How should I introduce an OFFSET term for a BINOMIAL response variable? I have a binomial response variable -proportion of removed fruits, or plant visited or not visited by a frugivore- in a GLMM. I would like to control for differences in the sampling effort (time) among plants. I know that offset terms are often used for count data as "offset(log(time))". However, I was not able to find the proper way for binomial data. I have seen some authors including the term just as "offset(time)" (without log transformation, although I get an error message) and others include "time" just as a covariate in the fixed part of the model. Could someone enlighten me?

A Poisson model with response $y$ reduces to a Binomial model with cloglog link and the same covariate structure in the transformed response
$$
z=\begin{cases}
1 & y > 0 \\
0 & y =0.
\end{cases}
$$
So use log effort offset and cloglog link.
