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# Re: st: how to interpret interaction effects in negative binomial model

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: how to interpret interaction effects in negative binomial model Date Tue, 23 Mar 2010 01:08:48 -0700 (PDT)

```--- On Tue, 23/3/10, WANG Shiheng wrote:
> I have a question about how to interpret the interaction
> items in negative binomial regression.
>
> In the following model “post” is a dummy variable (0 or
> 1) to indicate two different periods (0 represents the
> first period, 1 represents the second period).
> “treatment” is a dummy variable (0 or 1) to indicate two
> different groups –“treatment sample”(1) vs. “control
> sample” (0). The interaction is the product of the two
> dummies. The dependent variable is the number of analysts.
<snip>
>               coef       se
> post          .0610886  .0743914
> treatmen     -2.975135  .1591135
> post*treatment .214007  .0730457

I would analyse these results in terms of incidence rate
ratios, by adding the -irr- option. You can do it also by
hand, by computing irr = exp(coef) (but why do it yourself
if Stata can do it for you?). The basic logic behind this
type of interpretation of interaction terms in non-linear
models is discussed here:
http://www.maartenbuis.nl/wp/interactions.html

To come back to your case:

The expected number of analysist in the non-treatment group
increases by a factor exp(.061)= 1.06 (i.e. 6%) when a firm
went from the pre-period to the post-period. This ratio is
however not significant. [1]

This effect of post increases by a factor of exp(.214) =
1.24 (i.e. 24%) if the firm is in the treatment group. This
change in effect is significant. [1]

The expected number of analysists in the pre-period group
changes by a factor of exp(-2.975) = .05 (i.e. a change of
-95%) when a firm receives the treatment. This effect is
significant. [1]

This effect of treatment changes by a factor of exp(.214) =
1.24 (i.e. the effect becomes 24% less negative) in the
post-period. This effect is significant. [1]

Hope this helps,
Maarten

[1] It may come as a surprise that I use the test that
coef = 0 to test the hypothesis that exp(coef) = 1. The
logic behind this choice is discussed here:
http://www.stata.com/support/faqs/stat/2deltameth.html

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------

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