Re: st: probit with interaction dummies (significance and marginal effects)

[Andrea Bennett <mac.stata@gmail.com>]

Thank you so much!

May I sum up for clarification: When I am using e.g. a probit model  
with a dependent variable Y and include an interaction term  - 
female*wage- and I am primarily interested in the interaction effect  
of a woman with wage then it is save to use the standard regression  
output to interpret the direction (AND the significance?) from the  
regression table. E.g. if the beta-estimators are -female- ==0.5, - 
wage- == 0.34 and -female*wage- == -0.03 and all being significant  
then I can say that the wage effect is significantly smaller when  
being a woman? Does this also hold when one is formulating models like  
-female*low_education-, -female*mid_education-, -female- 
high_education-? Or did I misinterpret you line "as long as you  
interpret the effects in terms of the effect on the latent variable  
you are ok in simply using the output from -probit-"?

When I want to know if (and for which range) the interaction of female  
and wage has a significant effect on Y I should use -inteff-. When I  
want to do the same for the interaction of female with the education  
levels, then there is not yet consensus on how it shall be done.  
Norton et al. 2004 mention -predictnl- but urge to use it with extra  
care. Another source would be Rich Williams webpage.

Did I completely mess it up (I fear so!) or is it like I described?

Andrea


On Jul 17, 2008, at 6:13 PM, Maarten buis wrote:


> Regarding problem 1, this is just a matter of interpretation, as long
> as you interpret the effects in terms of the effect on the latent
> variable you are ok in simply using the output from -probit-, if you
> want to interpret the results in terms of the probability you should
> use -inteff-.
>
> Problem 2 is much harder to solve. Any solution would in one way or
> another try to controll for things that haven't been observed. It
> should not come as a surprise that that is hard (read: impossible).  
> So,
> the fact that "the solution" hasn't been implemented yet in Stata is
> not so much a problem with Stata but with the state of the statistical
> science: we know the problem, but we just don't know the answer.  
> Though
> Rich Williams discusses one solution on his website.
>
> -- Maarten
>
> --- Andrea Bennett <mac.stata@gmail.com> wrote:
>
> > Thanks for the link! Still, I wonder if there's really no Stata
> > command I could use to "simply" test if the interaction is
> > significant and what influence (direction) it has on the dependent
> > variable. I'd be just rather surprised if this does not exist
> > because it seems to me this is a very common issue in any regression
> > design (interaction effects).
> --- Maarten buis wrote:
> > > There are two distinct issues when interpreting interaction effects
> > > in a probit:
> > >
> > > 1) a significant positive (negative) interaction in terms of the
> > > latent
> > > variable does not mean a significant positive (negative)
> > > interaction effect in terms of the probability that y = 1.
> > >
> > > 2) The scale of the latent variable is identified by setting the
> > > residual variance at 1. If the residual variance differs between
> > > the groups than that means that the scale of the latent variable
> > > differs between the groups and when comparing differences in
> > > effects across the groups you are basically comparing apples and
> > > oranges.
>
> -----------------------------------------
> Maarten L. Buis
> Department of Social Research Methodology
> Vrije Universiteit Amsterdam
> Boelelaan 1081
> 1081 HV Amsterdam
> The Netherlands
>
> visiting address:
> Buitenveldertselaan 3 (Metropolitan), room Z434
>
> +31 20 5986715
>
> http://home.fsw.vu.nl/m.buis/
> -----------------------------------------
>
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