Hostname: page-component-74656f9884-2dmjx Total loading time: 0 Render date: 2026-11-08T13:03:51.584Z Has data issue: false hasContentIssue false
  • English
  • Français

A Maximum Likelihood Method for Fitting the Wandering Vector Model

Published online by Cambridge University Press:  01 January 2025

Geert De Soete  and
J. D. Carroll
Geert De Soete*
Affiliation:
University of Ghent
J. D. Carroll*
Affiliation:
Bell Laboratories
*
Requests for reprints should be sent to either Geert De Soete, Department of Psychology, University of Ghent, Henri Dunantlaan 2, B-9000 Ghent, Belgium; or to J. Douglas Carroll, Bell Laboratories, Room 2C-553, 600 Mountain Avenue, Murray Hill, New Jersey 07974.
Requests for reprints should be sent to either Geert De Soete, Department of Psychology, University of Ghent, Henri Dunantlaan 2, B-9000 Ghent, Belgium; or to J. Douglas Carroll, Bell Laboratories, Room 2C-553, 600 Mountain Avenue, Murray Hill, New Jersey 07974.
Get access Rights & Permissions [Opens in a new window]

Abstract

After introducing some extensions of a recently proposed probabilistic vector model for representing paired comparisons choice data, an iterative procedure for obtaining maximum likelihood estimates of the model parameters is developed. The possibility of testing various hypotheses by means of likelihood ratio tests is discussed. Finally, the algorithm is applied to some existing data sets for illustrative purposes.

Keywords

preferencepaired comparisons datamaximum likelihood multidimensional scalingmethod of successive categories

Information

Type
Original Paper
Information
Psychometrika , Volume 48 , Issue 4 , December 1983 , pp. 553 - 566
Copyright
Copyright © 1983 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.)

Article purchase

Temporarily unavailable

Footnotes

The first author is “Aspirant” of the Belgian “Nationaal Fonds voor Wetenschappelijk Onderzoek.” Part of the research reported in this paper was done while the first author stayed at the L. L. Thurstone Psychometric Laboratory of the University of North Carolina at Chapel Hill supported by a CRB Fellowship of the Belgian American Educational Foundation, Inc. The authors wish to express their gratitude to Thomas S. Wallsten and Joseph B. Kruskal for helpful discussions.

References

Akaike, H. On entropy maximization principle. In Krishnaiah, P. R. (Eds.), Applications of statistics . Amsterdam: North-Holland. 1977, 27–41.Google Scholar
Amemiya, T. The maximum likelihood, the minimum chi-square and the nonlinear weighted least-squares method in the general qualitative response model. Journal of the American Statistical Association, 1976, 71, 247–251.CrossRefGoogle Scholar
Bechtel, G. G. Multidimensional preference scaling, The Hague: Mouton, 1976.CrossRefGoogle Scholar
Bock, R. D., & Jones, L. V. The measurement of prediction of judgment and choice, San Francisco: Holden-Day, 1968.Google Scholar
Carroll, J. D. Individual differences and multidimensional scaling. In Shepard, R. N., Romney, A. K., & Nerlove, S. B. (Eds.), Multidimensional scaling: Theory and Applications in the behavioral sciences (Vol. 1) . New York: Seminar Press. 1972, 105–155.Google Scholar
Carroll, J. D. Models and methods for multidimensional analysis of preferential choice (or other dominance) data. In Lantermann, E. D. & Feger, H. (Eds.), Similarity and choice . Bern: Huber. 1980, 234–289.Google Scholar
Coombs, C. H. A theory of data, New York: Wiley, 1964.Google Scholar
De Soete, G. On the relation between two generalized cases of Thurstone's Law of Comparative Judgment. Mathématiques et Sciences humaines, 1983, 21, 47–57.Google Scholar
Halff, H. M. Choice theories for differentially comparable alternatives. Journal of Mathematical Psychology, 1976, 14, 244–246.CrossRefGoogle Scholar
Heiser, W., & De Leeuw, J. Multidimensional mapping of preference data. Mathématiques et Sciences humaines, 1981, 19, 39–96.Google Scholar
Jennrich, R. I., & Moore, R. H. Maximum likelihood estimation by means of nonlinear least squares. Proceedings of the American Statistical Association—Statistical Computing Section, 1975, 57-65.Google Scholar
Jones, L. V., & Jeffrey, T. E. A quantitative analysis of expressed preferences for compensation plans. Journal of Applied Psychology, 1964, 48, 201–210.CrossRefGoogle Scholar
Kruskal, J. B. Factor analysis and principal components. I. Bilinear models. In Kruskal, W. H. & Tanur, J. M. (Eds.), International encyclopedia of statistics. (Vol. 1) . New York: The Free Press. 1978, 307–330.Google Scholar
McFadden, D. Quantal choice analysis: a survey. Annals of Economic and Social Measurement, 1976, 5, 363–390.Google Scholar
Ramsay, J. O. Maximum likelihood estimation in multidimensional scaling. Psychometrika, 1977, 42, 241–266.CrossRefGoogle Scholar
Ramsay, J. O. The joint analysis of direct ratings, pairwise preferences, and dissimilarities. Psychometrika, 1980, 45, 149–165.CrossRefGoogle Scholar
Roskam, E. E., & Lingoes, J. C. MINISSA-I: Fortran IV(G) program for the smallest space analysis of square symmetric matrices. Behavioral Science, 1970, 15, 204–205.Google Scholar
Scheffé, H. An analysis of variance for paired comparisons. Journal of the American Statistical Association, 1952, 47, 381–400.Google Scholar
Schönemann, P. H., & Tucker, L. R. A maximum likelihood solution for the method of successive intervals allowing for unequal stimulus dispersions. Psychometrika, 1967, 32, 403–417.CrossRefGoogle Scholar
Sjöberg, L. Successive intervals scaling of paired comparisons. Psychometrika, 1967, 32, 297–308.CrossRefGoogle ScholarPubMed
Sjöberg, L. Choice frequency and similarity. Scandinavian Journal of Psychology, 1977, 18, 103–115.CrossRefGoogle Scholar
Sjöberg, L., & Capozza, D. Preference and cognitive structure of Italian political parties. Italian Journal of Psychology, 1975, 2, 391–402.Google Scholar
Slater, P. The analysis of personal preferences. British Journal of Statistical Psychology, 1960, 13, 119–135.CrossRefGoogle Scholar
Takane, Y. A maximum likelihood method for nonmetric multidimensional scaling: I. The case in which all empirical orderings are independent—Theory. Japanese Psychological Research, 1978, 20, 7–17.CrossRefGoogle Scholar
Takane, Y. Maximum likelihood estimation in the generalized case of Thurstone's model of comparative judgement. Japanese Psychological Research, 1980, 22, 188–196.CrossRefGoogle Scholar
Takane, Y. Multidimensional successive categories scaling: a maximum likelihood method. Psychometrika, 1981, 46, 9–18.CrossRefGoogle Scholar
Takane, Y., & Carroll, J. D. Nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities. Psychometrika, 1981, 46, 389–405.CrossRefGoogle Scholar
Thurstone, L. L. A law of comparative judgment. Psychological Review, 1927, 34, 273–286.CrossRefGoogle Scholar
Tucker, L. R. Intra-individual and inter-individual multidimensionality. In Gulliksen, H. & Messick, S. (Eds.), Psychological scaling: theory and applications . New York: Wiley. 1960, 155–167.Google Scholar
Wilks, S. S. Mathematical Statistics, New York: Wiley, 1962.Google Scholar