Canonical Correlation Analysis

  • Canonical correlation analysis identifies and measures the associations between two sets of variables, which can be conceptualized as latent variables, where each latent variable is based on one set of the observed variables.
  • The canonical correlation is optimized for maximizing the linear correlation between the two latent variables.
The Analysis Output

The analysis output can include:

  • Means and standard deviation of observed variables
  • The correlation matrix of observed variables
  • Canonical correlation results
    • Canonical correlation summary
    • Multivariate Significance Tests
    • Eigenvalues
  • Canonical coefficients (weights)
  • Canonical scores
  • Structure coefficients
    • Correlation between criterion variables (Y) and canonical variates
    • Correlation Between covariate variables and canonical variates
    • Canonical adequacy coefficients
  • Redundancy analysis
  • D'Agostino-Pearson test on observed variables and canonical scores

Example output from canonical correlation analysis of a published dataset*:

Canonical Analysis: Correlation Between Variables

Canonical Correlation Summary

Canonical Abalysis: Multivariate Significance Test

Eigenvalues and Canonical Correlations

Raw Canonical Coefficients (Criterion Variables)

Standardized Coefficients (Criterion Variables)

Raw Canonical Coefficients (Covariates)

Standardized Coefficients (Covariates

Canonical Analysis: Structure Coefficients (Criteria & Canonival Variates)

Canonical Analysis: Structure Coefficients (Covariates & Canonival Variates)

Canonical Analysis: Redundancy  Analysis

D'Agostino-Pearson Test on Observed Variables and Canonical Scores

* Sheskin, D.J. (2011). Handbook of Parametric and Non-parametric Statistical Procedures, 5th Edition, Chapman & Hall/CRC Press.