Re: st: probit with interaction dummies (significance and marginaleffects)

[Thomas Cornelissen <cornelissen@ewifo.uni-hannover.de>]

Hi Andrea,
My unserstanding of the questions you raised in your summing up is the following:

You suggested to interpret your coefficient on the interacted regressor directly from the probit regression output.
This is only correct if you want to interpret effects of the regressors on the latent variable y*=x'b+u which underlies your probit model.
If the latent variable y* of your probit model has a meaningful interpretation (propensity, utility) on which your interest focuses, then that's fine.
This is what Marten said about "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-".
(But then you should not use -dprobit- or -mfx- after probit but only the regression coefficents of -probit-).
If you opt for this interpretation, then you can also interprete multiple interactions (e.g. female interacted with two education dummies) in the same way as you would do it in a linear regression.

If you rather want to analyse effects on the probability P(y=1)=P(y*>0) then you should interprete the output of -inteff-. The question whether to use -inteff- or not is therefore not a question of the nature of the two interacted variables (dummies or continues or mixed),
because -inteff- can also deal with interactions of two dummies for example. But -inteff- can not deal with the situation when you interact female with more than one other variable, as you suggested with your two education dummies.
In that situation (if you are interpreting effects on P(y=1) and not on y*) then you have to produce your own inteff taylored to your model using -predictnl-.

My understanding of problem 2 raised by Maarten is that this is a deeper problem, that one should be aware of it, but that this problem does not affect your choice between interpreting effects on y* versus interpreting effects on P(y=1)
and therefore also not the choice between simple probit output versus the -inteff-/-predictnl- output.
Best regards,
Thomas

--
Thomas Cornelissen
Institute of Empirical Economics
Leibniz Universität Hannover, Germany



On Fri, Jul 18, 2008 at 5:00 AM, Andrea Bennett <mac.stata@gmail.com> wrote:
> 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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