Simulation study: Variability of mean LS within different simulation scenarios. Variability of mean logarithmic score for true negative binomial (NB) compared with arcsinh, (zero-inflated) Poisson and zero-inflated NB model (r = 1,…,100 iterations per scenario). Sample size: n = 20,50,100 subjects per group; k = 0.5,1,5,10,20,50 determines the amount of overdispersion. Each row is a different value of k (amount of overdispersion), and each plot shows the mean for each competing model. The column of panels on the right has the largest sample size n; the top row exhibits the results for highly overdispersed counts (k=0.5).