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


From   Alessandro Freire <alessandro.freire@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: Re: st: What is the effect of centering on marginal effects?
Date   Thu, 2 Aug 2012 10:41:43 -0300

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

On Thu, Aug 2, 2012 at 9:38 AM, Christopher Baum <kit.baum@bc.edu> wrote:
> <>
> On Aug 2, 2012, at 2:33 AM, Alessandro wrote:
>
>> 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 don't think this is quite true. See what happens to the VIF when the interacted variables are centered. Also note that the elasticity
> estimates change, and become very imprecise with centering.
>
> sysuse auto, clear
> qui reg price length weight c.length#c.weight
> estat vif
> margins, eyex(_all)
> // center from SSC (Jann)
> center price length weight
> qui reg c_price c_length c_weight c.c_length#c.c_weight
> estat vif
> margins, eyex(_all)
>
> Kit
>
>
> Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
>                              An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
>   An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html
>
>
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