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SAS/INSIGHT Software

Canonical Correlation

You can generate tables of output from canonical correlation analyses by setting options in the Canonical Correlation Options dialog or by selecting Canonical Correlations from the Tables menu.

The Canonical Correlations table contains the following:

The Eigenvalues table presents eigenvalues of the matrix R-1yy Ryx R-1xx Ryx'. These eigenvalues are equal to CanRsq/(1-CanRsq), where CanRsq is the corresponding squared canonical correlation. Also printed for each eigenvalue is the difference from the next eigenvalue, the proportion of the sum of the eigenvalues, and the cumulative proportion.

The table titled Test for H0: CanCorr[j]=0, j>=k, displays the likelihood ratio for the hypothesis that the current canonical correlation and all smaller ones are zero in the population.

The Correlations (Structure) table includes the correlations between the input X variables and the canonical variables. The scoring coefficients are the coefficients of the X variables that are used to compute canonical variable scores. The Std Scoring Coefs table includes the scoring coefficients of the standardized X variables, and the Raw Scoring Coefs table includes the scoring coefficients of the centered X variables.

[Figure]
Figure 1.16: Canonical Correlations Tables

The Correlations (Structure) table includes the correlations between the input Y,X variables and canonical variables.

The scoring coefficients are the coefficients of the Y or X variables that are used to compute canonical variable scores. The Std Scoring Coefs table includes the scoring coefficients of the standardized Y or X variables and the Raw Scoring Coefs table includes the scoring coefficients of the centered Y or X variables.

The Redundancy table gives the canonical redundancy analysis which includes the proportion and cumulative proportion of the raw (unstandardized) and standardized variance of set of Y and set of X variables explained by their own canonical variables and explained by the opposite canonical variables.

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