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I have a hard time interpreting my coefficients in my nonlinear regression. In particular, I have a negative binomial, with two dummy variables: Treatment and (being) foreigner, outcomes are count data.

In my first estimation, I have

     Variables |   Coef.     P>|z|     
     Treatment |   -0.05     0.896  
     Foreigner |   -0.7     .0.035   

So the treatment does not seem to have an impact and foreigner is significant.

In my second estimation, I have an interaction terms and thing dramatically changes. The AIC and BIC improves a lot.

            Variables |   Coef.     P>|z|     
            Treatment |   -0.9       0.04  
            Foreigner |   -1.8     0.001   
 Treatment Foreigner  |   2       0.001   

But how should interpret the effects? Is there a way of understand the general effect of treatment (independent of the foreigner?)

If I understand correctly, the treatment effect for non-foreigner is exp(-0.9)-1= -0.59, that is 59% less than control non-foreigner , and the treatment effect for foreigner is exp(-0.9+2)-1= 2.00, which is 200% more than the control foreigner. Is that right?

It is puzzling to me because I do not expect the effects are completely different for foreigner and non-foreigner.

I appreciate any help with the interpretations. Thanks a lot!

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I think your interpretation is correct, and that your results indicate that there is a major difference in treatment effect between the groups. Another way of looking at it is that the difference is primarily between non-treated foreigners and non-treated non-foreginers, with the former group having an outcome count of 83 percent less (1-exp(-1.8)) than the latter.

You can test this with your data by calculating the mean outcome count in the four different groups (four combinations of non-foreigner/foreginer and non-treated/treated). Comparing the means in the non-foreginer non-treated groups with the others should yield the same percentages.

Perhaps this is an observational study rather than a controlled trial, and the results are due to selection bias? If you provide some detalis about the study design and the treatment and outcome it might be easier to hypothesize about the results.

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