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


From   Ulrich Kohler <kohler@wzb.eu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: Re: st: What is the effect of centering on marginal effects?
Date   Thu, 02 Aug 2012 16:43:06 +0200

I totally aggree with Richard but I would add that all this just doesn't
matter if you show your results graphically:

. sysuse auto
. reg mpg i.foreign##c.weight##c.length
. margins foreign, at(weight=(1760(400)4860) length=(170 192.5 204))
. marginsplot, by(foreign)

-marginsplot- rocks!

Uli


Am Donnerstag, den 02.08.2012, 10:29 -0500 schrieb Richard Williams:
> 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
> OFFICE: (574)631-6668, (574)631-6463
> HOME:   (574)289-5227
> EMAIL:  Richard.A.Williams.5@ND.Edu
> WWW:    http://www.nd.edu/~rwilliam
> 
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