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


From   Nick Cox <njcoxstata@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 11:23:50 +0100

As my own earlier post indicated, people interested in -inteff- should
download the later version from 4-3. This won't help your problem.

On Mon, Apr 2, 2012 at 11:19 AM, Benjamin Niug
<benjamin.niug@googlemail.com> wrote:
> Sorry for the shortcomings of the description of my problem:
> @Nick: It is  SJ4-2: st0063;
> @Maarten: Norton, Wang, Ai (2004), "Computing interaction effects and
> standard errors in logit and probit models", The Stata Journal 4,
> Number 2, pp. 154-167.
>
> Besides:
> @Maarten: Thanks for the odds ratio hint. Do you know of other
> solutions as well?
>
> Am 2. April 2012 12:10 schrieb Maarten Buis <maartenlbuis@gmail.com>:
>> 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.
>>

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