Skip to main content
Log in

A direct approach to individual differences scaling using increasingly complex transformations

  • Published:
Psychometrika Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Reference notes

  • Bloxom, B.Individual differences in multidimensional scaling (ETS RM 68-45). Princeton, N. J.: Educational Testing Service, 1968.

    Google 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.

  • 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.

  • Harshman, R. A.PARAFAC2: Mathematical and technical notes (UCLA Working Papers in Phonetics 22). L. A., Calif.: 1972.

  • 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.

  • 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.

  • 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 (Krannert Graduate School of Management 587). W. Lafayette, Ind.: Purdue University, 1976.

    Google Scholar 

  • Feger, H. Personal communication.

References

  • Berge, Jos M. F. ten. Orthogonal procrustes rotation for two or more matrices.Psychometrika, 1977,42, 267–276.

    Google Scholar 

  • Borg, I. Geometric representation of individual differences. In J. C. Lingoes (Ed.).Geometric representations of relational data. Ann Arbor, Mich.: Mathesis Press, 1977.

    Google Scholar 

  • Borg, I. Ein Vergleich verschiedener Studien zur Lebensqualität.Zeitschrift für Sozialpsychologie, 1978 (in press).

  • 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.

    Google Scholar 

  • Carroll, J. D. & Wish, M. Models and methods for three-way multidimensional scaling. In D. H. Krantz, R. C. Atkinson, D. R. Luce, & P. Suppes (Eds.).Contemporary developments in mathematical psychology (Vol. 2). San Francisco, Calif.: W. H. Freeman, 1974.

    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 U. M. Lehr & F. E. Weinert (Eds.).Entwicklung und Persönlichkeit. Stuttgart, W. Germany: Kohlhammer, 1975.

    Google Scholar 

  • Fischer, G. H. & Roppert, J. Ein Verfahren der Transformationsanalyse faktoren-analytischer Ergebnisse. In J. Roppert & G. H. Fischer.Lineare Strukturen in Mathematik und Statistik. Wien, Austria: Physika Verlag, 1965.

    Google Scholar 

  • Gower, J. C. Generalized procrustean analysis.Psychometrika, 1975,40, 33–51.

    Google Scholar 

  • Guttman, L. A new approach to factor analysis: The radex. In P. F. Lazarsfeld (Ed.).Mathematical thinking in the social sciences. Glencoe, Ill.: The Free Press, 1954.

    Google Scholar 

  • Harman, H. H.Modern factor analysis. Chicago, Ill.: University of Chicago Press, 1967.

    Google Scholar 

  • Helm, C. E. & Tucker, L. R. Individual differences in the structure of color-perception.American Journal of Psychology, 1962,75, 437–444.

    Google Scholar 

  • Helm, C. E. Multidimensional ratio scaling analysis of perceived color relations.Journal of the Optical Society of America, 1964,54, 256–262.

    Google Scholar 

  • Horan, C. B. Multidimensional scaling: Combining observations when individuals have different perceptual structures.Psychometrika, 1969,34, 139–165.

    Google 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.

  • Levy, S. Use of the mapping sentence for coordinating theory and research: A cross-cultural example.Quality and Quantity, 1976,10, 117–125.

    Google Scholar 

  • Levy, S. & Guttman, L. On the multivariate structure of well-being.Social Indicators Research, 1975,2, 361–388.

    Google Scholar 

  • Lingoes, J. C.The Guttman-Lingoes nonmetric program series. Ann Arbor, Mich.: Mathesis Press, 1973.

    Google Scholar 

  • Lingoes, J. C. Progressively complex linear transformations for finding geometric similarities among data structures. In H. Hudson (Ed.).Classifying cultural and social data. San Francisco, Calif.: Jossey-Bass, 1978 (in press).

    Google Scholar 

  • Lingoes, J. C. & Schönemann, P. H. Alternative measures of fit for the Schönemann-Carroll matrix fitting algorithm.Psychometrika, 1974,39, 423–427.

    Google 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.

    Google 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. Unpublished doctoral dissertation, University of Illinois, Urbana, Illinois, 1974.

    Google Scholar 

  • MacCallum, R. C. Effects of conditionality on INDSCAL and ALSCAL weights.Psychometrika, 1977,42, 297–305.

    Google Scholar 

  • Schönemann, P. H. A generalized solution of the orthogonal procrustes problem.Psychometrika, 1966,31, 1–10.

    Google 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.

    Google Scholar 

  • Schönemann, P. H. An algebraic solution for a class of subjective metrics models.Psychometrika, 1972,37, 441–451.

    Google 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.

    Google Scholar 

  • Torgerson, W. S.Theory and methods of scaling. New York, N. Y.: Wiley, 1958.

    Google Scholar 

  • Tucker, L. R. Relations between multidimensional scaling and three-mode factor analysis.Psychometrika, 1972,37, 333–367.

    Google Scholar 

  • Wish, M. & Carroll, J. D. Applications of individual differences scaling to studies of human perception and judgement. In E. C. Carterette & M. P. Friedman (Eds.),Handbook of perception (Vol. 2). New York, N. Y.: Academic Press, 1974.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lingoes, J.C., Borg, I. A direct approach to individual differences scaling using increasingly complex transformations. Psychometrika 43, 491–519 (1978). https://doi.org/10.1007/BF02293810

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02293810

Key words

Navigation