Canonical Correlation Analysis
You can generate tables of output from canonical correlation analyses
by setting options in the Canonical Correlation Options dialog
shown in Figure 40.8
or from the Tables menu shown in
Figure 40.11. Select Canonical Correlations from the
Tables menu to display the canonical correlation dialog
shown in Figure 40.23.
Figure 40.23: Canonical Correlation Dialog
The Canonical Correlations table contains the following:
- CanCorr, the canonical correlations, which are always nonnegative
- Adj. CanCorr, the adjusted canonical correlations,
which are asymptotically less biased than the raw correlations
and may be
negative. The adjusted canonical correlations may not be computable, and
they are displayed as missing values if two canonical correlations are nearly
equal or if some are close to zero. A missing value is also displayed if
an adjusted canonical correlation is larger than a previous adjusted
canonical correlation.
- Approx Std. Error, the approximate standard
errors of the canonical correlations
- CanRsq, the squared canonical correlations
- Eigenvalues,
the eigenvalues of the matrix
R^{-1}_{yy} R_{yx} R^{-1}_{xx} R_{yx}'.
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.
- Test for H0: CanCorrj=0, j>=k,
the likelihood ratio for the hypothesis that the current canonical
correlation and all smaller ones are zero in the population
- Approx F based on Rao's approximation to the distribution of the
likelihood ratio
- Num DF and Den DF (numerator and denominator
degrees of freedom) and
Pr > F (probability level)
associated with the F statistic
Figure 40.24 shows tables of canonical correlations.
Figure 40.24: 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.
Figure 40.25 shows a table of correlations
between the Y, X variables and the first two
canonical variables from the Y and X variables
and the tables of scoring coefficients
of the standardized Y and X variables.
Figure 40.25: Correlations and Scoring Coefficients Tables
The Redundancy table gives the canonical redundancy analysis,
which includes the proportion and cumulative proportion of
the raw (unstandardized) and the standardized variance of
the set of Y and the set of X variables explained by their
own canonical variables and explained by the opposite
canonical variables.
Figure 40.26 shows tables of redundancy
of standardized Y and X variables.
Figure 40.26: Redundancy Tables
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.