lm is slow because it has to set up the design matrix (X) each time. See ?model.matrix and ?model.matrix.lm for how to do this once separately from lm (and then use lm.fit).
I am far from an expert on numerical algebra, but I'm pretty sure your comments below are incorrect in the sense that "naive" methods are **not** universally better then efficient numerical algebra methods using,say, QR decompositions. It will depend very strongly on the size and specific nature of the problem. Big Oh Complexity statements ( O(n) or O(n^2), etc.) are, after all, asymptotic. There is also typically a tradeoff between computational accuracy (especially for ill-conditioned matrices) and speed which your remarks seem to neglect. -- Bert Bert Gunter Genentech Nonclinical Biostatistics 650-467-7374 -----Original Message----- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of ivo welch Sent: Wednesday, March 25, 2009 2:30 PM To: Dimitris Rizopoulos Cc: r-help Subject: Re: [R] very fast OLS regression? thanks, dimitris. I also added Bill Dunlap's "solve(qr(x),y)" function as ols5. here is what I get in terms of speed on a Mac Pro: ols1 6.779 3.591 10.37 0 0 ols2 0.515 0.21 0.725 0 0 ols3 0.576 0.403 0.971 0 0 ols4 1.143 1.251 2.395 0 0 ols5 0.683 0.565 1.248 0 0 so the naive matrix operations are fastest. I would have thought that alternatives to the naive stuff I learned in my linear algebra course would be quicker. still, ols3 and ols5 are competitive. the built-in lm() is really problematic. is ols3 (or perhaps even ols5) preferable in terms of accuracy? I think I can deal with 20% speed slow-down (but not with a factor 10 speed slow-down). regards, /iaw On Wed, Mar 25, 2009 at 5:11 PM, Dimitris Rizopoulos <d.rizopou...@erasmusmc.nl> wrote: > check the following options: > > ols1 <- function (y, x) { > coef(lm(y ~ x - 1)) > } > > ols2 <- function (y, x) { > xy <- t(x)%*%y > xxi <- solve(t(x)%*%x) > b <- as.vector(xxi%*%xy) > b > } > > ols3 <- function (y, x) { > XtX <- crossprod(x) > Xty <- crossprod(x, y) > solve(XtX, Xty) > } > > ols4 <- function (y, x) { > lm.fit(x, y)$coefficients > } > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
