Constrained Multidimensional Scaling in N Spaces | Psychometrika | Cambridge Core (original) (raw)

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.

References

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

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