[R] refitting lm() with same x, different y

[William Valdar]

> From: Brian Ripley
> 
> As a first shot, use lm with a matrix response.  That fits them all at once 
> with one QR-decomposition.  No analogue for glm or lmer, though, since for 
> those the iterative fits run do depend on the response.

Thanks Brian, that's very helpful. Also thanks to Kevin Wright who 
suggested using lsfit(x,Y) as being faster than lm for a Y matrix.

I've since worked out that I can bypass even more lm machinery by basing 
my permutation test significance thresholds on the RSS from qr.resid().
Since,

     y = QRb + e
   Q'y = Rb + Q'e
   RSS = || Q'y - Rb ||

then I can do

   X.qr <- qr(X)

once, and for every instance of y calculate

   e   <- qr.resid(X.qr, y)
   rss <- e %*% e

recording them in

   rss.for.all.fits[i] <- rss

which gives me an empirical distribution of RSS scores. The degrees of 
freedom in my X matrix are constant throughout (I should have said that 
before), so all RSS's are on a level footing and map trivially to the 
p-value. I can therefore take the RSS at, say, the 5th percentile, turn it 
into a p-value and report that as my 5% threshold.

Thanks again,

William

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Dr William Valdar               ++44 (0)1865 287 717
Wellcome Trust Centre           valdar at well.ox.ac.uk
for Human Genetics, Oxford      www.well.ox.ac.uk/~valdar