Area under curve (AUC) for the different combinations of effects and distributions.

In the analysis, the best model (Poisson, negative binomial and zero-inflated negative binomial for count data) with and without effect was identified and compared to each other using BML. Delta AUC is also given to illustrate the difference between the two models utilizing the two different data types (counts and frequencies). Note that the analyses using count data always perform better than the analyses using frequency data, though the difference is, in some cases marginal, e.g. random slope models drawn from datasets built on negative binomial or lognormal Poisson distribution.