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The popular Bayesian meta-analysis expressed by Bayesian normal-normalhierarchical model (NNHM) synthesizes knowledge from several studies and ishighly relevant in practice. Moreover, NNHM is the simplest Bayesianhierarchical model (BHM), which illustrates problems typical in more complexBHMs. Until now, it has been unclear to what extent the data determines themarginal posterior distributions of the parameters in NNHM. To address thisissue we computed the second derivative of the Bhattacharyya coefficient withrespect to the weighted likelihood, defined the total empirical determinacy(TED), the proportion of the empirical determinacy of location to TED (pEDL),and the proportion of the empirical determinacy of spread to TED (pEDS). Weimplemented this method in the R package \texttt{ed4bhm} and considered twocase studies and one simulation study. We quantified TED, pEDL and pEDS underdifferent modeling conditions such as model parametrization, the primaryoutcome, and the prior. This clarified to what extent the location and spreadof the marginal posterior distributions of the parameters are determined by thedata. Although these investigations focused on Bayesian NNHM, the methodproposed is applicable more generally to complex BHMs.

Quantification of empirical determinacy: the impact of likelihood  weighting on posterior location and spread in Bayesian meta-analysis  estimated with JAGS and INLA