Interpretation of log transformed predictor in negative binomial regression

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?

• Why did you transform the predictor? – Dimitriy V. Masterov Sep 17 '14 at 22:54
• It is very skewed with some large outliers (more than 4 SD above the mean) – Joe Sep 19 '14 at 18:26
• And what problem does that cause with the NBR? – Dimitriy V. Masterov Sep 19 '14 at 18:38