Skip to main content
Log in

A procedure for ordering object pairs consistent with the multidimensional unfolding model

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

A procedure for ordering object (stimulus) pairs based on individual preference ratings is described. The basic assumption is that individual responses are consistent with a nonmetric multidimensional unfolding model. The method requires data where a numerical response is independently generated for each individual-object pair. In conjunction with a nonmetric multidimensional scaling procedure, it provides a vehicle for recovering meaningful object configurations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Reference note

  • Rabinowitz, G. B.Spatial models of electoral choice: An empirical analysis (Working papers in methodology No. 7). Chapel Hill, North Carolina: Institute for Research in Social Science, 1973.

    Google Scholar 

References

  • Campbell, A., Converse, P. E., Miller, W. E., & Stokes, D. E.The American Voter. New York: Wiley, 1960.

    Google Scholar 

  • Carroll, J. D. Individual differences and multidimensional scaling. In R. N. Shepard, A. K. Romney & S. B. Nerlove (Eds.),Multi-dimensional scaling. Volume 1, Theory. New York: Seminar Press, 1972.

    Google Scholar 

  • Converse, P. E. The nature of belief systems in mass publics. In D. E. Apter (Ed.),Ideology and discontent. New York: Free Press, 1964.

    Google Scholar 

  • Converse, P. E., Miller, W. E., Rusk, J. G., & Wolfe, A. C. Continuity and change in American politics: Parties and issues in the 1968 election.American Political Science Review, 1969,63, 1083–1105.

    Google Scholar 

  • Coombs, C. H. Psychological scaling without a unit of measurement.Psychological Review, 1950,57, 145–158.

    Google Scholar 

  • Coombs, C. H.A theory of data. New York: Wiley, 1964.

    Google Scholar 

  • Davidson, J. A. A geometrical analysis of the unfolding model: non-degenerate solutions.Psychometrika, 1972,37, 193–216.

    Google Scholar 

  • Davidson, J. A. A geometrical analysis of the unfolding model: general solutions.Psychometrika, 1973,38, 305–336.

    Google Scholar 

  • Davis, O. A. & Hinich, M. A mathematical model of policy formation in a democratic society. In J. Bernd (Ed.),Mathematical applications in political science II. Dallas: Southern Methodist University Press, 1966.

    Google Scholar 

  • Davis, O. A., Hinich M., & Ordeshook, P. An expository development of a mathematical model of the electoral process.American Political Science Review, 1970,64, 426–448.

    Google Scholar 

  • Downs, A.An economic theory of democracy. New York: Harper and Row, 1957.

    Google Scholar 

  • Gleason, T.Multidimensional scaling of sociometric data. Ann Arbor: Institute for Social Research, 1969.

    Google Scholar 

  • Guttman, L. A general nonmetric technique for finding the smallest coordinate space for a configuration of points.Psychometrika, 1968,33, 469–506.

    Google Scholar 

  • Hays, W. L. & Bennett, J. F. Multidimensional unfolding: determining configuration from complete rank order preference data.Psychometrika, 1961,26, 221–238.

    Google Scholar 

  • Jones, B. D. Some considerations in the use of nonmetric multidimensional scaling.Political Methodology, 1974,1, 1–30.

    Google Scholar 

  • Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis.Psychometrika, 1964,29, 1–27 (a).

    Google Scholar 

  • Kruskal, J. B. Nonmetric multidimensional scaling: a numerical method.Psychometrika, 1964,29, 28–42 (b).

    Google Scholar 

  • Kruskal, J. B. & Carroll, J. D. Geometric models and badness of fit functions. In P. R. Krishnaiah (Ed.),International symposium of multivariate analysis, Dayton, Ohio, 1968. New York: Academic Press, 1969.

    Google Scholar 

  • Mauser, G. A. A structural approach to predicting patterns of electoral substitution. In R. N. Shepard, A. K. Romney, and S. B. Nerlove (Eds.),Multidimensional scaling. Volume 2, Applications. New York: Seminar Press, 1972.

    Google Scholar 

  • Mueller, J. E. Presidential popularity from Truman to Johnson.American Political Science Review, 1970,66, 979–995.

    Google Scholar 

  • Royden, H. L.Real analysis. London: Macmillan, 1968.

    Google Scholar 

  • Schoneman, P. H. On metric multidimensional unfolding.Psychometrika, 1970,35, 349–366.

    Google Scholar 

  • Stokes, D. E. Spatial models of party competition.American Political Science Review, 1963,57, 368–377.

    Google Scholar 

  • Weisberg, H. F. & Rusk, J. G. Dimensions of candidate evaluations.American Political Science Review, 1970,64, 1167–1185.

    Google Scholar 

  • Young, F. W. TORSCA—A FORTRAN IV program for nonmetric multidimensional scaling.Behavioral Science, 1968,13, 343–344.

    Google Scholar 

  • Young F. W. Nonmetric multidimensional scaling: Recovery of metric information.Psychometrika, 1970,35, 455–473.

    Google Scholar 

  • Zinnes, J. L. & Griggs, R. A. Probabilistic, multidimensional unfolding analysis.Psychometrika, 1974,39, 327–350.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The author wishes to thank Jack Hoadley, Larry Mayer, Sheldon Newhouse, Stuart Rabinowitz, Forrest Young, and three anonymous reviewers for their useful suggestions.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rabinowitz, G. A procedure for ordering object pairs consistent with the multidimensional unfolding model. Psychometrika 41, 349–373 (1976). https://doi.org/10.1007/BF02293560

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02293560

Key words

Navigation