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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
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.
Cliff, Norman. 1966. “Orthogonal Rotation to Congruence.”Psychometrika 31:33–42.
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.
Eckart, C. and Gale Young. 1936. “The Approximation of One Matrix by Another of Lower Rank”Psychometrika 1: 211–18.
Gower, John C. 1975. “Generalized Procrustes Analysis”.Psychometrika 40 (March): 33–51.
Green, Paul E. with J. Douglas Carroll 1976.Mathematical Tools for Applied Multivariate Analysis. New York: Academic Press 286–92.
— with contributions by J. D. Carroll. 1978.Analying Multivariate Data. Hinsdale, IL: The Dryden Press.
—, and Yoram Wind. 1973.Multiatribute Decisions in Marketing A Measurement Approach. Hinsdale, IL: Dryden Press.
Horst, Paul. 1961. “Relations Among Two Sets of Measures”.Psychometrika 26: 129–49.
Hotelling, Harold. 1936. “Relations Between Two Sets of Variates.”Biometrika 28: 321–77.
Kettenring, John R. 1971. “Canonical Analysis of Several Sets of Variables”.Biometrika 58: 433–51.
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.
Neidell, Lester A. 1972. “Procedures for Obtaining Similarities Data”,Journal of Marketing Research 9 (August): 335–7.
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.
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.
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.
Author information
Authors and Affiliations
Rights 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
Issue Date:
DOI: https://doi.org/10.1007/BF02723323