If the SIMPLE option is specified, PROC CANCORR produces
means and standard deviations for each input variable.
If the CORR option is specified, PROC CANCORR produces
correlations among the input variables.
Unless the NOPRINT option is specified, PROC CANCORR displays a table of
canonical correlations containing the following:
- Canonical Correlations. These are always nonnegative.
- Adjusted Canonical Correlations (Lawley 1959),
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 Standard Errors, which are the approximate
standard errors of the canonical correlations
- Squared Canonical Correlations
of INV(E)*H, which are equal to
CanRsq/(1-CanRsq), where CanRsq is the
corresponding squared canonical correlation.
Also displayed for each eigenvalue is the Difference
from the next eigenvalue, the Proportion of the sum
of the eigenvalues, and the Cumulative proportion.
- Likelihood Ratio for the hypothesis that
the current canonical correlation and all
smaller ones are 0 in the population.
The likelihood ratio for all canonical
correlations equals Wilks' lambda.
- Approx F statistic based on Rao's approximation to the distribution of
the likelihood ratio (Rao 1973, p. 556; Kshirsagar 1972,
- Num DF and Den DF (numerator and denominator
degrees of freedom) and Pr > F (probability
level) associated with the F statistic
Unless you specify the NOPRINT option,
PROC CANCORR produces a table
of multivariate statistics for the null hypothesis that
all canonical correlations are zero in the population.
These statistics are described in the section
"Multivariate Tests" in Chapter 3, "Introduction to Regression Procedures."
The statistics are as follows:
- Wilks' Lambda
- Pillai's Trace
- Hotelling-Lawley Trace
- Roy's Greatest Root
For each of the preceding statistics, PROC CANCORR displays
- an F approximation or upper bound
- Num DF, the numerator degrees of freedom
- Den DF, the denominator degrees of freedom
- Pr> F, the probability level
Unless you specify the SHORT or NOPRINT option, PROC CANCORR displays the
If you specify the REDUNDANCY option, PROC CANCORR displays
- both Raw (unstandardized) and Standardized
Canonical Coefficients normalized to give
canonical variables with unit variance.
Standardized coefficients can be used to compute
canonical variable scores from the standardized
(zero mean and unit variance) input variables.
Raw coefficients can be used to compute canonical variable
scores from the input variables without standardizing them.
- all four Canonical Structure matrices, giving Correlations
Between the canonical variables and the original variables
- the Canonical Redundancy Analysis (Stewart and Love 1968;
Cooley and Lohnes 1971), including Raw (unstandardized)
and Standardized Variance and Cumulative Proportion of the
Variance of each set of variables Explained by Their Own
Canonical Variables and Explained by The Opposite
- the Squared Multiple Correlations of each variable with the
first m canonical variables of the opposite set, where
m varies from 1 to the number of canonical correlations
If you specify the VDEP option, PROC CANCORR performs multiple
regression analyses with the VAR variables as dependent
variables and the WITH variables as regressors.
If you specify the WDEP option, PROC CANCORR performs multiple
regression analyses with the WITH variables as
dependent variables and the VAR variables as regressors.
If you specify the VDEP or WDEP option and also specify the ALL
PROC CANCORR displays the following items.
You can also specify individual options to request
a subset of the output generated by the ALL option; or you
can suppress the output by specifying the NOPRINT option.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.