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?