I mainly want to make sure that I'm making the correct interpretation here.
I built a negative binomial regression model predicting a count variable. There was evidence of overdispersion or I would have used regular Poisson. The predictor variable (also a count) was skewed, so I transformed it using a natural log.
The results are coef=0.341 or IRR=1.407 (Incident rate ratio)
So, holding all other variables in the model constant, for every 1 log unit increase in the predictor, the rate ratio increases by 1.407? Or for every 1 unit increase in the predictor, the outcome will increase by 0.341 units? Is that correct?
Can I backtransform the results for an easier interpretation?