Reading many help pages, I see that a common way to correct for overdispersion is to fit models using quasibinomial or betabinomial distributions. However, I can't find help concerning how far correction is achieved nor how to be confident that a reliable model has been fitted.
I am interested in mutation data from many genes that fall into 10 ordered classes. Each observation comprises a number of bases surveyed (
N) and the number of substitutions observed (
S). Overdispersion is great (~22!) because the genes vary considerably in how fast they are evolving. There is also the issue that
N also varies a lot from <100 up to >30,000.
I want to test the hypothesis that average substitution rate (
S/N) increases with class number. I have tried the following options:
(awful!) Ignore the fact the data are binomial, set a minimum N>=1000, and fit a Gaussian model with S/N as the response. Fit is poor, though arguably not dreadful.
Use cbind(S, N-S) and fit a model with a quasibinomial error structure. Seems to give a similar answer that avoids the crazily low P-values I get when using family=binomial, but how do I know if the degree of correction is valid?
This seems a relatively simple problem, but I want to make sure the model is fitted properly and is, if anything, conservative.