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Biometrika 1995 82(3):553-560; doi:10.1093/biomet/82.3.553
© 1995 by Biometrika Trust
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Articles

Common canonical variates

BEAT E. NEUENSCHWANDER1 and BERNARD D. FLURY2

1 Swiss Federal Office of Public Health, Division of Epidemiology Heβ-Straβe 27 E, 3097 Liebefeld, Switzerland
2 Department of Mathematics, Indiana University Rawles Hall, Bloomington, Indiana 47405, U.S.A.

Received for publication 1 April 1994. Revision received 1 February 1995.
  Abstract

Canonical correlation analysis measures the linear relationship between two random vectors X1 and X2 as the maximum correlation between linear combinations of X1 and linear combinations of X2. Several generalisations of canonical correlation analysis to k2 random vectors X1 ..., Xk have been proposed in the literature (Kettenring, 1971, 1985), based on the principle of maximising some generalised measure of correlation. In this paper we propose an alternative generalisation, called common canonical variates, based on the assumption that the canonical variates have the same coefficients in all k sets of variables. This generalisation is applicable in situations where all Xi have the same dimension. We present normal theory maximum likelihood estimation of common canonical variates, and illustrate their use on a morphometric data set.

Key Words: Canonical correlation analysis • Eigenvalue • Eigenvector • Maximum likelihood estimation • Morphometric data • Multivariate normal distribution • Wishart distribution


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