43, 3141.CrossRefGoogle Scholar
Hubert, L. J. & Levin, J. R. Evaluating object set partitions: Free-sort analysis and some generalizations. Journal of Verbal Learning and Verbal Behavior, 1976, 15, 459470.CrossRefGoogle Scholar
Hubert, L. J. & Schultz, J. V. Quadratic assignment as a general data analysis strategy. British Journal of Mathematical and Statistical Psychology, 1976, 29, 190241.CrossRefGoogle Scholar
Kendall, M. G. Rank correlation methods, 4th ed., New York: Hafner, 1970.Google Scholar
Lawler, E. L. The quadratic assignment problem: A brief review. In Roy, B.(Eds.), Combinatorial programming: Methods and applications. Dordrecht: Reidel. 1975, 351360.Google Scholar
Lyerly, S. B. The average Spearmen rank correlation coefficient. Psychometrika, 1952, 17, 421428.CrossRefGoogle Scholar
Mantel, N. The detection of disease clustering and a generalized regression approach. Cancer Research, 1967, 27, 209220.Google Scholar
Mielke, P. W., Berry, K. J., & Johnson, E. S. Multi-response permutation procedures for a priori classifications. Communications in Statistics—Theory and Methods, 1976, 5, 14091424.CrossRefGoogle Scholar
Mirkin, B. G. Approximation problems in relation space and the analysis of nonnumeric methods. Automation and Remote Control, 1974, 35, 14241431.Google Scholar
Page, E. B. Ordered hypotheses for multiple treatments: A significance test for linear ranks. Journal of the American Statistical Association, 1963, 58, 216230.CrossRefGoogle Scholar
Schucany, W. R. & Frawley, W. H. A rank test for two group concordance. Psychometrika, 1973, 38, 249258.CrossRefGoogle Scholar