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Re: st: AW: Interpreting interactions in probit and logit models

From   Maarten buis <[email protected]>
To   [email protected]
Subject   Re: st: AW: Interpreting interactions in probit and logit models
Date   Mon, 11 Jan 2010 00:41:27 -0800 (PST)

--- On Sun, 10/1/10, Fabio Zona wrote:

> From: Fabio Zona <[email protected]>
> I am updated with the recent advancements on appropriate 
> methodologies to check for sig of interaction effects on 
> probability. I just want to know better the difference 
> between a. sig of an interaction effect on probability
> versus b. sig. of an interaction effect on a latent variable.
> My problem is: I have some interaction coefficients which
> are sig; however, the inteff and other tests show that the
> interaction term has no sig effect on probability. 
> Hence, I only have significance of an interaction
> coefficient, and can onluy interpret is as a sig effect on a
> latent variable.
> If I interpret the interaction effects in terms of the
> effect on the latent variable, what does this exactly mean?
> What can I infer from this?

The easiest way is to look at the exponentiated coeficients in a logistic
regression. Those can be directly interpreted as the ratio change in 
effect (in terms of odds ratios) for a unit change in one of its 
consituent variables. The siginificance can differ from what you get when
you look at effect sizes in terms of probability, as odds ratios and risk 
differences measure something sublty different. Odds ratios can be thought
of as relative effects and risk differences as absolute effects. Which effect size you want depends on your question. In particular do you want
to control for changes in the marginal distribution of your dependent and 
independent variable. For example, if your dependent variable is whether 
or not a respondent is unemployed, and you are comparing two regions, in 
one the unemployment rate is high and in the other it is low, and you are 
interested in the effect of being a women on being unemployed. It could  
be that in both regions the odds of being unemployed is twice as high for
women as it is for men, however since the baseline odds of being unemployed
is much higher in one region, there difference in probability of being 
unemployed between men and women would be much larger in high unemployment
area than in the low unemployment area. So the odds ratio "controls" for
differences in the baseline unemployment rate, while the risk difference
does not.

As practical point, many disciplines are used to one type of question and 
tend to automatically consider one type of effect as "correct" and the 
other as "biased". In my sub-discipline, the risk differences are often 
treated as biased, while in economics they only seem to know risk 
difference, often called marginal effects. This is obviously narrow 
minded of both disciplines, but it is a constraint we must learn to live 

Hope this helps,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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