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Re: st: mean centering


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: mean centering
Date   Mon, 21 Jan 2013 12:44:35 -0500

Thanks for the link!

Michael Heath's comparison gives both operation counts and relative
error.  As he says, the relative error of Householder QR is the best
possible, but SVD is more robust and reliable (at the cost of a
substantially greater operation count).

David Hoaglin

On Mon, Jan 21, 2013 at 10:16 AM, JVerkuilen (Gmail)
<jvverkuilen@gmail.com> wrote:
> On Mon, Jan 21, 2013 at 8:59 AM, David Hoaglin <dchoaglin@gmail.com> wrote:
>
>> I don't think one needs the SVD to solve a least-squares problem.
>
> I think the idea was that it was the most numerically stable
> algorithm, but that QR was the most practical for the vast majority of
> problems. The class in question was taught by Mike Heath, who is one
> of the big names in scientific computing, but my copy of the book is
> elsewhere and it was quite a while ago. To the Google:
>
> http://www.cse.uiuc.edu/heath/scicomp/notes/chap03.pdf
>
> Near the end of the slides he's got a comparison of the different methods.
>
>
>
> The
>> SVD, however, provides the information for the detailed diagnosis of
>> collinearity developed by Belsley, Kuh, and Welsch (1980).
>
> Yes, and -biplot- can be very helpful to look through X variables if
> one scales appropriately, though it wouldn't deal with the column of
> 1s appropriately, so I think that a regression diagnostic biplot would
> need to be adapted appropriately. Hmmm, hadn't thought of that.
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