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

[Prof Brian Ripley]

William,

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.

Brian

On Mon, 18 Apr 2005, William Valdar wrote:

> Dear All,
>
> Is there is a fast way of refitting lm() when the design matrix stays 
> constant but the response is different? For example,
>
> y1 ~ X
> y2 ~ X
> y3 ~ X
> ...etc.
>
> where y1 is the 1st instance of the response vector. Calling lm() every time 
> seems rather wasteful since the QR-decomposition of X needs to be calculated 
> only once. It would be nice if qr() was called only once and then the same 
> QR-factorization used in all subsequent fits. However, I can't see a way to 
> do this easily. Can anybody else?
>
> Why do I want to do this? I'm fitting ~1000 different X's to a response 
> vector (for biologists: 1000 genetic markers to a measured phenotype with 
> 2000 cases) and wish to establish global significance thresholds for multiple 
> testing. The fits have a complex dependency structure that makes the 
> Bonferroni correction inappropriate. So I intend to refit all ~1000 X's with 
> a shuffled response many times. However, this runs too slow for my needs.
>
> Of course, not having to redo QR will only help if QR is a rate limiting step 
> in lm(), so if anybody can tell me it's not, then that would be very helpful 
> too. I would also like to do this for glm() and lmer() fits. Ideally.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595