[R] qr and Moore-Penrose

[Peter Dalgaard BSA]

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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