I am studying the factors that influence mosquito feeding behavior. In the experiments, N mosquitoes are exposed to a host for a duration t. At the end of this exposure, we count how many mosquitoes (k) fed. This is repeated across several hosts, but the duration of exposure varied. I want to incorporate the duration in the response, a bit like an offset, so that the model considers that a longer exposure increases the proportion of fed mosquitoes we observe at the end. I was thinking of doing :
model <- glmmTMB(k/(N*t) ~ x1 + x2 + ...,
family = binomial(link = "logit"),
weights = N*t)
But I feel like that might be wrong. My response is no longer a proportion that can reach one (even if k = N), and that might mean that I cannot interpret odd ratios for instance : the probability of success and failure is not straightforward.
What would be your suggestion?
FYI I intend to perform model selection to know if I should use a betabinomial rather than a binomial error distribution, as well as incorporate random effects (intercept only). This is why I use glmmTMB as I find it makes this kind of selection easier.