[R] very fast OLS regression?

[Gavin Simpson]

On Wed, 2009-03-25 at 16:28 -0400, ivo welch wrote:
> Dear R experts:
> 
> I just tried some simple test that told me that hand computing the OLS
> coefficients is about 3-10 times as fast as using the built-in lm()
> function.   (code included below.)  Most of the time, I do not care,
> because I like the convenience, and I presume some of the time goes
> into saving a lot of stuff that I may or may not need.  But when I do
> want to learn the properties of an estimator whose input contains a
> regression, I do care about speed.
> 
> What is the recommended fastest way to get regression coefficients in
> R?  (Is Gentlemen's weighted-least-squares algorithm implemented in a
> low-level C form somewhere?  that one was always lightning fast for
> me.)

No one has yet mentioned Doug Bates' article in R News on this topic,
which compares timings of various methods for least squares
computations.

Douglas Bates. Least squares calculations in R. R News, 4(1):17-20, June
2004.

A Cholesky decomposition solution proved fastest in base R code, with an
even faster version developed using sparse matrices and the Matrix
package.

You can find Doug's article here:

http://cran.r-project.org/doc/Rnews/Rnews_2004-1.pdf

HTH

G

> 
> regards,
> 
> /ivo
> 
> 
> 
> bybuiltin = function( y, x )   coef(lm( y ~ x -1 ));
> 
> byhand = function( y, x ) {
>   xy<-t(x)%*%y;
>   xxi<- solve(t(x)%*%x)
>   b<-as.vector(xxi%*%xy)
>   ## I will need these later, too:
>   ## res<-y-as.vector(x%*%b)
>   ## soa[i]<-b[2]
>   ## sigmas[i]<-sd(res)
>   b;
> }
> 
> 
> MC=500;
> N=10000;
> 
> 
> set.seed(0);
> x= matrix( rnorm(N*MC), nrow=N, ncol=MC );
> y= matrix( rnorm(N*MC), nrow=N, ncol=MC );
> 
> ptm = proc.time()
> for (mc in 1:MC) byhand(y[,mc],x[,mc]);
> cat("By hand took ", proc.time()-ptm, "\n");
> 
> ptm = proc.time()
> for (mc in 1:MC) bybuiltin(y[,mc],x[,mc]);
> cat("By built-in took ", proc.time()-ptm, "\n");
> 
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