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

[Maarten Buis <maartenlbuis@gmail.com>]

On Thu, Aug 2, 2012 at 3:41 PM, Alessandro Freire wrote:
> 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).

Here I have to disagree: If you interpret coefficients correctly than
they are more robust estimates of effects.

Average marginal effects require that your sample is representative
with respect to all variables in your model, while effects in the
natural metric of the model are more robust as they relax that
requirement with respect to the
explanatory/right-hand-side/independent/x-variables.

Marginal effects at the average (or other representative) values of
explanatory variables have their uses, but often have an arbitrary
feel about them; why did you choose the average and not some other
value? With effects in terms of the natural metric of the model you
don't need to evaluate it at some specific point.

Correct marginal effects of interaction terms can be highly variable
across individuals, thus limiting the usefulness of a single number
summary like the average marginal effect. It is often more correct ---
but not very useful --- to say that the marginal effect of the
interaction terms is significantly positive for some, significantly
negative for others, and non-significant for the rest. Again, effects
in terms of the natural metric of the model do not suffer from this
problem.

I don't say that marginal effects are completely useless, but I do say
that they are used way too much.

> 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.

Again I have to disagree: centering allows you to turn the
coefficients into effects without resorting to additional programs
like -margins-, especially with interaction effects. Consider the
following (extreme but not unrealistic) example:

*---------------------- begin example ------------------------
sysuse nlsw88, clear
gen byr = 1988-age
label var byr "year of birth"

// effect of grade is for cohort born in year 0
// effect of byr is for women with 0 years of education
glm wage union c.grade##c.byr i.race c.ttl_exp##c.ttl_exp, ///
    link(log) vce(robust) eform
*----------------------- end example -------------------------

We use the log link, so the natural metric for the effects in this
model are ratios of mean wages. The interaction term between byr and
grade, means that the main effect of grade is for the cohort born in
the year 0 (a rather drastic extrapolation). We can see that according
to our model women with 1 more year of education born in the year 0
are expected to earn (1-.11)*100%=-89% less. Of course you should not
take this result seriously.

You could compute more relevant effect from this result (e.g. using
-lincom _b[grade]+1950*_b[c.grade#c.byr], eform-). However, it is
safer is to center your variables, as the commands needed for
centering are typically easier, and thus less bug-prone, than the
post-estimation commands, and that way you do cannot forget to use the
post-estimation commands. In the case of the example I would do this
as follows:

*---------------------- begin example ------------------------
// center byr at 1950 and change unit to decades
// center grade at 12 (highschool)
gen c_byr = (byr - 1950	)/10
gen c_grade = grade - 12


// effect of grade is for cohort born in year 1950
// effect of byr is for women with 12 years of education
glm wage union c.c_grade##c.c_byr i.race c.ttl_exp##c.ttl_exp, ///
    link(log) vce(robust) eform
*----------------------- end example -------------------------

Hope this helps,
Maarten

---------------------------------
Maarten L. Buis
WZB
Skill Formation and Labor Markets
Reichpietschufer 50
10785 Berlin
Germany


http://www.maartenbuis.nl
---------------------------------
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