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

From   Thomas Cornelissen <>
Subject   Re: st: probit with interaction dummies (significance and marginaleffects)
Date   Wed, 30 Jul 2008 12:27:27 +0200

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 Cornelissen
Institute of Empirical Economics
Leibniz Universität Hannover, Germany

On Fri, Jul 18, 2008 at 5:00 AM, Andrea Bennett <> 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?


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 <> 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
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

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

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