redundancy {candisc} | R Documentation |
Canonical Redundancy Analysis
Description
Calculates indices of redundancy (Stewart & Love, 1968) from a canonical correlation analysis. These give the proportion of variances of the variables in each set (X and Y) which are accounted for by the variables in the other set through the canonical variates.
Usage
redundancy(object, ...)
## S3 method for class 'cancor.redundancy'
print(x, digits = max(getOption("digits") - 3, 3), ...)
Arguments
object |
A |
... |
Other arguments |
x |
A |
digits |
Number of digits to print |
Details
The term "redundancy analysis" has a different interpretation and implementation in the
environmental ecology literature, such as the vegan.
In that context, each Y_i
variable is regressed separately on the predictors in X
,
to give fitted values \widehat{Y} = [\widehat{Y}_1, \widehat{Y}_2, \dots
.
Then a PCA of \widehat{Y}
is carried out to determine a reduced-rank structure of
the predictions.
Value
An object of class "cancor.redundancy"
, a list with the
following 5 components:
Xcan.redun |
Canonical redundancies for the X variables, i.e., the total fraction of X variance accounted for by the Y variables through each canonical variate. |
Ycan.redun |
Canonical redundancies for the Y variables |
X.redun |
Total canonical redundancy for the X variables,
i.e., the sum of |
Y.redun |
Total canonical redundancy for the Y variables |
set.names |
names for the X and Y sets of variables |
Functions
-
print(cancor.redundancy)
:print()
method for"cancor.redundancy"
objects.
Author(s)
Michael Friendly
References
Muller K. E. (1981). Relationships between redundancy analysis, canonical correlation, and multivariate regression. Psychometrika, 46(2), 139-42.
Stewart, D. and Love, W. (1968). A general canonical correlation index. Psychological Bulletin, 70, 160-163.
Brainder, "Redundancy in canonical correlation analysis", https://brainder.org/2019/12/27/redundancy-in-canonical-correlation-analysis/
See Also
Examples
data(Rohwer, package="heplots")
X <- as.matrix(Rohwer[,6:10]) # the PA tests
Y <- as.matrix(Rohwer[,3:5]) # the aptitude/ability variables
cc <- cancor(X, Y, set.names=c("PA", "Ability"))
redundancy(cc)
##
## Redundancies for the PA variables & total X canonical redundancy
##
## Xcan1 Xcan2 Xcan3 total X|Y
## 0.17342 0.04211 0.00797 0.22350
##
## Redundancies for the Ability variables & total Y canonical redundancy
##
## Ycan1 Ycan2 Ycan3 total Y|X
## 0.2249 0.0369 0.0156 0.2774