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Encyclopedia > Canonical analysis
Canonical Analysis - Wikipedia

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Canonical Analysis

Canonical analysis, an integral part of the general linear model for the analysis of data, belongs to a family of methods which involve solving the characteristic equation for its latent roots and vectors. Canonical analysis describes formal structures in hyperspace, defined by orthogonal references axes and invariant with respect to rotation of their coordinates. In this type of solution, rotation leaves many optimizing properties preserved, provided it takes place in certain ways and in a subspace. This rotation from the maximum intervariate correlation structure into a different, simpler and more meaningful structure increases the interpretability of the obtained structures. In this the canonical analysis differs from the Hotelling’s (1936) canonical variate analysis, designed to obtain the maximum (canonical) correlation between a set of predictor and a set of criterion canonical variates.

References

Cliff, N. and Krus, D. J. (1976) Interpretation of canonical analysis: Rotated vs. unrotated solutions. Psychometrika, 41, 1, 35-42.

Hotelling, H. (1936) Relations between two sets of variates. Biometrika, 28, 321-377

Krus, D.J., et al. (1976) Rotation in Canonical Analysis. Educational and Psychological Measurement, 36, 725-730.

Liang, K.H., Krus, D.J., & Webb, J.M. (1995) K-fold crossvalidation in canonical analysis. Multivariate Behavioral Research, 30, 539-545. Results from FactBites:

 Canonical analysis - Wikipedia, the free encyclopedia (275 words) Canonical analysis belongs to a group of methods which involve solving the characteristic equation for its latent roots and vectors. The difference between the canonical variate analysis and canonical analysis is analogous to the difference between the principal components analysis and factor analysis, each with its characteristic set of communalities, eigenvalues and eigenvectors. Liang, K.H., Krus, D.J., and Webb, J.M. (1995) K-fold crossvalidation in canonical analysis.
 Multivariate statistics - Wikipedia, the free encyclopedia (267 words) Canonical correlation analysis tries to establish whether or not there are linear relationships among two sets of variables (covariates and response). Discriminant function or canonical variate analysis attempt to establish whether a set of variables can be used to distinguish between two or more groups. Multivariate analysis of variance (MANOVA) methods extend analysis of variance methods to cover cases where there is more than one dependent variable and where the dependent variables cannot simply be combined.
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