I am working with proportion data (very limited ~20 data points) for a response variable (RV), i.e. proportion of mature females out of total number of females sampled. The maturity is assessed by 6 distinct maturity stages.
I started out with a binomial distribution GLM
(M3), which was overdispersed, I calculated the dispersion statistic to be ~115. Subsequently, I tried a beta distribution
(M4), the model validation here suggested it was an okay fit (as okay as it can be with 20 dps).
However, upon reading this paper I realized that the beta distribution is not strictly a good fit for my RV, because the proportion is derived from discrete data, as opposed to continuous. The paper pointed me to the beta-binomial distribution
(M5), which I had no issue running. After that, out of curiosity I ran
AIC() on all three models to compare them. This was the result:
AIC(M3, M4, M5) df AIC M3 2 2335.20106 M4 3 -14.56873 M5 3 265.97071
My question is, why is the beta model
(M4)seemingly performing so much better than the beta-binomial
(M5) according to AIC? Is this due to overfitting? Or should I not have done the beta model in the first place because its wrong for my type of proportion data, and just ignore AIC?