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!