The CANCORR Procedure

Overview

The CANCORR procedure performs canonical correlation, partial canonical correlation, and canonical redundancy analysis.

Canonical correlation is a technique for analyzing the relationship between two sets of variables -each set can contain several variables. Canonical correlation is a variation on the concept of multiple regression and correlation analysis. In multiple regression and correlation, you examine the relationship between a linear combination of a set of X variables and a single Y variable. In canonical correlation analysis, you examine the relationship between a linear combination of the set of X variables with a linear combination of a set of Y variables. Simple and multiple correlation are special cases of canonical correlation in which one or both sets contain a single variable.

The CANCORR procedure tests a series of hypotheses that each canonical correlation and all smaller canonical correlations are zero in the population. PROC CANCORR uses an F approximation (Rao 1973; Kshirsagar 1972) that gives better small sample results than the usual $\chi^2$ approximation. At least one of the two sets of variables should have an approximate multivariate normal distribution in order for the probability levels to be valid.

Both standardized and unstandardized canonical coefficients are produced, as well as all correlations between canonical variables and the original variables. A canonical redundancy analysis (Stewart and Love 1968; Cooley and Lohnes 1971) can also be performed. PROC CANCORR provides multiple regression analysis options to aid in interpreting the canonical correlation analysis. You can examine the linear regression of each variable on the opposite set of variables. PROC CANCORR uses the least-squares criterion in linear regression analysis. PROC CANCORR can produce a data set containing the scores of each observation on each canonical variable, and you can use the PRINT procedure to list these values. A plot of each canonical variable against its counterpart in the other group is often useful, and you can use PROC PLOT with the output data set to produce these plots. A second output data set contains the canonical correlations, coefficients, and most other statistics computed by the procedure.

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