[R] Cancor
Irena Komprej
irena.komprej at telemach.net
Mon Sep 13 13:30:22 CEST 2004
Dear Gabor,
thank you for your answer, but I am still a little confused because the
values of the xcoef and ycoef are so small. It is true, that I receive
very similar results to the cancor, if I use the proposed formula with
z <- svd(cov(x,y) %*% solve(var(y), cov(y,x)) %*% solve(var(x)))
sqrt(z$d) # canonical correlations
isqrt((nrow(x)-1)*var(x)) %*% z$u # xcoef
But, why do I need the nrow(x)-1)* in isqrt()?
In the literature, if you use the proposed calculation, the a's are
calculated as z$u %*% isqrt(var(x)).
I have this problem, because I need structural coefficients to calculate
Redundancy measure and according to literature, they are calculated as
a's%*%var(x).
The coefficients from cancor are so small that my redundancy measure iz
almost zero, despite the high correlation coefficient.
I have, on the other hand, calculated correlation between x and their
corresponding canonical variables as:
cor(x, x%*%xcoef)
and results were good.
Can I use these results as structural correlations in Redundancy measure
calculation?
Thank you again and best regards
Irena Komprej
________________________________________________________________
Irena Komprej <irena.komprej <at> telemach.net> writes:
>
> I am strugling with cancor procedure in R. I cannot figure out the
> meaning of xcoef and of yxcoef.
> Are these:
> 1. standardized coefficients
> 2. structural coefficients
> 3. something else?
>
Look at the examples at the bottom of ?cancor from which its evident
xcoef is such that x %*% cxy$xcoef are the canonical variables. (More
at the end of this post.)
> I have tried to simulate canonical correlation analysis by checking
the
> eigenstructure of the expression:
>
> Sigma_xx %*% Sigma_xy %*% Sigma_yy %*% t(Sigma_xy).
>
> The resulting eigenvalues were the same as the squared values of
> cancor$cor. I have normalized the resulting eigenvectors, the a's with
>
> sqrt(a'%*%Sigma_xx%*%t(a)), and similarly the b's with
> sqrt(b'%*%Sigma_yy%*%t(b)).
>
> The results differed considerably from xcoef and ycoef of the cancor.
Run the example in the help page to get some data and some
output:
set.seed(1)
example(cancor)
# Also, define isqrt as the inverse square root of a postive def matrix
isqrt <- function(x) {
e <- eigen(x)
stopifnot( all(e$values > 0) )
e$vectors %*% diag(1/sqrt(e$values)) %*% solve(e$vectors)
}
# we can reconstruct the canonical correlations and xcoef
# in the way you presumably intended like this:
z <- svd(cov(x,y) %*% solve(var(y), cov(y,x)) %*% solve(var(x)))
sqrt(z$d) # canonical correlations
isqrt((nrow(x)-1)*var(x)) %*% z$u # xcoef
Another thing you can do is to type
cancor
at the R prompt to view its source and see how it works using
the QR decomposition.
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