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Optimal Scaling of Paired Comparison and Rank Order Data: An Alternative to Guttman's Formulation

Published online by Cambridge University Press:  01 January 2025

Shizuhiko Nishisato
Shizuhiko Nishisato*
Affiliation:
The Ontario Institute for Studies in Education
*
Requests for reprints should be sent to Shizuhiko Nishisato, Department of Measurement, Evaluation and Computer Applications, The Ontario Institute for Studies in Education, 252 Bloor Street West, Toronto, Ontario, Canada, M5S 1V6.
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Abstract

A formulation, which is different from Guttman's is presented. The two formulations are both called the optimal scaling approach, and are proven to provide identical scale values. The proposed formulation has at least two advantages over Guttman's. Namely, (i) the former serves to clarify close relations of the optimal scaling approach to those of Slater and the vector model of preferential choice, and (ii) in addition to the stimulus scale values, it provides scores for the subjects, which indicate the degrees of response consistency (transitivity), relative to the optimum solution. The method is assumption-free and capable of multidimensional analysis.

Keywords

Guttman's modelSlater's modelthe vector model of preferential choiceranking and individual differences
Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 2 , June 1978 , pp. 263 - 271
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

This study was partly supported by the National Research Council Grant (No. A4581) to S. Nishisato. The author is indebted to Dr. Bert F. Green, Jr., Mr. Tomoichi Ishizuka, and anonymous reviewers for their valuable comments on an earlier draft.

References

Reference Notes

Carroll, J. D. & Chang, J. J. Nonparametric multidimensional analysis of paired comparisons data. Paper presented at the joint meeting of the Psychometric and Psychonomic Societies, Niagara Falls, October 1964.Google Scholar
Carroll, J. D. & Chang, J. J. How to use MDPREF, a computer program for multidimensional analysis of preference data. Unpublished report, Bell Laboratories, 1968.Google Scholar
Nishisato, S. Optimal scaling as applied to different forms of data, 1976, Toronto: Department of Measurement and Evaluation, The Ontario Institute for Studies in Education.Google Scholar
de Leeuw, J. Canonical analysis of categorical data, 1973, The Netherlands: University of Leiden.Google Scholar

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