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

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: probit with interaction dummies (significance and marginal effects) Date Thu, 17 Jul 2008 15:45:25 +0100 (BST)

```--- Andrea Bennett <mac.stata@gmail.com> wrote:
> I am a little confused after reading multiple posts from the
> Statalist how I can make sure I do interpret interaction dummies
> correctly when using a probit estimation.

I have no easy solution but I hope I may clarify the issue a bet. To
see the problems it is useful to look at probit in a partucular way:

There is a latent variable (y*) which is a linear function of your
explanatory variables and a normally distributed error term. You
observe y, which is one when y*>0 and is 0 when y*<0.

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. This issue is discussed
in (Norton et al. 2004)

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. Rich Williams
has collected a large amount of material on this issue at:
http://www.nd.edu/~rwilliam/oglm/index.html

Hope this helps,
Maarten

E. C. Norton, H. Wang, and C. Ai. 2004. Computing interaction effects
and standard errors in logit and probit models Stata Journal Volume 4
Number 2: pp. 154-167.
http://www.stata-journal.com/article.html?article=st0063

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Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
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