st: Why -margins- does not present marginal effects for interaction terms

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

I asked Stata Tech support why the -margins- command does not produce 
marginal effects for interaction terms. They said I was free to 
forward this to the list. I think this is very consistent with what I 
and others have been saying the last few days, and with what I have said at

http://www.nd.edu/~rwilliam/stats/Margins01.pdf

http://www.statajournal.com/article.html?article=st0260

I think they are basically saying that yes, you could compute a 
marginal effect for an interaction term, and it wouldn't be wrong, 
but would you really want to? There are better ways of getting at the 
things researchers are really interested in.

> From: Stata Technical Support <tech-support@stata.com>
> To: Richard Williams <Richard.A.Williams.5@nd.edu>
> Date: Mon, 7 Jan 2013 14:15:13 -0500
> Subject: Re: Marginal effects of interaction terms
>
>
> Dear Richard,
>
>
> From our experience, when users ask for "interaction effects", they 
> are mostly
> interested in some way to explain or visualize the interaction.
>
> As you pointed out, the philosophy behind -margins-, is that you enter actual
> variables in your model, and you compute the effects of those actual variables
> on the prediction. If your model includes x1, x2, and x1*x2, the variables in
> your model are x1 and x2.
>
> -margins-, with the option -dydx()-, answers questions like the following:
>
>         If I increment x1 on one unit, how much will my prediction be
>         affected?
>
> We can't change x1*x2 without also making changes to x1 and x2, so it is
> impossible to try to explain the effect of x1*x2 in isolation of x1 and x2.
>
> Usually, when a researcher wants to see how two variables interact, the most
> natural way to do that is to use -margins- with a range of values specified in
> the -at()- option, then follow it up with a call to -marginsplot-.  For
> example, the following shows how sex and age affect the marginal predicted
> probability of a positive outcome:
>
>         . webuse nhanes2, clear
>         . logit heartatk age i.sex  i.sex#c.age age c.age#c.age bmi
>         . margins sex, at(age = (20(5)75))
>         . marginsplot
>
> Besides the documentation in -[R] margins- and -[R] marginsplot-, there is
> also a nice article about this in the last issue of the Stata News, available
> at:
>
>         http://www.stata.com/stata-news/statanews.27.4.pdf
>
> We are aware that there are other takes to the construction of marginal
> effects, and some authors report a second derivative as the marginal effect
> due to the interaction between two continuous variables.  We find nothing
> wrong with this practice, except that a single number rarely tells the whole
> story in this case.  It was for this reason and our belief that most
> researchers are interested in other things that we decided to only implement
> effects based on first order derivatives in -margins-.
>
> With the addition of -contrast- and contrast operators in -margins- in Stata
> 12, it is possible to compute all the discrete interaction effects.  The
> contrast operators can be combined with continuous variables in the -dydx()-
> option to compute effects of interactions that also contain a single
> continuous variable.
>
>
> Sincerely,
>
> Isabel
>
>
> Isabel Canette, Ph.D.
> Senior Statistician
> StataCorp LP

-------------------------------------------
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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