  The popular Bayesian meta-analysis expressed by Bayesian normal-normal
hierarchical model (NNHM) synthesizes knowledge from several studies and is
highly relevant in practice. Moreover, NNHM is the simplest Bayesian
hierarchical model (BHM), which illustrates problems typical in more complex
BHMs. Until now, it has been unclear to what extent the data determines the
marginal posterior distributions of the parameters in NNHM. To address this
issue we computed the second derivative of the Bhattacharyya coefficient with
respect 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). We
implemented this method in the R package \texttt{ed4bhm} and considered two
case studies and one simulation study. We quantified TED, pEDL and pEDS under
different modeling conditions such as model parametrization, the primary
outcome, and the prior. This clarified to what extent the location and spread
of the marginal posterior distributions of the parameters are determined by the
data. Although these investigations focused on Bayesian NNHM, the method
proposed is applicable more generally to complex BHMs.
