Spotfire Statistica® Canonical Analysis

Canonical Analysis investigates the relationship between two sets of variables. This is known as canonical correlation and is a special case of the general linear model.  It may be used by: 

• a medical researcher studying the relationship of various risk factors to the development of a group of symptoms
• sociologist investigating the relationship between predictors of social mobility 
• marketing employee exploring customer data to help with campaign "next steps"

Available techniques are eigenvalues, correlation coefficients, significance test of the canonical correlations, canonical weights, canonical scores, factor structure, variance, redundancy, and practical significance.  In equation form, redundancy is:

Redundancy_left = [s(loadings_left²)/p]*R_c²

Redundancy_right = [s(loadings_right²)/q]*R_c²

In these equations, p denotes the number of variables in the first (left) set of variables, and q denotes the number of variables in the second (right) set of variables; R_c² is the respective squared canonical correlation.

Note that you can compute the redundancy of the first (left) set of variables given the second (right) set, and the redundancy of the second (right) set of variables, given the first (left) set. Because successively extracted canonical roots are uncorrelated, you could sum up the redundancies across all or only the first significant roots. This provides a single index of redundancy as proposed by Stewart and Love, 1968.