Skip to main content
Log in

A simple procedure for finding a composite of several multidimensional scaling solutions

  • Published:
Journal of the Academy of Marketing Science Aims and scope Submit manuscript

Abstract

One of the better known procedures for finding a representative composite of several different MDS solutions is based on Carroll’s generalized canonical correlation model (Carroll 1968). However, the program for implementing the fitting of this model has not received wide distribution. The present paper provides a simple computational method for implementing Carroll’s approach and shows its relationship to ordinary principal components analysis. In addition, we provide an algorithm for computing the parameters of Carroll’xs model in the presence of missing data. Each method is illustrated with data sets drawn from a marketing research study.

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.

Similar content being viewed by others

References

  • Carroll, J. Douglas. 1968. “Generalization of Canonical Correlation Analysis to Three or More Sets of Variables.”Proceedings of the American Psychological Association: 227 8.

  • —, Paul E. Green, and Catherine M. Schaffer. 1986. “Interpoint Distance Comparisons in Correspondence Analysis.”Journal of Marketing Research 23 (August): 271–80.

    Article  Google Scholar 

  • Cliff, Norman. 1966. “Orthogonal Rotation to Congruence.”Psychometrika 31:33–42.

    Article  Google Scholar 

  • Deming, W. E. and F. F. Stephan. 1940. “On a Least Squares Adjustment of a Sampled Frequency Table when the Expected Marginal Totals are Known”.Annals of the Mathematical Statistics 11:427–44.

    Google Scholar 

  • Eckart, C. and Gale Young. 1936. “The Approximation of One Matrix by Another of Lower Rank”Psychometrika 1: 211–18.

    Article  Google Scholar 

  • Gower, John C. 1975. “Generalized Procrustes Analysis”.Psychometrika 40 (March): 33–51.

    Article  Google Scholar 

  • Green, Paul E. with J. Douglas Carroll 1976.Mathematical Tools for Applied Multivariate Analysis. New York: Academic Press 286–92.

    Google Scholar 

  • — with contributions by J. D. Carroll. 1978.Analying Multivariate Data. Hinsdale, IL: The Dryden Press.

    Google Scholar 

  • —, and Yoram Wind. 1973.Multiatribute Decisions in Marketing A Measurement Approach. Hinsdale, IL: Dryden Press.

    Google Scholar 

  • Horst, Paul. 1961. “Relations Among Two Sets of Measures”.Psychometrika 26: 129–49.

    Article  Google Scholar 

  • Hotelling, Harold. 1936. “Relations Between Two Sets of Variates.”Biometrika 28: 321–77.

    Google Scholar 

  • Kettenring, John R. 1971. “Canonical Analysis of Several Sets of Variables”.Biometrika 58: 433–51.

    Article  Google Scholar 

  • Kristof, W. and B. Vingersky. 1971. “Generlization of the Orthogonal Procrustes Rotation Procedure to Two or More Matrices.”Proceedings of the 79th Annual Convention of the American Psychological Association: 81–90.

  • Moinpour, Reza, J. M. McCullough, and Douglas MacLachlan. 1976. “Time Changes in Perception: A Longitudinal Application of Multidimensional Scaling”.Journal of Marketing Research 13 (August): 245–53.

    Article  Google Scholar 

  • Neidell, Lester A. 1972. “Procedures for Obtaining Similarities Data”,Journal of Marketing Research 9 (August): 335–7.

    Article  Google Scholar 

  • Ritchie, J. R. Brent. 1974. “An Exploratory Analysis of Nature and Extent of Individual Differences in Perception”Journal of Marketing Research 11 (February): 41–9.

    Article  Google Scholar 

  • Schönemann, Peter H. and Robert M. Carroll. 1970. “Fitting One Matrix to Another Under Choice of a Central Dilation and Rigid Motion”.Psychometrika 35: 245–56.

    Article  Google Scholar 

  • Summers, John O. and David B. MacKay. 1976. “On the Validity and Reliability of Direct Similarity Judgments.”Journal of Marketing Research 13 (August): 289–95.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Green, P.E., Carroll, J.D. A simple procedure for finding a composite of several multidimensional scaling solutions. JAMS 16, 25–35 (1988). https://doi.org/10.1007/BF02723323

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02723323

Keywords

Navigation