# how to interpret interaction effects in negative binomial model

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## 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: [hidden email] * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/
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## Re: how to interpret interaction effects in negative binomial model

 --- 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. >               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.htmlTo 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--------------------------       * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/