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Re: st: interaction effect with logit


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: interaction effect with logit
Date   Wed, 5 Sep 2012 16:54:09 +0200

On Wed, Sep 5, 2012 at 2:34 PM, Luca Fumarco wrote:
> 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.)

I don't disagree with Norton et al. on what an interaction effect in a
logit model is: it is a ratio of odds ratios. This is exactly the
point of my Stata tip.

We disagree on the point of interpretability: he claims that he they
cannot understand that, I claim I do and that you can too. The logic
is to take it step by step: start with the baseline odds to refresh
the audience's memory about what an odds is, move on to one of the
main effect to refresh the audience's memory about that we are
comparing groups with ratios rather than differences, and than go to
the interaction effect.

We also disagree on the usefulness of marginal effects. In essence I
see marginal effects as attempts to get an interpretation like a
linear probability model without admitting that in essence you
estimated a linear probability model in disguise. As a consequence you
get the worst of two models. So if you really believe that you want
effects in terms of constant differences (and differences in
differences for the interaction effects), be honest and estimate a
linear probability model with all the associated advantages and
disadvantages. Otherwise use a logit and interpret the results in its
natural metric: odds, and odds ratios (and ratios of odds ratios for
interaction terms).

Hope this clarifies things,
Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

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

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