Bayesian hierarchical models fitted to complex survey data often use weighted pseudo-posteriors, followed by a correction to match a design-based sandwich covariance. Correcting every parameter can needlessly widen or spuriously narrow credible intervals for parameters stabilized by shrinkage or identified by between-group variation. We propose the Design Effect Ratio (DER) to guide selective correction. It is the ratio of each parameter's design-based sandwich variance under a declared target to its model-based posterior variance. For hierarchical Gaussian models, we derive exact finite-sample decompositions under balance and common-design-effect assumptions. Fixed-effect DERs scale with the design effect, attenuated by the between-group share of identifying variation. Random-effect DERs factor into design effect, shrinkage, and a group-count term; a conservation identity links the two levels. A general matrix formula covers arbitrary parameter blocks and non-Gaussian likelihoods. We evaluate the diagnostic in a simulation with informative two-stage sampling and a re-analysis of the 2019 National Survey of Early Care and Education, reporting both design-PSU and model-group variance targets. These analyses distinguish survey-sensitive parameters from those protected by shrinkage and show how selective correction avoids the interval distortions caused by blanket rescaling. The R package svyder implements the workflow.

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