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

 From David Hoaglin To statalist@hsphsun2.harvard.edu Subject Re: st: What is the effect of centering on marginal effects? Date Wed, 1 Aug 2012 13:50:14 -0400

```Dear Alessandro,

Some of your statements are puzzling.

Centering predictor variables can have a substantial effect on
collinearity.  Belsley, Kuh, and Welsch (1980) discuss this and other
aspects of (multi)collinearity; see, for example, Section 3.4.

Since centering the predictor variables affects only the intercept,
the interpretation of the other regression coefficients is not
affected by the centering.  In your example, b1 tells how Y changes
per unit change in X (b1 is a slope, and I am assuming that X is not
dichotomous), adjusting for the contributions of the other predictors
in the model (e.g., Z).

If one creates an interaction predictor from X1 and X2 by centering
them and taking the product, (X1 - a1)(X2 - a2), the coefficients of
X1 and X2 will usually change.  If b is the coefficient of this
interaction predictor, adding b(X1 - a1)(X2 - a2) to the model is
bX1X2 - (ba2)X1 - (ba1)X2 + (ba1a2).
Ordinarily, when a model contains an interaction effect, it should
also contain the corresponding "main effects."

David Hoaglin

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

On Wed, Aug 1, 2012 at 9:54 AM, Alessandro Freire
<alessandro.freire@gmail.com> wrote:
> Dear Lisa,
>
> Centered and uncentered models are algebraically equivalent (see
> Brambor et al, "Understanding Interaction Models: Improving Empirical
> Analyses" 2006). The only difference is that, in an uncentered model,
> the coefficient of b1 corresponds to the marginal effect of a one unit
> change in X when the conditioning variable Z is zero, while the
> corresponding coefficient on the centered model gives you the marginal
> effect of a change in X when Z is at its mean.
>
> This means that centering variables will not reduce multicollinearity
> on your model. I am not familiar with the mfx command, but I would
> suggest you to either perform the estimation of marginal effects by
> hand (see https://files.nyu.edu/mrg217/public/interaction.html) or use
> the margins command, which supports factor variables, if you are using
> Stata 11.
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```