I am doing binomial GLM using relative abundance, for example: model<-glm(cbind(number_pres,number_abs)~Var1+Var2+Var3+Var4..., family=binomial, data=Data). My sample size is about 700, and I have about 15 explanatory variables. I can't use Poisson because the total number of "trials" varies per sample point (relative abundance account for this), and I'd prefer not to simplify to presence/absence.
My global model is overdispersed (residual deviance/ degrees of freedom = 2.8), and has some funny patterns in the residuals (see below).
The overdispersion remains whether I add interactions, polynomials, transform variables, remove influential points, remove variables which had VIF ~4 (the highest VIF of the set). Removing the influential point and the highest VIF does seem to help with the residual patterns, but not overdispersion. I can use family=quasibinomial, but then of course many of the variables are no longer significant, and I find this harder to interpret/understand. If possible I'd like to just fix the overdispersion.
Two things I suspect may be causing issues are the high number of zeros in my species data, and something to do with spatial autocorrelation. I did a few tests and spatial autocorrelation of residuals might be a minor issue (in "car" Durbinwatsontest showed reject null of no autocorrelation, but in "gstat" variogram the semivariance hovered around 2-2.5). I repeated the model using presence/absence in a bernouilli glm (overdispersion doesn't exist for bernouilli), there are no residual patterns, and I get similar results when using a zero-inflated binomial glm (package glmmADMB). I have yet to find a zero-inflated model for binomial glm with proportions, but maybe this indicates that zeros aren't the problem either.
Should I just use quasibinomial glms for my model, and the subsequent nested model set? Or is there a solution I am missing?