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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 08:59:19 -0500

For interpretability alone, it's hard to see why centering at a
suitable value should not be the default.

I don't think one needs the SVD to solve a least-squares problem.  The
SVD, however, provides the information for the detailed diagnosis of
collinearity developed by Belsley, Kuh, and Welsch (1980).  They start
by scaling the columns of the predictor matrix so that each has length
1.  If the predictors include the constant, however, they do not
center the other predictors.  A collinearity relation can involve the
constant.

David Hoaglin

D.A. Belsley, E. Kuh, and R.E. Welsch.  Regression Diagnostics.  Wiley, 1980.

On Mon, Jan 21, 2013 at 1:11 AM, JVerkuilen (Gmail)
<jvverkuilen@gmail.com> wrote:
> On Sun, Jan 20, 2013 at 8:56 PM, David Hoaglin <dchoaglin@gmail.com> wrote:
>> The QR decomposition is not a panacea.  If the matrix of predictor
>> variables is ill-conditioned enough, some loss of precision can still
>> result.  We might do well to regard centering as preventive medicine.
>
> It's been a while since my scientific computing class (highly useful!)
> but I seem to recall that the SVD is the best possible, while QR is
> the most practical in terms of computation for most problems. If
> conditioning is bad enough nothing really helps. And of course
> rescaling and or centering helps eliminate issues such as having one
> variable scaled in millions and the other in millionths, which just
> makes needless trouble for finite precision arithmetic.
>
> The main reason I advocate it for students is to help make
> interpretation easier, though, which it definitely does.
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