Abstract
This paper explores some of the problems associated with traditional canonical correlation. A response surface methodology is developed to examine the stability of the derived linear functions, where one wishes to investigate how much the coefficients can change and still be in an ɛ-neighborhood of the globally optimum canonical correlation value. In addition, a discrete (or constrained) canonical correlation method is formulated where the derived coefficients of these linear functions are constrained to be in some small set, e.g., {1, 0, −1}, to aid in the interpretation of the results. An example concerning the psychographic responses of Wharton MBA students of the University of Pennsylvania regarding driving preferences and life-style considerations is provided.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Reference notes
Hausman, R., Constrained multivariate analysis,Unpublished Memorandum, Bell Laboratories, Holmdel, N.J., 1980a.
Hausman, R., Constrained principal components,Unpublished Memorandum, Bell Laboratories, Holmdel, N.J., 1980b.
Kettenring, J. R., Canonical analysis,Unpublished Memorandum, Bell Laboratories, Murray Hill, N.J., 1979.
References
Anderson, T. W.,Introduction to Multivariate Statistical Analysis, New York: John Wiley & Sons, 1958.
Bard, Y.,Nonlinear Parameter Estimation, New York: Academic Press, 1974.
Bartlett, M. S., On the theory of statistical regression,Proceedings of the Royal Society of Edinburgh, 1933,53, pp. 260–283.
Bentler, P. M., & Woodwards, J. A., Regression on linear composites: Statistical theory and applications.Multivariate Behavioral Research Monographs, 1979, No. 79-1.
Bibby, J., & Toutenberg, H.,Prediction and improved estimation in linear models. New York: Wiley, 1977.
Bibby, J., Some Effects of Rounding Optimal Estimates,Working Paper, The Open University, England, 1980.
Chambers, J.,Computational Methods for Data Analysis, New York: John Wiley & Sons, 1977.
Cliff, N. & Krus, D. J., Interpretation of canonical analysis: rotated vs. unrotated solutions,Psychometrika, 1976,4, 35–42.
Cooley, W. W., Canonical correlation, Paper presented at the 74-th Annual Convention,American Psychological Association (mimeograph), 1965.
Cooley, W. W. & Lohnes, P. R.,Multivariate Procedures for the Behavioral Sciences, New York: John Wiley & Sons, 1962.
Darlington, R. B. & Bishop, C. H., Increasing test validity by considering interitem correlations,Journal of Applied Psychology, 1966,50, 322–330.
Darlington, R. B., Reduced-variance regression.Psychological Bulletin, 1978,85, 1238–1255.
Dempster, A. P., Estimation in multivariate analysis, inMultivariate Analysis (P. R. Krishnaiah, ed.), New York: Academic Press, 1966, 315–334.
Garfinkel, R. S. and Nemhauser, G. L.,Integer Programming, New York: John Wiley & Sons, 1972.
Gnanadesikan, R.,Methods for Statistical Data Analysis of Multivariate Observations, New York: John Wiley & Sons, 1977.
Green, B. R. Jr., Parameter sensitivity in multivariate methods.Multivariate Behavioral Research, 1977,12, 263–287.
Green, P. E., Carroll, J. D., & DeSarbo, W. S., An extended application of the δ2 measure of predictor-variable importance,Proceedings of the American Marketing Association Educator's Conference, Chicago: A.M.A., 1979.
Hotelling, H., Relations between two sets of variates,Biometrika, 1936,28, 321–377.
Kendall, M. G., and Stuart, A. S.,The Advanced Theory of Statistics, Vol. 3, New York: Hafner Publishing Co., 1966.
Kendall, M. G.,A Course in Multivariate Analysis, 4-th impression, New York: Hafner Publishing Co., 1968.
Levine, M. S.,Canonical Analysis and Factor Comparisons, Beverly Hills: Sage Publications 1977.
Lin, S. and Kernighan, M., An effective heuristic algorithm for the traveling salesman problem,Operations Research, 1973,21, 498–516.
Meredith, W. Canonical correlations with fallible data,Psychometrika, 1964,29, 55–65.
Pruzek, R. M., & Frederick, R. C., Weighting predictors in linear models: Alternatives to least squares and limitations of equal weights.Psychological Bulletin, 1978,85, 254–266.
Reingold, E. M., Nievergelt, J., & Deo, N.,Combinatorial Algorithms, Englewood Cliffs, New Jersey: Prentice Hall, 1977.
Roy, S. N.,Some Aspects of Multivariate Analysis, New York: John Wiley and Sons, Inc., 1957.
Scheffé, H.,The Analysis of Variance, New York: John Wiley and Sons, Inc., 1959.
Thorndike, R. M., Weiss, D. J., & Davis, R. V., Canonical correlation of vocational interests and vocational needs,Journal of Counseling Psychology, 1968,15, 101–106.
Thorndike, R. M. & Weiss, D. J., A Study of the stability of canonical correlations and canonical components,Educational and Psychological Measurement, 1973,33, 123–134.
Wainer, H., Estimating coefficients in linear models: It don't make no nevermind.Psychological Bulletin, 1976,83, 213–217.
Wainer, H., On the sensitivity of regression and regressors.Psychological Bulletin, 1978,85, 267–273.
Weinberg, S. L. & Darlington, R. B., Canonical analysis when number of variables is large relative to sample size,Journal of Educational Statistics, 1976,1, 313–332.
Winer, B. J., Statistics and data analysis: Trading bias for reduced mean square error.Annual Review of Psychology, 1978,29, 647–6811.
Vinod, H. D., Canonical ridge and econometrics of joint production,Journal of Econometrics, 1977,4, 147–166.
Author information
Authors and Affiliations
Additional information
Wayne S. DeSarbo, Robert Jausman, Shen Lin, and Wesley Thompson are all Members of Technical Staff at Bell Laboratories. We wish to express our gratitude to the editor and reviewers of this paper for their insightful remarks.
Rights and permissions
About this article
Cite this article
DeSarbo, W.S., Hausman, R.E., Lin, S. et al. Constrained canonical correlation. Psychometrika 47, 489–516 (1982). https://doi.org/10.1007/BF02293711
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02293711