acape

Canonical correlation analysis between two sets of variables made on the same objects.

Computes the interrelationships between two sets of variables made on the same objects without data. The canonical correlation is the maximum correlation between linear functions of the two vector variables. Linearity is important because the analysis is performed on the correlation matrix which reflect linear relationships. After this there may to locate additional pairs of functions that maximally correlate, subject to the restriction that the functions in each new pair must be uncorrelated with all previously located functions in both domains (orthogonal). Geometrically, the canonical model can be considered an exploration of the extent to which objects occupy the same relative positions in one measurement space as they do in the other. With p predictor and q criterion variables, we have min(p,q) of canonical coefficients. A complete procedure follows with a test of significance of canonical correlations through the Bartlett's test.

It needs to input the X,Y-data matrices and alpha-significance (default = 0.05).

The outputs are the canonical functions, correlations between the canonical and original variables, proportion of variance extracted, redundancy and Chi-square tests with successive roots removed.