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Re: st: Binary Choice Model and fixed effects - interpreting the interaction effects?


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Binary Choice Model and fixed effects - interpreting the interaction effects?
Date   Mon, 2 Apr 2012 12:10:55 +0200

On Mon, Apr 2, 2012 at 11:57 AM, Benjamin Niug wrote:
> I want to estimate a binary choice model accunting for time-invariant
> fixed effects (I read I could use the -xtlogit- or -clogit- command).
>
> y_it = b_1*x_1_it*x_2_it+b_2*x_1_it + b_3*x_2_it
>
> However, I have included an interaction effect which I want to
> interpret correctly - as pointed out by Ai and Norton (2004) this is
> not trivial. They suggest to use a user written command called
> -inteff-. This command works well if -logit- is used, however, it does
> not work if -xtlogit- or -clogit- is used.

Please note that just author-year references are not appreciated on
this list. Please give the complete reference. This is discussed on
the Statalist FAQ. The logic is that this is a multi-disciplinary
list. Even if a citation is so famous within your
(sub-(sub-)discipline that author-year suffices, this is likely not to
be the case for the rest of the world. However, often many disciplines
will have independently faced (and solved) the same problem, and they
have something useful to say about the subject.

You have a double problem here: a) interpreting marginal effects of
interaction terms is hard, and b) interpreting marginal effects in
multi-level/panel/fixed effects models is hard. So the combination of
the two means that that is going to be very hard.

However, the solution is simple: don't do marginal effects but
interpret your coefficients in the natural metric of the model. In
this case the odds of success. Odds, odds ratios and ratios of odds
ratios have an undeserved reputation of being hard to interpret. You
can see an example of how easy that is here in:

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

Hope this helps,
Maarten

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


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