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

 From Andrea Bennett To statalist@hsphsun2.harvard.edu Subject Re: st: probit with interaction dummies (significance and marginal effects) Date Thu, 17 Jul 2008 17:52:38 +0200

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).

Any other good advice is greatly appreciated!

Kind regards,

Andrea

On Jul 17, 2008, at 4:45 PM, Maarten buis wrote:

```--- 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

-----------------------------------------
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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