I conducted an analysis where I used binomial logistic regression to analyze x successes in n trials (where n varies between observations) in aggregate (using the R syntax
cbind(successes,failures) ~ predictor). To account for the overdispersion I observed in the data, I fitted a quasibinomial logistic regression.
Now I have come up against a reviewer asking why I did not use a negative binomial regression. In this answer, Ben Bolker suggests that one could use Poisson or negative binomial with an offset if the number of successes is low, i.e. the count does not approach the upper bound. This is not the case in my dataset, but I would like a reference to back this up in my response to the reviewer.
Does anyone have a reference that demonstrates the conceptual concerns in the answer above? I have already checked Agresti and McCullagh and Nelder.