regression on a matrix

From: Martin Maechler

"ReidH" == Huntsinger, Reid <reid_huntsinger at merck.com>
    on Thu, 3 Mar 2005 17:24:22 -0500 writes:
    ReidH> You might use lsfit instead and just do the whole Y
    ReidH> matrix at once. That saves all the recalculation of
    ReidH> things involving only X.

yes,  but in these cases, we have been recommending
lm.fit() instead -- just so you use the identical internal
numeric code as lm() and still have the `benefit' of not having
to re-build the design matrix X .
Yes, but ?lm.fit says y has to be a vector, while ?lsfit says y can be a
matrix.  If lm.fit can handle y as a matrix, its help page should be
updated.

Andy
Martin Maechler, ETH Zurich

    ReidH> Reid Huntsinger

    ReidH> -----Original Message----- From:
    ReidH> r-help-bounces at stat.math.ethz.ch
    ReidH> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf
    ReidH> Of Eduardo Leoni Sent: Thursday, March 03, 2005 5:16
    ReidH> PM To: r-help at stat.math.ethz.ch Subject: [R]
    ReidH> regression on a matrix

    ReidH> Hi -

    ReidH> I am doing a monte carlo experiment that requires to
    ReidH> do a linear regression of a matrix of vectors of
    ReidH> dependent variables on a fixed set of covariates (one
    ReidH> regression per vector). I am wondering if anyone has
    ReidH> any idea of how to speed up the computations in
    ReidH> R. The code follows:

    ReidH> #regression function #Linear regression code qreg <-
    ReidH> function(y,x) { X=cbind(1,x) m<-lm.fit(y=y,x=X)
    ReidH> p<-m$rank

    ReidH>   r <- m$residuals n <- length(r) rss <- sum(r^2)
    ReidH> resvar <- rss/(n - p)

    ReidH>   Qr <- m$qr p1 <- 1:p R <- chol2inv(Qr$qr[p1, p1,
    ReidH> drop = FALSE]) se <- sqrt(diag(R) * resvar) b <-
    ReidH> m$coefficients return(c(b[2],se[2])) }

    ReidH> #simulate a <- c(1,.63,.63,1) a <- matrix(a,2,2) c <-
    ReidH> chol(a) C <- 0.7 theta <- 0.8 sims <- 1000 n<-20

    ReidH> u <- rnorm(n,0,sqrt(1-C)) w <-
    ReidH> rgamma(n,C/theta,1/theta) e <- rnorm(n,0,sqrt(w))

    ReidH> x1 <- rnorm(n) x <- x1*c[2,2]+c[1,2]*w v <- e+u y <-
    ReidH> 1+x+v w <- rgamma(n,C/theta,1/theta)

    ReidH> #create matrix of dep variable newdep <-
    ReidH> matrix(rnorm(length(y)*sims,y,sqrt(w)),c(length(y),sims))

    ReidH> monte <- apply(newdep,2,qreg,x=x)

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