Fig. 2

Posterior distributions of the central slope coefficients of the Bayesian negative binomial models. Pink: single-level model (varying-intercept, fixed-slope), parameters \(\alpha , \gamma , \delta\). Blue and green: multilevel models (blue: intercepts and slopes partially pooled across regions; green: intercepts partially pooled across regions and periods, slopes partially pooled across regions), hyperparameters \(\alpha _0, \gamma _0, \delta _0\). 95% credible intervals are shown as shaded areas under the curves around the median point estimates.