Does offset always have to be on log scale with NB GLMM? I'm using a negative binomial GLMM with R package lme4 to detect differences in time mothers spend feeding before and after birth (inf_cat).
    inf30.feed <- glmer.nb(feeding ~ (inf_cat) + 
                    offset(total_inf_cat) + (1|female), 
                    data=mother_ownno_inf30)

My model has an offset of the total amount of time spent observing the individual. I'm still relatively new to GLMMs in R and I've been looking at a lot of examples online, many of which have the offset in a log scale.
Does the offset always have to be on a log scale? Why? And when is it appropriate to do?

Normally, an offset is used when we are modelling some sort of rate data (e.g. deaths per 100,000, crashes per 100,000 etc).
This is naturally modelled as some sort of ratio so have data in the form of $E(y_i)/n_i$
In GLM, we model the expectation through some sort of link function, so
$$ g^{-1}(E(y_i)/n_i) = \mathbf{x}^T\beta$$
With the logarithmic link function, we have
$$ \log(E(y_i)) = \mathbf{x}^T\beta + \log(n_i) $$
from application of log rules.  So to answer your question, the offset is not always a log.  It depends on the link function you use.
