From vogranovich at jumptrading.com  Tue Mar 17 18:14:45 2009
From: vogranovich at jumptrading.com (Vadim Ogranovich)
Date: Tue, 17 Mar 2009 12:14:45 -0500
Subject: [Rd] lsfit w/ rank-deficient x
In-Reply-To: <22D850BC39A25742977325ADDE208E770271F71FC6@chiexchange02.w2k.jumptrading.com>
References: <22D850BC39A25742977325ADDE208E770271F71FC6@chiexchange02.w2k.jumptrading.com>
Message-ID: <22D850BC39A25742977325ADDE208E770271F71FC9@chiexchange02.w2k.jumptrading.com>

Actually, the correct permutation is given by the inverse of qr$pivot:

foo$coefficients[foo$qr$pivot] <- foo$coefficients

Here foo is an object returned by lsfit, see below.



-----Original Message-----
From: Vadim Ogranovich
Sent: Friday, March 13, 2009 5:25 PM
To: 'r-devel at r-project.org'
Subject: lsfit w/ rank-deficient x

Dear R-devel,

It seems that lsfit incorrectly reports coefficients when the input matrix 'x' is rank-deficient, see the example below:

## here values of 'b' and 'c' are incorrectly swapped
> x <- cbind(a=rnorm(100), b=0, c=rnorm(100)); y <- rnorm(100); lsfit(x, y)$coef
 Intercept          a          b          c
-0.0227787  0.1042860 -0.1729261  0.0000000
Warning message:
In lsfit(x, y) : 'X' matrix was collinear

## correct values
> lsfit(x[,-2], y)$coef
 Intercept          a          c
-0.0227787  0.1042860 -0.1729261


I looked inside the lsfit code and it appears that even though rank-deficiency is detected there is no attempt to patch the coefficients. Why is that?

Taking clues from the code it appears that the following trick might do the work:

> foo <- lsfit(x, y)
Warning message:
In lsfit(x, y) : 'X' matrix was collinear
> structure(foo$coefficients[foo$qr$pivot], names=names(foo$coefficients))
  Intercept           a           b           c
 0.14857345 -0.07473099  0.00000000  0.12835155


Is this reliable or there are cases when it may fail?

Thanks,
Vadim

P.S.

> version
               _
platform       i386-pc-mingw32
arch           i386
os             mingw32
system         i386, mingw32
status
major          2
minor          7.1
year           2008
month          06
day            23
svn rev        45970
language       R
version.string R version 2.7.1 (2008-06-23)
>

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[Rd] lsfit w/ rank-deficient x
Vadim Ogranovich