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st: interaction effect in logit model with orthogonal predictors (-inteff-)


From   "Eva Poen" <eva.poen@gmail.com>
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   st: interaction effect in logit model with orthogonal predictors (-inteff-)
Date   Thu, 13 Mar 2008 11:34:55 +0000

Hello,

I have a question concerning interaction effects in logit models. In
my model, a subset of the regressors are mutually exclusive dummy
variables (i.e. orthogonal). They represent different categories of a
single variable. The regression looks like this:

- xi: logit y i.x*i.cat1 cat2 cat3 other regressors -

where the dependent variable y is a dummy, x is a dummy (take female,
for instance), cat1-cat3 represent three categories of a variable
where the base category has been omitted, and other regressors can be
dummies or continuous variables.

To compute the interaction effect of x and cat1 I can use the -inteff-
routine. Looking at inteff.ado and logit_dd.ado, I can see that in
order to compute that effect, four predictions are obtained from the
model for each observation: one for each combination of x and cat1
being 1 or 0.

However, this means that for each observation, cat1 is set to 1 for
some of the computations, leaving the values of cat2 and cat3
unchanged. But it is impossible for an observation to have cat1=1 and
cat2=1 at the same time. The interaction effects for these
observations seem rather hypothetical to me.

What is the appropriate thing to do? Taking the interaction effects
from -inteff- and not worrying about orthogonal predictors, or
changing the routine to take care of orthogonal predictors accordingly
(i.e. changing cat2 and cat3 to zero if appropriate in the
calculations). I tried the latter, and it does make a difference with
my data.

Thanks,
Eva
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