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

[Richard Williams <richardwilliams.ndu@gmail.com>]

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


-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
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EMAIL:  Richard.A.Williams.5@ND.Edu
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