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


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu
Subject   Re: Re: st: What is the effect of centering on marginal effects?
Date   Thu, 02 Aug 2012 10:29:53 -0500

At 08:41 AM 8/2/2012, Alessandro Freire wrote:
Dear all,

Indeed, centering variables will inevitably result in different
coefficients and standard errors compared to an uncentered model. Even
though, this is due to the fact that these coefficients correspond to
different quantities of interest in each model.

That is, a centered model is no more "accurate" than an uncentered
model. If we estimated the marginal effect of a one unit change in X
at a given value of Z from the estimates of both centered and
uncentered models, we would obtain the same results. One should not
confuse coefficients with effects ( see Kam & Franzese, "Modeling and
Interpreting Interactive Hypotheses in Regression Analysis: A
Refresher and Some Practical Advice" 2005).

Thus, centering variables brings no meaningful changes whatsoever,
since it adds no new information to the estimation of parameters.
Centering was a common procedure during the 1980s due to computational
imprecision issues, but it makes little sense, if any, nowadays.

Alessandro

I agree that you rarely if ever need to center because of computational issues. But, I think centering can be an aid to interpretation. Lets take a real simple model:

reg y x

In this model, the intercept is the predicted value for a person with a score of 0 on x. If, say, x ranges from 400 to 1200, then such a person or even somebody close to that person cannot exist.

Suppose instead you do

reg y xcentered

Now, the intercept represents the predicted value of a person with average values on x. That person or somebody close to that person probably does exist, so the intercept has a little more intuitive value in that case.

As the model gets more complicated -- you add dummy variables, interaction terms, etc -- the value of centering as an aid to interpretation can go up.

Part of the reason I bring this up -- I've seen students look at models like

reg y female x
reg y female x female*x

The coefficient for female changes sign or becomes insignificant when you add the interaction, and they start making up some weird story about how the effect of female changes when you control for the interaction of female*x. Centering helps to avoid such weird stories; and even if you don't use it it is helpful to see how the main effects of something like female are dependent on the coding of x.

I discuss these issues more in this handout:

http://www.nd.edu/~rwilliam/stats2/l53.pdf


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Richard Williams, Notre Dame Dept of Sociology
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