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

 From "Stephen P. Jenkins" To Subject RE: Re: st: probit with interaction dummies (significance and marginal effects) Date Sat, 26 Jul 2008 16:19:58 +0100

```> Date: Fri, 25 Jul 2008 06:04:42 -0400
> From: "Erasmo Giambona" <e.giambona@gmail.com>
> Subject: Re: st: probit with interaction dummies
> (significance and marginal effects)
>
> Dear Statalisters,
>
> I have found this thread particulalrly interesting. I have found the
> questions asked by Andrea and especially the answer of Marteen very
> useful. However, despite having read a lot about it over the last
> several days, it is still hard for me to have a good intuition on
how
> to intepret interaction terms in logit regressions. I have also
found
> that papers in finance (my field) usually miss to provide a clear
> interpretation of interaction terms in logit regressions.
>
> I truly hope some other people might join the thread to
> provide more insights.
>
> Here is my major source of confusion. Consider the case of
interaction
> of two continuos variables (e.g., profit and number of employees) in
a
> logit model. The dependent variable is 1 if the firm's ceo is fired
> and zero otherwise. The coefficient estimate on the interaction from
> the logit output is positive (for example, +0.25) and statistically
> significant. I interpret this to mean that the odds that the ceo is
> fired are higher when both profit and number of employees are large
> (small) in absolute term (rather than changes). However, Ali et al.
> (2004) show that the marginal effect for the interaction of two
> continuos variables can be negative even if its coefficient estimate
> is positive. Assuming that the marginal effect is negative (e.g.,
> - -0.2) in my example, I would interpret this to mean that the
> likelihood of firing the ceo decreases by 20% on average as the
> interaction term increases by 1%.
>
> Assuming that my way of interpreting coefficient and marginal effect
> of the interaction term in a logit is correct, I would still find it
> hard to reconcile the "seemingly contradictory" evidence of the
above
> example.
>
> I hope this can stimulate further discussion on the issue.
>
> Best regards,
> Erasmo
>
> Reference
> Norton, Wang, & Ai. 2004. Computing interaction effects in logit and
> probit models. The Stata Journal 4(2):103116.

recommend using post-estimation predicted probabilities as a way to
explore these issues -- either using -nlcom- or -predictnl- depending
on what you want to do. (This works for either probit or logit
models.)  I think I recall that all of Norton et al's calculations can
be done using these commands, and more.

The idea is to use predicted probabilities to in effect explore what
Peter Lachenbruch <Peter.Lachenbruch@oregonstate.edu> yesterday
described as "effect modification:  the effect of predictor A is
different at different levels of predictor B."   You can calculate how
probabilities vary for different combinations of regressor values
(where some of those may include interactions).

For a very clear exposition of how to use a predicted probability
approach, see "Group comparisons and other issues in interpreting
models for categorical outcomes using Stata
by J. Scott Long", North American Stata Users' Group Meetings 2006,
to the pdf of presentation appears to be broken, but the pdf file is
inside the zip file that is also there.)

Although not directly about the interaction effects case, there is
relevant material included in Scott's superb presentation. He shows
how to get standard errors as well as predicted probabilities, and
also how to graph the results in an informative manner.

Stephen
-------------------------------------------------------------
Professor Stephen P. Jenkins <stephenj@essex.ac.uk>
Director, Institute for Social and Economic Research
University of Essex, Colchester CO4 3SQ, U.K.
Tel: +44 1206 873374.  Fax: +44 1206 873151.
http://www.iser.essex.ac.uk
Survival Analysis using Stata:
http://www.iser.essex.ac.uk/teaching/degree/stephenj/ec968/

Learn about the UK's new household panel survey, the United Kingdom
Household Longitudinal Study: http://www.iser.essex.ac.uk/ukhls/

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