Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-02-11T09:36:32.284Z Has data issue: false hasContentIssue false
  • English
  • Français

Constrained Multidimensional Scaling in N Spaces

Published online by Cambridge University Press:  01 January 2025

Bruce Bloxom
Bruce Bloxom*
Affiliation:
Vanderbilt University
*
Requests for reprints should be sent to Bruce Bloxom, Department of Psychology, Vanderbilt University, Nashville, Tennessee 37240.
Get access Rights & Permissions [Opens in a new window]

Abstract

A gradient method is used to obtain least squares estimates of parameters of the m-dimensional euclidean model simultaneously in N spaces, given the observation of all pairwise distances of n stimuli for each space. The procedure can estimate an additive constant as well as stimulus projections and the metric of the reference axes of the configuration in each space. Each parameter in the model can be fixed to equal some a priori value, constrained to be equal to any other parameter, or free to take on any value in the parameter space. Two applications of the procedure are described.

Keywords

individual differences in multidimensional scalingleast squares estimation
Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 3 , September 1978 , pp. 397 - 408
Copyright
Copyright © 1978 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.)

References

Reference Notes

Carroll, J. D., Green, P. E., & Carmone, F. J. CANDELINC: A new method for multidimensional analysis with constrained solutions. Paper presented at the meeting of the International Congress of Psychology, Paris, France, July 1976.Google Scholar
Carroll, J. D., & Prezansky, S. MULTILINC: Multi-way CANDELINC. Paper presented at the meeting of the American Psychological Association, San Francisco, August 1977.Google Scholar
Gruvaeus, G. T., Jöreskog, K. G. A computer program for minimizing a function of several variables, 1970, Princeton, N. J.: Educational Testing Service.Google Scholar
Noma, E., &Johnson, J. Constraining nonmetric multidimensional scaling configurations, 1977, Ann Arbor: The University of Michigan, Human Performance Center.Google Scholar

References

Abelson, R. P. A technique and a model of multidimensional attitude scaling. Public Opinion Quarterly, 1954, 18, 405–418.CrossRefGoogle Scholar
Bentler, P. M., & Weeks, D. G. Restricted multidimensional scaling models. Journal of Mathematical Psychology, 1978, 17, 138–151.CrossRefGoogle Scholar
Carroll, J. D., & Chang, J. J. Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition. Psychometrika, 1970, 35, 283–319.CrossRefGoogle Scholar
Cooper, L. G. A new solution to the additive constant problem in metric multidimensional scaling. Psychometrika, 1972, 37, 311–322.CrossRefGoogle Scholar
Horan, C. B. Multidimensional scaling: Combining observations when individuals have different perceptual structures. Psychometrika, 1969, 34, 139–165.CrossRefGoogle Scholar
Jöreskog, K. G. A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 1969, 34, 183–202.CrossRefGoogle Scholar
Krane, W. R. Least squares estimation of individual differences in multidimensional scaling. British Journal of Mathematical and Statistical Psychology, 1978, (in press).CrossRefGoogle Scholar
McGee, V. E. Multidimensional scaling of N sets of similarity measures: A nonmetric individual differences approach. Multivariate Behavioral Research, 1968, 3, 233–248.CrossRefGoogle Scholar
Schöneman, P. H. An algebraic solution for a class of subjective metrics models. Psychometrika, 1972, 37, 441–451.CrossRefGoogle Scholar
Seitz, V. R. Multidimensional scaling of dimensional preferences: A methodological study. Child Development, 1971, 42, 1701–1720.CrossRefGoogle ScholarPubMed
Torgerson, W. S. Theory and methods of scaling, 1958, New York: John Wiley & Sons.Google Scholar
Tucker, L. R. Relations between multidimensional scaling and three-mode factor analysis. Psychometrika, 1972, 37, 3–27.CrossRefGoogle Scholar
Zinnes, J. L., & Wolff, R. P. Single and multidimensional same-different judgements. Journal of Mathematical Psychology, 1977, 16, 30–50.CrossRefGoogle Scholar