Maarten--
It only makes sense to look at marginal effects at the mean if the
vector of means of the explanatory variables is a sensible point to
examine the marginal effect for; if that vector represents a unit that
is not observed in the data, or cannot be observed, as is often the
case--for example, with many binary explanatory variables in the list
of explanatory variables, it is rare that a vector of means represents
a sensible point at which to examine the marginal effect. It may be
that the combinations of mean x1 and mean x2 are logically
inconsistent, even, so that point could never exist.
Capturing the distribution of explanatory variables is precisely the
aim of looking at the mean marginal effect rather than the marginal
effect at the mean, but I agree looking at marginal effects for
various specific vectors of explanatory variables, for vectors that
represent some hypothetical unit of interest, also makes sense; I just
don't think the mean vector often falls in this category, and
certainly does not by default--it is an assertion that needs to be
examined in each specific case that a marginal effect at the mean is
informative in any way.
Of course, in practice, the marginal effect at the mean is often very
close to any average of observation-specific marginal effects you
might actually be interested in, but that does not change the
essential point. I don't think my statement is a bit strong, in other
words--I could make it even stronger and back it up with examples--and
yet I think we are not too far apart in our fundamental attitudes
toward marginal effects.
On Fri, Jan 22, 2010 at 5:53 AM, Maarten buis <[email protected]> wrote:
>
> --- Austin Nichols wrote:
>> You should really not use -mfx- or -dprobit- at all, as the marginal
>> effect at the mean is not informative for most purposes
>
> I think that is a bit strong. When it comes to interpreting these
> interaction effects with marginal effects I would probably use both,
> as the average marginal effects not only include differences in
> effect but also differences in the distribution of the controll
> variables. The marginal effects at the means, by necesity control
> for this. So by looking at both I get an idea of how much is due
> differences in effects and how much is due to differences in
> distributions of the controll variables.
>
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