[R] Higher Dimensional Matrices

[downunder]

Hi Bill. Thanks for your extensive hints especially with arrays. 
That solves my problem now and I am also able to control for every
combination of variables.

Have a merry christmas. lars


> 
> x <- read.table("C:/.....dat")
> dim(x) #200x10
> a <- matrix(0,200,10)
> for (i in 1:10)
> a[,i] <- residuals(lm(x[,i]~1+x[,1]+x[,2]))
> b <- matrix(0,200,10)
> for (i in 1:10)
> b[,i] <- residuals(lm(x[,i]~1+x[,1]+x[,2]))
> #a=round(a,5)
> #b=round(b,5)
> d <- cor(a,b)
> d

But a and b are the same, aren't they?  Why do you need to compute
them twice?  Why not just use cor(a, a) [which is the same as cor(a),
of course]?

There is a more serious problem here, though.  Your residuals are
after regression on x[, 1:2] so if you *select* x[, 1:2] as the
y-variables in your regression then the residuals are going to be
zero, but in practice round-off error.  so the first two rows and
columns of d will be correlations with round-off error,
i.e. misleading junk.  It doesn't make sense to include the
conditioning variables in the correlation matrix *conditioning on
them*.  Only the 8 x 8 matrix of the others among themselves is
defined, really.

So how do we do it?  Here are a few pointers.

To start, here is a function that uses a somewhat more compact way of
finding the partial correlations than your method.  Sorting out how it
works should be a useful exercise.

partialCorr <- function (cond, mat) 
	cor(qr.resid(qr(cbind(1, mat[, cond])), mat[, -cond]))

To find the matrix of partial correlations conditioning on x[, 1:2]
you would use

d <- partialCorr(c(1,2), x)

So how to do it for all possible conditioning pairs of variables.
Well you could do it in an obvious loop:

cmats <- array(0, c(8,8,45))
k <- 0
for(i in 1:9) for(j in (i+1):10) {
    k <- k+1
    cmats[, , k] <- partialCorr(c(i, j), x)
}

Now the results are in a 3-way array, but without any kind of labels.
Perhaps you should think about how to fix that one yourself...

With more than two conditioning variables you should probably use a
function to generate the subsets of the appropriate size rather than
trying to write ever more deeply nested loops.  There are plenty of
functions around to do this.

Bill Venables.

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