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

 From jhilbe@aol.com To statalist@hsphsun2.harvard.edu Subject Subject: st: how to interpret interaction effects in negative binomial model Date Tue, 23 Mar 2010 11:42:42 -0400

I have written an appendix for a forthcoming book on constructing and interpreting interactions for count models. I'll send it to the email address given in your communication. If you happen to have a copy of my book, Logistic Regression Models (2009, Chapman & Hall/CRC) , I devote an entire chapter to the construction and interpretation of interactions for logistic models. The logic of construction is fairly much the same -- but not identical -- for count models. The interpretation, of course, differs. But for an overview of constructing interactions for nonlinear models it is I think a good resource. If you have it available you may want to check it out. But this appendix should give you guidance on resolving your query specifically for count models such as the negative binomial. .
```
Joseph Hilbe

From: "WANG Shiheng" <acwang@ust.hk>
```
Subject: st: how to interpret interaction effects in negative binomial model
```
Dear all,

```
I have a question about how to interpret the interaction items in negative binomial regression.
```
```
In the following model â€œpostâ€ is a dummy variable (0 or 1) to indicate two different periods (0 represents the first period, 1 represents the second
```period).  â€œtreatmentâ€ is a dummy variable (0 or 1) to indicate two
```
different groups â€“â€œtreatment sampleâ€(1) vs. â€œcontrol sampleâ€ (0). The
```interaction is the product of the two dummies. The dependent variable is
the number of analysts. My research objective is to examine whether the
number of analysts changes over the two periods, and whether the changes
over periods differ between the treatment sample and control sample.

I have the following questions for the estimates below:

```
(1) the coefficient on "post" is not significant, does this mean that the
```change in the number of analysts from period 1 to period2 is not
statistically significant in the control group?

(2) the coefficient on the interaction term "post*treatment" is
significantly positive, does this mean that the change in the number of
analysts from period 1 to period2 is significantly greater in the
```
treatment sample than the control sample? How to interpret the coefficient
```on the interaction term exactly? How can I calculate if the changes in
```
number of analysts from period 1 to period 2 differ between the treatment
```sample and control sample?

```
Negative binomial regression Number of obs = 30274 Dispersion = mean Wald chi2(37) = . Log pseudolikelihood = -27412.392 Prob > chi2 = .
```
```
```(Std.Err.adjusted for 45 clusters in n)
```
- -------------------------------------------------------------------------
```--
|             Robust
```
Analysts | Coef. Std. Err. z P>|z| [95% Conf. Interval] - -----------+-------------------------------------------------------------
```
```
post .0610886 .0743914 0.82 0.412 -.0847159 .2068931 treatmen -2.975135 .1591135 -18.70 0.000 -3.286992 -2.663278 post*treatment .214007 .0730457 2.93 0.003 .0708402 .3571739 - -------------------------------------------------------------------------
```--

- --

Shiheng Wang

Assistant Professor
Department of Accounting
Hong Kong University of Science and Technology

Tel: 852 2358 7570
Fax: 852 2358 1693
Email: acwang@ust.hk

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```