# R: glm.nb and when to consider using an offset or including a covariate

I'm using glm.nb to test for differences in the likelihood of accumulating overtime hours among employees across multiple departments. Department is the only information I have on which to base a comparison.

The data are overdispursed and the following negative binomial improves the model significantly oner the poisson and quasipoisson alternatives:

m1 <-glm.nb(Over ~ Dept, data = DF)


I'd like to understand the difference in interpretation between including an employee's total available hours (not on vacation, leave, etc.) in the model as an offset (an exposure variable) or as a covariate.

m1 <-glm.nb(Over ~ Dept + offset(log(HoursAvail)),data = DF)
m2 <-glm.nb(Over ~ Dept + HoursAvail,data = DF)


It seems that hours available should be accounted for in some way. If included as a covariate, should the log of HoursAvail be used instead?