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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.
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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

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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

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