DOI: 10.1007/bf02310791. Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition

Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition

10.1007/bf02310791

Crossref journal-article

Cambridge University Press (CUP)

Psychometrika (56)

Abstract

An individual differences model for multidimensional scaling is outlined in which individuals are assumed differentially to weight the several dimensions of a common “psychological space”. A corresponding method of analyzing similarities data is proposed, involving a generalization of “Eckart-Young analysis” to decomposition of three-way (or higher-way) tables. In the present case this decomposition is applied to a derived three-way table of scalar products between stimuli for individuals. This analysis yields a stimulus by dimensions coordinate matrix and a subjects by dimensions matrix of weights. This method is illustrated with data on auditory stimuli and on perception of nations.

Bibliography

Carroll, J. D., & Chang, J.-J. (1970). Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of âEckart-Youngâ Decomposition. Psychometrika, 35(3), 283â319.

Authors 2

J. Douglas Carroll (first)
Jih-Jie Chang (additional)

References 28 Referenced 3,470

{'volume-title': 'Multidimensional Scaling: Theory and Applications in the Behavioral Sciences', 'year': '1971', 'author': 'Carroll', 'key': 'S003331230003951X_CR4'} / Multidimensional Scaling: Theory and Applications in the Behavioral Sciences by Carroll (1971)
Green, P. E. & Morris, T. W. Individual difference models in multidimensional scaling: an empirical comparison. Unpublished manuscript, University of Pennsylvania, 1969.
10.1007/BF02289341
{'volume-title': 'Theory and methods of scaling', 'year': '1958', 'author': 'Torgerson', 'key': 'S003331230003951X_CR19'} / Theory and methods of scaling by Torgerson (1958)
10.1207/s15327906mbr0302_7
Wish, M. Individual differences in perceived similarity and friendship of nations. Submitted to Journal of Personality and Social Psychology. (b).
{'volume-title': 'Attitude research reaches new heights', 'year': '1971', 'author': 'Green', 'key': 'S003331230003951X_CR9'} / Attitude research reaches new heights by Green (1971)
10.1007/BF02289464
Rao, V. R. The salience of price in the perception and evaluation of product quality: A multidimensional measurement model and experimental test. Unpublished doctoral dissertation, University of Pennsylvania, 1970.
10.1007/BF02290154 / Psychometrika / The ‘idealized individual’ interpretation of individual differences in multidimensional scaling by Cliff (1968)
{'key': 'S003331230003951X_CR14', 'first-page': '335', 'volume-title': 'Multivariate analysis', 'author': 'Lyttkens', 'year': '1966'} / Multivariate analysis by Lyttkens (1966)
Carroll, J. D. & Chang, J. J. A “quasi-nonmetric” version of INDSCAL, a procedure for individual differences multidimensional scaling. Paper presented at the meeting of the Psychometric Society, Stanford, March, 1970.
10.1007/BF02288367
{'volume-title': 'Attitude research reaches new heights', 'year': '1971', 'author': 'Wish', 'key': 'S003331230003951X_CR25'} / Attitude research reaches new heights by Wish (1971)
{'volume-title': 'Multidimensional scaling: Theory and applications in the behavioral sciences', 'year': '1971', 'author': 'Wish', 'key': 'S003331230003951X_CR26'} / Multidimensional scaling: Theory and applications in the behavioral sciences by Wish (1971)
Kruskal, J. B. How to use MDSCAL, a program to do multidimensional scaling and multidimensional unfolding. Unpublished report, Bell Telephone Laboratories, 1968.
10.1007/BF02289454
10.1016/0022-2496(66)90017-4 / Journal of Mathematical Psychology / Metric structures in ordinal data by Shepard (1966)
{'key': 'S003331230003951X_CR28', 'first-page': '498', 'article-title': 'TORSCA, a FORTRAN IV program for Shepard-Kruskal multidimensional scaling analysis', 'volume': '12', 'author': 'Young', 'year': '1967', 'journal-title': 'Behavioral Science'} / Behavioral Science / TORSCA, a FORTRAN IV program for Shepard-Kruskal multidimensional scaling analysis by Young (1967)
{'key': 'S003331230003951X_CR20', 'first-page': '109', 'volume-title': 'Contributions to mathematical psychology', 'author': 'Tucker', 'year': '1964'} / Contributions to mathematical psychology by Tucker (1964)
10.1121/1.1974822
{'volume-title': 'Multidimensional scaling of individual differences in perception and judgment', 'year': '1970', 'author': 'Carroll', 'key': 'S003331230003951X_CR5'} / Multidimensional scaling of individual differences in perception and judgment by Carroll (1970)
Green, P. E. & Rao, V. R. Dissimilarities data-disaggregate analysis. Unpublished manuscript, University of Pennsylvania (Chapter 3 of monograph, in preparation, entitled: User's guide to multidimensional scaling: A comparison of approaches and algorithms), 1970.
10.1002/j.2333-8504.1968.tb00567.x
{'key': 'S003331230003951X_CR23', 'volume-title': 'General Systems', 'volume': '15', 'author': 'Wish', 'year': '1970'} / General Systems by Wish (1970)
10.1007/BF02289557
{'key': 'S003331230003951X_CR27', 'first-page': '391', 'volume-title': 'Multivariate analysis', 'author': 'Wold', 'year': '1966'} / Multivariate analysis by Wold (1966)
Bricker, P. D. , Pruzansky, S. , & McDermott, B. J. Recovering spatial information from subjects' clusterings of auditory stimuli. Paper presented at the meeting of The Psychonomic Society, St. Louis, October–November 1968.

Dates

Type	When
Created	19 years, 6 months ago (Feb. 14, 2006, 11:53 p.m.)
Deposited	4 months, 3 weeks ago (April 2, 2025, 11:36 p.m.)
Indexed	35 minutes ago (Aug. 27, 2025, 2:53 p.m.)
Issued	54 years, 11 months ago (Sept. 1, 1970)
Published	54 years, 11 months ago (Sept. 1, 1970)
Published Online	7 months, 3 weeks ago (Jan. 1, 2025)
Published Print	54 years, 11 months ago (Sept. 1, 1970)

Funders 0

None

BibTeX

@article{Carroll_1970, title={Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition}, volume={35}, ISSN={1860-0980}, url={http://dx.doi.org/10.1007/bf02310791}, DOI={10.1007/bf02310791}, number={3}, journal={Psychometrika}, publisher={Cambridge University Press (CUP)}, author={Carroll, J. Douglas and Chang, Jih-Jie}, year={1970}, month=sep, pages={283–319} }

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