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Matching Models in the Analysis of Cross-Classifications

Published online by Cambridge University Press:  01 January 2025

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

Inference models motivated by the combinatorial chance literature and the concept of object matching may be used in the analysis of a contingency table if the conditional assumption of fixed row and column totals is imposed. More specifically, by developing a matching reinterpretation for several problems of interest in the prediction analysis of cross-classifications—as defined by Hildebrand, Laing and Rosenthal, appropriate significance tests can be given that may differ from those justified by the more common multinomial models. In the course of the paper the distinction between a degree-1 statistic (based on the relationship between single objects) and a degree-2 statistic (based on the relationship between object pairs) is reviewed in some detail. Also, several specializations are presented to topics of current methodological importance in psychology; for instance, a number of references are made to the measurement of nominal scale response agreement between two raters.

Keywords

distribution-free testscombinatorial chancenominal scale response agreement

Information

Type
Original Paper
Information
Psychometrika , Volume 44 , Issue 1 , March 1979, pp. 21 - 41
Copyright
Copyright © 1979 The Psychometric Society

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Footnotes

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

References

Reference Note

Hubert, L. J.Alternative inference models based on matching for a weighted index of nominal scale response agreement. Unpublished manuscript, 1978.Google Scholar

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