Figure 2. Effect of varying sample size of the random intercept term (number of populations) on parameter estimates in the presence of overdispersion.

Parameter estimates and 95% intervals for 3 different levels of replication of the random intercept term under 4 combinations of overdispersion and model type. Yellow circles, Beta-Binomial overdispersion and an observation-level random effect (OLRE) model; blue circles, overdispersed Binomial data and OLRE model; yellow diamonds, Beta-Binomial data and a Beta-Binomial model; blue diamonds, overdispersed Binomial data and a Beta-Binomial model. Beta-Binomial data were analysed using Bayesian Hierarchical Beta-Binomial mixed models and so error bars are 95% credible intervals. ‘β_prey,’ slope parameter for effect of number of prey items consumed; ‘μ_pop,’ mean value of population random intercept term; ‘σ_pop,’ standard deviation of population random effect. For all simulations σ_ε, was set to 3 for overdispersed Binomial models, and ϕ set to 2 for Beta-Binomial models.