I am analyzing proportion data with GLMM in which the number of occurrence a behaviour of interest has been displayed and has not been displayed are concatenated and fitted as a single response variable.
Fitting a conventional bimodial model with glmer and computing the dispersion statistic as the sum of square of the pearson's residuals/residual degree of freedom returns a value of 4.9, suggesting a high overdispersion.
I then fitted a similar model in glmmADMB but specified a beta-binomial error structure instead, which I thought would be appropriate to account for the large variance in my data. The model runs smoothly and estimated parameters, standard errors and p-value look more realistic than the binomial model. However at my surprise, the dispersion statistic calculated as described above returned a value very similar to the one obtained when fitting the binomial model. I was wondering whether this is something I have to worry about and indicate that the model is inappropriate or that the overdispersion statistic is of no relevance anymore when using beta-binomial error structure