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article · The American Statistician · 1982

Understanding Canonical Correlation through the General Linear Model and Principal Components

Keith E. Muller

Cited by 48Abstract and details only

Abstract

Abstract Canonical correlation has been little used and little understood, even by otherwise sophisticated analysts. An alternative approach to canonical correlation, based on a general linear multivariate model, is presented. Properties of principal component analysis are used to help explain the method. Standard computational methods for full rank canonical correlation, techniques for canonical correlation on component scores, and canonical correlation with less than full rank are discussed. They are seen to be essentially equivalent when the model equation for canonical correlation on component scores is presented. The two approaches to less than full rank situations are equivalent in some senses, but quite different in usefulness, depending on the application. An example dataset is analyzed in detail to help demonstrate the conclusions.

Cite this paper

APA 7

Muller, K. E. (1982). Understanding Canonical Correlation through the General Linear Model and Principal Components. The American Statistician, 36(4), 342–354. https://doi.org/10.1080/00031305.1982.10483045

MLA 9

Muller, Keith E. “Understanding Canonical Correlation through the General Linear Model and Principal Components.” The American Statistician, vol. 36, no. 4, 1982, pp. 342–54, https://doi.org/10.1080/00031305.1982.10483045.

Chicago

Muller, Keith E. 1982. “Understanding Canonical Correlation through the General Linear Model and Principal Components.” The American Statistician 36 (4): 342–54. https://doi.org/10.1080/00031305.1982.10483045.

Harvard

Muller, K.E. (1982) ‘Understanding Canonical Correlation through the General Linear Model and Principal Components’, The American Statistician, 36(4), pp. 342–354. Available at: https://doi.org/10.1080/00031305.1982.10483045.

BibTeX
@article{muller1982understanding,
  title = {{Understanding Canonical Correlation through the General Linear Model and Principal Components}},
  author = {Muller, Keith E.},
  journal = {The American Statistician},
  volume = {36},
  number = {4},
  pages = {342--354},
  year = {1982},
  doi = {10.1080/00031305.1982.10483045}
}

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