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Re: st: Interpreting triple interactions


From   Philip Ender <ender97@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Interpreting triple interactions
Date   Wed, 8 Sep 2010 08:12:53 -0700

Erasmo Giambona <e.giambona@gmail.com> wrote:

I am using panel data to estimate an Investment model. On the
right-hand-side, I have a triple interaction term involving 3 dummy
variables. Namely, whether the firm is Small (S), whether the firm is
European (E), and finally wether New Accounting (NA)standards are in
place. The regression also includes all the individual dummies as well
as their pairwise interactions. 7 regressors in total. My variable of
interest is the triple interaction, which essentially is a
difference-in-difference-in-differences estimator. The triple
interaction (S*E*NA)enters the regression with a positively
significant coefficient.

I am having hard time interpreting this result. Does the positive
triple interaction mean that Small, European firms, after New
Accounting standards are investing more than Small European firms
prior to the New Accounting standards?

Can somebody provide some help including some good reference if available?

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

Dear Erasmo-

One way of looking at this interaction is that there is a 2-way
interaction that differs for each level of the third variable.  A good
starting point is to get your eight cell means and try graphing them
in various combinations.  You didn't mention which version of Stata
that you use so below there are links for both Stata 11 and earlier.

If you have Stata 11, you might find this page helpful:

http://www.ats.ucla.edu/stat/stata/faq/margins_3way.htm

Id you are using Stata 10 or earlier this presentation at the 2008
Fall North American Stata Users Group meeting may be useful:

ender_3way_anova.pdf

Best of luck.

-- 
Phil Ender
UCLA Statistical Consulting Group
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