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st: interaction effect with logit


From   Luca Fumarco <luca.fumarco@lnu.se>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: interaction effect with logit
Date   Wed, 5 Sep 2012 14:34:26 +0200

Dear Stastalisters,

I have a problem of interpretation. I am going to use a very simple model, just two variables X1 and X2, plus a term representing their interaction X1*X2.
The problem is given by the nature of the dependent variable, which is a dummy.

In Maarten L. Buis, "Stata tip 87: Interpretation of interactions in non-linear models",  The Stata Journal (2010) Vol. 10 No. 2, pp. 305-308, and from discussion with fellow researchers I understand that the logit model is better. 
However, in Edward C. Norton, Hua Wang, Chunrong Ai, "Computing interaction effects and standard errors in logit and probit models",  The Stata Journal (2004) 4, Number 2, pp. 154–167, they illustrate how what we would tend to interpret as an odd ratio is instead  something different....the ratio of odds ratios (i.e.,odds ratio for X1|X2=1/odds ratio for X1|X2=0) !?

I do not see in which way the computational issue illustrate in Norton et al. is solved using the logit, since also this model is affected by the issue (see paragraph 2.6 Odds ratio in Norton et al.)

Cordially

Luca 

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