Skip to main content
Log in

Influence in canonical correlation analysis

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

The perturbation theory of the generalized eigenproblem is used to derive influence functions of each squared canonical correlation coefficient and the corresponding canonical vector pair. Three sample versions of these functions are described and some properties are noted. As particular applications, the influence function of the squared multiple correlation coefficient and influence functions of eigenvalues and eigenvectors in correspondence analysis are obtained. Three numerical examples are briefly discussed.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

  • Calder, P. (1986).Influence functions in multivariate analysis. Unpublished doctoral dissertation, University of Kent.

  • Campbell, N. A. (1978). The influence function as an aid in outlier detection in discriminant analysis.Applied Statistics, 27, 251–258.

    Google Scholar 

  • Cook, R. D., & Weisberg, S. (1982).Residuals and influence in regression. New York: Chapman and Hall.

    Google Scholar 

  • Critchley, F. (1985). Influence in principal components analysis.Biometrika, 72, 627–636.

    Google Scholar 

  • Cramer, E. M., & Nicewander, W. A. (1979). Some symmetric, invariant measures of multivariate association.Psychometrika, 44, 43–54.

    Google Scholar 

  • Devlin, S. J., Gnanadesikan, R., & Kettenring, J. R. (1975). Robust estimation and outlier detection with correlation coefficients.Biometrika, 62, 531–545.

    Google Scholar 

  • Escofier, B., & Le Roux, B. (1976). Influence d'un élément sur les facteurs en analyse des correspondances [Influence of an element on the factors in correspondence analysis].Cahiers de l'Analyse des Ponnées, 1, 297–318.

    Google Scholar 

  • Fisher, R. A. (1940). The precision of discriminant functions.Annals of Eugenics, 10, 422–429.

    Google Scholar 

  • Frets, G. P. (1921). Heredity of head form in man.Genetica, 3, 193–384.

    Google Scholar 

  • Greenacre, M. J. (1984).Theory and applications of correspondence analysis. New York: Academic Press.

    Google Scholar 

  • Hampel, F. R. (1974). The influence curve and its role in robust estimation.Journal of the American Statistical Association, 69, 383–393.

    Google Scholar 

  • Pack, P., & Jolliffe, I. T. (1992). Influence in correspondence analysis.Applied Statistics.

  • Radhakrishnan, R., & Kshirsagar, A. M. (1981). Influence functions for certain parameters in multivariate analysis.Communications in Statistics-Theory and Methods, 10, 515–529.

    Google Scholar 

  • Romanazzi, M. (1989).Derivatives of eigenvalues and eigenvectors in the generalized eigenproblem dependent on a parameter (Unpublished Technical Report). Venice, Italy: University of Venice “Ca′ Foscari”, Statistical Laboratory.

    Google Scholar 

  • Romanazzi, M. (1990). Influence functions of eigenvalues and eigenvectors in multidimensional data analysis. In K. Momirovic & V. Mildner (Eds.),IX COMPSTAT-Proceedings in computational statistics (pp. 211–216). Heidelberg: Physica-Verlag.

    Google Scholar 

  • Romanazzi, M. (1991). Influence in canonical variates analysis.Computational Statistics & Data Analysis, 11, 143–164.

    Google Scholar 

  • Seber, G. A. F. (1983).Multivariate observations. New York: Wiley.

    Google Scholar 

  • Tanaka, Y. (1984). Sensitivity analysis in Hayashi's third method of quantification.Behaviormetrika, 16, 31–44.

    Google Scholar 

  • Tanaka, Y. (1988). Sensitivity analysis in principal component analysis: influence on the subspace spanned by principal components.Communications in Statistics-Theory and Methods, 17, 3157–3175.

    Google Scholar 

  • Tanaka, Y. (1989). Influence functions related to eigenvalue problems which appear in multivariate analysis.Communications in Statistics-Theory and Methods, 18, 3991–4010.

    Google Scholar 

  • Tanaka, Y., & Odaka, Y. (1989). Influential observations in principal factor analysis.Psychometrika, 54, 475–485.

    Google Scholar 

  • Tanaka, Y., & Tarumi, T. (1988). Sensitivity of the geometrical representation obtained by correspondence analysis to some small changes of data. In S. Das Gupta & J. K. Ghosh (Eds.),Proceedings of the international conference on advances in multivariate statistical analysis (pp. 499–511). Calcutta: Indian Statistical Institute.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

We thank the Editor and the anonymous reviewers for their helpful comments. This research was carried out with the financial support of the Italian Ministry of the University and the National Research Council.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Romanazzi, M. Influence in canonical correlation analysis. Psychometrika 57, 237–259 (1992). https://doi.org/10.1007/BF02294507

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02294507

Key words

Navigation