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Re: st: What is the effect of centering on marginal effects?


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: What is the effect of centering on marginal effects?
Date   Thu, 2 Aug 2012 14:12:20 -0400

Richard,

Collinearity can cause problems in the numerical computation, but that
is by no means the whole story.  I was reacting to the statement that
"centering variables will not reduce multicollinearity," which is
simply incorrect.

The condition indexes that David Belsley developed are closely related
to the condition number that numerical analysts assign to a
least-squares problem, derived from the singular-value decomposition
of the matrix of data on the predictor variables.

A near linear dependency (collinearity) can degrade the variances of
the estimated coefficients of the predictors involved in the
dependency.  Belsley's coefficient variance decomposition is designed
to reveal such problems.

Near dependencies can arise when variables are not functionally
related.  The problems with monomials such as X, X^2, X^3, ..., are
sometimes alleviated by using orthogonal polynomials.

David Hoaglin

On Wed, Aug 1, 2012 at 4:16 PM, Richard Williams
<richardwilliams.ndu@gmail.com> wrote:
>
> I am not sure why that is much of a concern though. Sure, if one variable is
> computed from another, there will tend to be collinearity, e.g. X will
> usually be correlated with X^2; femaleXses will tend to be correlated with
> female and ses. Further, centering continuous vars will tend to reduce
> collinearity. But, so what? Unless the software is having trouble converging
> to a solution, the collineairity doesn't really matter. Centering may make
> the results easier to interpret, but collinearity in and of itself in these
> situations usually doesn't create much grief.
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