Canonical correlation analysis

The main idea

Canonical correlation analysis (CCorA) is suitable when you wish to examine linear relationships between two data sets where it is unclear what are response and what are explanatory variables. It attempts to find axes of maximum linear correlation between two corresponding data matrices. As it treats all variables equally, asserting no causal structure, it is a symmetrical canonical analysis.

CCorA is closely related to principal components analysis (PCA). Each data matrix is subject to a separate PCA and the individual solutions are then rotated to maximise correlation between their principal axes. In some cases, it may be more informative to perform a single PCA after concatenating the two data matrices.

  • Highly correlated variables may not be of ecological interest. Do not be mislead into thinking that strong correlations necessarily imply ecological importance.