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# Re: st: Margins after xtprobit, re.

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: Margins after xtprobit, re. Date Tue, 30 Aug 2011 19:46:37 +0200

```On Tue, Aug 30, 2011 at 6:47 PM, natasha agarwal wrote:
> I was trying to estimate the following model:
>
> xi: xtprobit expdum a b a*b y14-y18 i.industry i.region, re
>
> where a = continuous and b = categorical.
>
> Now I wanted to compute the average partial effect of the
> specification with the main interest lying at the estimated
> coefficient on the interaction term.
>
> I use margins, predict(pu0) dydx(*)
>
> I do get the marginal effects for all the variables in the
> specification but I wanted to know whether the average marginal effect
> calculated by margins for the interaction term is correct and how
> would one interpret the same?

The marginal effect for the interaction term is wrong, see: Norton et
al. (2004). In general if you want to use -margins- you should not use
-xi- but use the factor variable notation instead. It is crucial that
all interactions are also created with the factor variable notation. A
consequence will be that no marginal effects for the interaction term
will be computed, but that is much better than a wrong marginal
effect...

There is no easy way to get correct average marginal effects for
interaction terms in such multi-level model, as doing that right you
also need to average over unobserved group level error term. The best
and easiest way is to use -xtlogit- and interpret the odds ratios.
They have a bad reputation as being hard to interpret, but if you take
the logic step by step it becomes suddenly easy. See for example: Buis
(2010). A compendium of several statalist post on this issue can be
found at <http://www.maartenbuis.nl/publications/interactions.html>.

Hope this helps,
Maarten

Maarten L. Buis (2010) "Stata tip 87: Interpretation of interactions
in non-linear models", The Stata Journal, 10(2), pp. 305-308.

Edward Norton, Hua Wang, and Chunrong Ai (2004) "Computing interaction
effects and standard errors in logit and probit models" The Stata
Journal, 4(2): 154-167.

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

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