# Re: [R] Higher Dimensional Matrices

From: <Bill.Venables_at_csiro.au>
Date: Tue 26 Dec 2006 - 00:59:45 GMT

> -----Original Message-----

> From: r-help-bounces@stat.math.ethz.ch
> [mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of downunder
> Sent: Monday, 25 December 2006 12:31 PM To: r-help@stat.math.ethz.ch
> Subject: [R] Higher Dimensional Matrices
>
>
> Hi all.
>
> I want to calculate partial correlations while controlling for one
> or more variables. That works already fine when I control for
> example just for x[,1] and x[,2] that gives me one single
> correlation matrix and i have to to it for x [,1]...x[,10]. That
> would give me out 10 matrices. Controlling for 2 Variables 100
> matrices. how can I run a loop to get f.e the 10 or 100 matrices at
> once? I appreciate for every hint. have nice holidays.

I don't quite understand this. You have 10 variables and you want to find the partial correlations controlling for two of them at a time. If you take each possible set of two variables to condition upon at a time, this would give you choose(10, 2) = 45 matrices, wouldn't it? Where do you get '10 or 100' matrices from?

>
> greetings lars
>
> 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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