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Re: st: interactions in non-linear models


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: interactions in non-linear models
Date   Sun, 20 Jun 2010 01:31:27 -0700 (PDT)

--- On Sat, 19/6/10, Fabio Zona wrote:
> is it correct to say that, when testing interaction effects
> in dichotomous dependent variables:
> 
> - one can use logistic regression instead of logit, and the
> coefficient express the effects on a multiplicative scale

you can either use -logit- in combination with the -or- option
or -logistic-, both will give you the odds ratios for the main
effects, and the ratio of odds ratios for the interaction 
effect.
 
> - the significance of interaction coefficient is tested
> ONLY by looking at the significance of the interaction
> coeffiicent itself, with no need to calculate the marginal
> effects using inteff by Ai and Norton, 2003

Depends on the null-hypothesis that you want to test. The point
I try to make in my forthcomming Stata tip that you refer to is
not that one is the right method for testing interaction effects,
rather that both test subtly different null-hypotheses. 
 
> - by presenting the effects on a multiplicative scale, the
> logistic regression allows to test interaction effects AND
> to control for differences in baseline odds.

That is what you do when looking at odds ratios. However, 
whether you want to controll for differences in the baseline
odds is a substantive question. If you don't then you are better
off looking at -inteff- (I believe that the newest versions can 
be downloaded from <http://www.unc.edu/~enorton/>).
 
> I ask you this as an interpretation of the Stata tip :
> interpretation of interactions in non-linear models, by
> Maarten Buis.

This Stata tip has been accepted for publication, but hasn't
appeared yet. A pre-publication draft can be found at:
<http://www.maartenbuis.nl/publications/interactions.html>

> Last question: in other words, if I test an interaction (or
> multiple interactions at the same time!) using logistic
> (instead of logit) and the interaction coefficients are are
> - says - positive and significant, can I be safe that the
> interactions are positive and significant? And what does
> this says to me (as compared to logit model, which needs
> inteff)? what's the difference in interpretation?

The difference is not between -logit- and -logistic-, but 
between marginal effects and odds ratios. In other words,
how you define the effect: An effect is just a comparison
of the expected outcome between (real or counterfactual) 
groups. Such a comparison can take place by compute a 
difference, in which case you look at a marginal effect,
or a ratio, in which case you look at the odds ratio.

Linear regression (-regress-) is a model that is build for
the interpretation of effects in terms of differences. Many 
non-linear models like logistic regression models 
(-logit- and -logistic-) or Poisson reggresion and their
kin (-poisson-, -zip-, -nbreg-, etc.) or survival analysis
models (-streg-, -cloglog-) are build such that the 
interpretation in terms of ratios is the most natural
interpretation. So that is why interpretation of interaction
effects in terms of ratios is so much easier in these models.

What that difference means in substantive terms I refer
to the example in the Stata tip, I don't know of a better
way of explaining that difference than concrete example.

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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