[R] qr and Moore-Penrose
Peter Dalgaard BSA
p.dalgaard at biostat.ku.dk
Wed Jun 30 13:35:13 CEST 1999
Torsten Hothorn <hothorn at amadeus.statistik.uni-dortmund.de> writes:
> yesterday I had a little shock using qr (or lm). having a matrix
> X <- cbind(1,diag(3))
> y <- 1:3
> the qr.coef returns one NA (because X is singular). So I computed the
> Moore-Penrose inverse of X (just from the definition) and I get a correct
> result. Whats wrong about qr in this situation?
Ummm, what exactly do you perceive as a problem here?
> X <- cbind(1, diag(3)); # singular matrix
> y <- 1:3
> Xp <- qr(X);
> b1 <- qr.coef(Xp, y); # contains NA
> b2 <- mpinv(X)%*%y # least square fit using Moore-Penrose
> X%*%b2 # == y
...and so is X[,-4] %*% b1[-4] (or, equivalently, X%*%b1 if you
replace the NA with a 0).
O__ ---- Peter Dalgaard Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics 2200 Cph. N
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
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