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

[jhilbe@aol.com]

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 “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. 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
- 
-------------------------------------------------------------------------
--

Your help is greatly appreciated.

- --

Shiheng Wang

Assistant Professor
Department of Accounting
School of Business and Management
Hong Kong University of Science and Technology

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


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