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A Direct Approach to Individual differences Scaling using Increasingly Complex Transformations

Published online by Cambridge University Press:  01 January 2025

James C. Lingoes  and
Ingwer Borg
James C. Lingoes*
Affiliation:
The University of Michigan
Ingwer Borg
Affiliation:
Rheinisch-Westfälische Technische Hochschule
*
Requests for reprints should be sent to James C. Lingoes, The University of Michigan, 1005 North University Building, Ann Arbor, Michigan 48109.
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Abstract

A family of models for the representation and assessment of individual differences for multivariate data is embodied in a hierarchically organized and sequentially applied procedure called PINDIS. The two principal models used for directly fitting individual configurations to some common or hypothesized space are the dimensional salience and perspective models. By systematically increasing the complexity of transformations one can better determine the validities of the various models and assess the patterns and commonalities of individual differences. PINDIS sheds some new light on the interpretability and general applicability of the dimension weighting approach implemented by the commonly used INDSCAL procedure.

Keywords

individual differences scalingprocrustean transformationsmatrix fittingconfiguration similarity

Information

Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 4 , December 1978 , pp. 491 - 519
Copyright
Copyright © 1978 The Psychometric Society

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References

Reference Notes

Bloxom, B. Individual differences in multidimensional scaling, 1968, Princeton, N. J.: Educational Testing Service.CrossRefGoogle Scholar
Borg, I. & Lingoes, J. C. What weight should weights have in the analysis of individual differences? (Michigan Mathematical Psychology Program Tech. Rep. 76-5). Ann Arbor, Mich.: 1976.Google Scholar
Carroll, J. D. & Chang, J. J. IDIOSCAL (Individual Differences In Orientation Scaling): A generalization of INDSCAL allowing idiosyncratic reference systems as well as an analytic approximation to INDSCAL. Paper presented at the Psychometric Society meetings, Princeton, N. J.: 1972.Google Scholar
Harshman, R. A. PARAFAC2: Mathematical and technical notes (UCLA Working Papers in Phonetics 22). L. A., Calif.: 1972.Google Scholar
Helm, C. E. A multidimensional ratio scaling analysis of color relations (Technical Report of Princeton University and the Educational Testing Service). Princeton, N. J.: 1959.Google Scholar
Lingoes, J. C. A neighborhood preserving transformation for fitting configurations. Paper presented at The U. S.-Japan Conference on Multidimensional Scaling, La Jolla, Calif.: 1975.Google Scholar
Schönemann, P. H., Carter, F. S., & James, W. L. Contributions to subjective metrics scaling: I. COSPA, a fast method for fitting and testing Horan's model, and an empirical comparison with INDSCAL and ALSCAL, 1976, W. Lafayette, Ind.: Purdue University.Google Scholar
Feger, H. Personal communication.Google Scholar

References

ten Berge, Jos M. F. Orthogonal procrustes rotation for two or more matrices. Psychometrika, 1977, 42, 267–276.CrossRefGoogle Scholar
Borg, I. Geometric representation of individual differences. In Lingoes, J. C. (Eds.), Geometric representations of relational data, 1977, Ann Arbor, Mich.: Mathesis Press.Google Scholar
Borg, I. Ein Vergleich verschiedener Studien zur Lebensqualität. Zeitschrift für Sozialpsychologie, 1978 (in press).Google Scholar
Borg, I. & Lingoes, J. C. Ein direkter Transformationsansatz der multidimensionalen Analyse dreimodaler Datenmatrizen: Theorie und Anwendungen. Zeitschrift für Sozialpsychologie, 1977, 8, 98–114.Google 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, 283–320.CrossRefGoogle Scholar
Carroll, J. D. & Wish, M. Models and methods for three-way multidimensional scaling. In Krantz, D. H., Atkinson, R. C., Luce, D. R. & Suppes, P. (Eds.), Contemporary developments in mathematical psychology (Vol. 2), 1974, San Francisco, Calif.: W. H. Freeman.Google Scholar
Feger, H. Die Erfassung individueller Einstellungsstrukturen. Zeitschrift für Sozialpsychologie, 1974, 5, 57–105.Google Scholar
Feger, H. Längsschnittliche Erfassung intraindividueller Unterschiede bei Einstellungsstrukturen. In Lehr, U. M. & Weinert, F. E. (Eds.), Entwicklung und Persönlichkeit, 1975, Stuttgart, W. Germany: Kohlhammer.Google Scholar
Fischer, G. H. & Roppert, J. Ein Verfahren der Transformationsanalyse faktoren-analytischer Ergebnisse. In Roppert, J. & Fischer, G. H. (Eds.), Lineare Strukturen in Mathematik und Statistik, 1965, Wien, Austria: Physika Verlag.Google Scholar
Gower, J. C. Generalized procrustean analysis. Psychometrika, 1975, 40, 33–51.CrossRefGoogle Scholar
Guttman, L. A new approach to factor analysis: The radex. In Lazarsfeld, P. F. (Eds.), Mathematical thinking in the social sciences, 1954, Glencoe, Ill.: The Free Press.Google Scholar
Harman, H. H. Modern factor analysis, 1967, Chicago, Ill.: University of Chicago Press.Google Scholar
Helm, C. E. & Tucker, L. R. Individual differences in the structure of color-perception. American Journal of Psychology, 1962, 75, 437–444.CrossRefGoogle ScholarPubMed
Helm, C. E. Multidimensional ratio scaling analysis of perceived color relations. Journal of the Optical Society of America, 1964, 54, 256–262.CrossRefGoogle ScholarPubMed
Horan, C. B. Multidimensional scaling: Combining observations when individuals have different perceptual structures. Psychometrika, 1969, 34, 139–165.CrossRefGoogle Scholar
Kristof, W. & Wingersky, B. Generalization of the orthogonal procrustes rotation procedure for more than two matrices. Proceedings of the 79th Annual Convention of the American Psychological Association, 1971, 89–90.Google Scholar
Levy, S. Use of the mapping sentence for coordinating theory and research: A cross-cultural example. Quality and Quantity, 1976, 10, 117–125.CrossRefGoogle Scholar
Levy, S. & Guttman, L. On the multivariate structure of well-being. Social Indicators Research, 1975, 2, 361–388.CrossRefGoogle Scholar
Lingoes, J. C. The Guttman-Lingoes nonmetric program series, 1973, Ann Arbor, Mich.: Mathesis Press.Google Scholar
Lingoes, J. C. Progressively complex linear transformations for finding geometric similarities among data structures. In Hudson, H. (Eds.), Classifying cultural and social data, 1978, San Francisco, Calif.: Jossey-Bass.Google Scholar
Lingoes, J. C. & Schönemann, P. H. Alternative measures of fit for the Schönemann-Carroll matrix fitting algorithm. Psychometrika, 1974, 39, 423–427.CrossRefGoogle Scholar
Lingoes, J. C. & Borg, I. Procrustean individual differences scaling: PINDIS. Journal of Marketing Research, 1976, 13, 406–407.Google Scholar
Lingoes, J. C. & Borg, I. Procrustean individual differences scaling: PINDIS. Journal of Marketing Research, Sozialpsychologie, 1977, 8, 210–217.Google Scholar
Lissitz, R. W. Schönemann, P. H., & Lingoes, J. C. A solution to the weighted procrustes problem in which the transformation is in agreement with the loss function. Psychometrika, 1976, 41, 547–550.CrossRefGoogle Scholar
MacCallum, R. C. A comparison of two individual differences models for multidimensional scaling: Carroll and Chang's INDSCAL and Tucker's three-mode factor analysis, 1974, Urbana, Illinois: University of Illinois.Google Scholar
MacCallum, R. C. Effects of conditionality on INDSCAL and ALSCAL weights. Psychometrika, 1977, 42, 297–305.CrossRefGoogle Scholar
Schönemann, P. H. A generalized solution of the orthogonal procrustes problem. Psychometrika, 1966, 31, 1–10.CrossRefGoogle Scholar
Schönemann, P. H. & Carroll, R. M. Fitting one matrix to another under choice of a central dilation and a rigid motion. Psychometrika, 1970, 35, 245–255.CrossRefGoogle Scholar
Schönemann, P. H. An algebraic solution for a class of subjective metrics models. Psychometrika, 1972, 37, 441–451.CrossRefGoogle Scholar
Takane, Y., Young, F., & de Leeuw, J. Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features. Psychometrika, 1977, 42, 7–67.CrossRefGoogle Scholar
Torgerson, W. S. Theory and methods of scaling, 1958, New York, N. Y.: Wiley.Google Scholar
Tucker, L. R. Relations between multidimensional scaling and three-mode factor analysis. Psychometrika, 1972, 37, 333–367.CrossRefGoogle Scholar
Wish, M. & Carroll, J. D. Applications of individual differences scaling to studies of human perception and judgement. In Carterette, E. C. & Friedman, M. P. (Eds.), Handbook of perception (Vol. 2), 1974, New York, N. Y.: Academic Press.Google Scholar