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An Individual Difference Model for the Multidimensional Analysis of Preference Data

Published online by Cambridge University Press:  01 January 2025

Peter H. Schönemann  and
Ming Mei Wang
Peter H. Schönemann
Affiliation:
Purdue University
Ming Mei Wang
Affiliation:
Purdue University
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Abstract

A model for the analysis of paired comparison data is presented which combines features of the BTL-model with features of the Unfolding model. The model is metric, mathematically tractable, and has an exact algebraic solution. Since it is multidimensional and allows for individual differences, it is thought to be more realistic for some choice situations than either the Thurstone model or the BTL-model. No claim is made that the present model will be appropriate for all conceivable choice situations. Rather, it is argued that the fact that it is explicitly falsifiable is a point in its favor.

Type
Original Paper
Information
Psychometrika , Volume 37 , Issue 3 , September 1972 , pp. 275 - 309
Copyright
Copyright © 1972 The Psychometric Society

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Footnotes

*

This work was supported by a grant of the United States Public Health Service (1 R03 MH19139 01 MSM) and a David Ross (XR) grant of the Purdue Research Foundation (PRF 2132), both of which are gratefully acknowledged. We also owe thanks to Dr. Terry Cooper, whose careful scrutiny of an earlier draft of this paper allowed us to reduce the number of errors from n to n-1.

References

Blumenthal, L. M. Theory and applications of distance geometry, 1970, New York: ChelseaGoogle Scholar
Bock, D. and Jones, L. The measurement and prediction of judgment and choice, 1968, San Francisco: Holden DayGoogle Scholar
Bradley, R. A. Incomplete block rank analysis: On the appropriateness of the model for a method of paired comparisons. Biometrics, 1954, 10, 375–390CrossRefGoogle Scholar
Bradley, R. A. and Terry, M. E. Rank analysis of incomplete block designs. I. The method of paired comparisons. Biometrika, 1952, 39, 324–345Google Scholar
Coombs, C. H. On the use of inconsistency of preferences in psychological measurement. Journal of Experimental Psychology, 1958, 55, 1–7CrossRefGoogle ScholarPubMed
Coombs, C. H. A theory of data, 1964, New York: WileyGoogle Scholar
David, H. A. The method of paired comparisons, 1963, New York: HefnerGoogle Scholar
Ellis, B. Basic concepts of measurement, 1968, Cambridge: Cambridge University PressGoogle Scholar
Green, P. E. and Carmone, F. J. Multidimensional scaling: An introduction and comparison of nonmetric unfolding techniques. Journal of Marketing Research, 1969, VI, 330–341CrossRefGoogle Scholar
Gulliksen, H. A least squares solution for paired comparisons with incomplete data. Psychometrika, 1956, 21, 125–134CrossRefGoogle Scholar
Krantz, D. H. Rational distance functions for multidimensional scaling. Journal of Mathematical Psychology, 1967, 4, 226–245CrossRefGoogle Scholar
Luce, R. D. Individual choice behavior, 1959, New York: WileyGoogle Scholar
Luce, R. D. A choice theory analysis of similarity judgments. Psychometrika, 1961, 26, 151–163CrossRefGoogle Scholar
Luce, R. D. and Suppes, P. Preference, utility, and subjective probability. In Luce, R. D., Bush, R. R., and Galanter, E. (Eds.), Handbook of mathematical psychology. Vol. III, 1965, New York: WileyGoogle Scholar
Mosteller, F. Remarks on the method of paired comparisons: III. A test of significance for paired comparisons when equal standard deviations and equal correlations are assumed. Psychometrika, 1951, 16, 207–218CrossRefGoogle Scholar
Mosteller, F. The mystery of the missing corpus. Psychometrika, 1958, 23, 279–289CrossRefGoogle Scholar
Noether, G. Remarks about a paired comparison model. Psychometrika, 1960, 25, 357–367CrossRefGoogle Scholar
Pfanzagl, J. Theory of measurement, 1968, New York: WileyGoogle Scholar
Popper, K. The logic of scientific discovery, 1959, New York: Basic BooksGoogle Scholar
Schönemann, P. H. On metric multidimensional unfolding. Psychometrika, 1970, 35, 349–366 (a)CrossRefGoogle Scholar
Schönemann, P. H. A note on Gulliksen's (1956) least squares solution for incomplete data. British Journal of Mathematical and Statistical Psychology, 1970, 23, 69–71 (b)CrossRefGoogle Scholar
Suppes, P. an Zinnes, J. L. Basic measurement theory. In Luce, R. D., Bush, R. R., and Galanter, E. (Eds.), Handbook of mathematical psychology. Vol. I., 1963, New York: WileyGoogle Scholar
Thurstone, L. L. A law of comparative judgment. Psychological Review, 1927, 34, 273–286CrossRefGoogle Scholar
Thurstone, L. L. Multiple factor analysis, 1948, Chicago: University of Chicago PressGoogle Scholar