I have a data set that consists of video observations of carpenter bee nests under three treatments: a control, mothers removed and mothers and worker removed. I have counts of twenty behaviours as response variables, and I am looking at how each differs between treatments. There are different numbers of nests under each treatment, and different numbers of observations in each nest, so I have treated nest as a random factor, e.g for biting behavior:
glmmTMB(Biting ~ treatment + (1|nest), offset=log(noBees), data=biteTest, ziformula=~1, family="poisson")
As the number of bees in an observation is predictive of the number of behaviours I would like to fit a model in glmmTMB with the number of bees in an observation as exposure/offset, and another with total behaviours as exposure/offset. Because some observations have no bees visible, and some have no activity, I have the problem of a zero offset for some observations.
My intuition is to drop the zero observations, but I am concerned that this may bias my data to treatments with more bees/activity. Shouldn't observations of zero bees/activity be important to understanding the difference between treatments? If I drop the zeros how do I justify this statistically, perhaps with a reference to a published paper. I am struggling to find similar examples in ecological or behavioural literature.
My other thought was to include + 1 in my offset, but then I'm not sure how to interpret estimated marginal effects (means).