Bayesian hierarchical models fit to complex survey data require variance correction for the sampling design, yet applying this correction uniformly harms parameters already protected by the hierarchical structure. We propose the Design Effect Ratio -- the ratio of design-corrected to model-based posterior variance -- as a per-parameter diagnostic identifying which quantities are survey-sensitive. Closed-form decompositions show that fixed-effect sensitivity depends on whether identifying variation lies between or within clusters, while random-effect sensitivity is governed by hierarchical shrinkage. These results yield a compute-classify-correct workflow adding negligible overhead to Bayesian estimation. In simulations spanning 54 scenarios and 10,800 replications of hierarchical logistic regression, selective correction achieves 87-88% coverage for survey-sensitive parameters -- matching blanket correction -- while preserving near-nominal coverage for protected parameters that blanket correction collapses to 20-21%. A threshold of 1.2 produces zero false positives, with a separation ratio of approximately 4:1. Applied to the 2019 National Survey of Early Care and Education (6,785 providers, 51 states), the diagnostic flags exactly 1 of 54 parameters for correction; blanket correction would have narrowed the worst remaining interval to 4.3% of its original width. The entire pipeline completes in under 0.03 seconds, bridging design-based and model-based survey inference.

翻译：针对复杂调查数据拟合的贝叶斯层次模型需要对抽样设计进行方差校正，但统一应用此类校正会损害已受层次结构保护的参数。本文提出设计效应比率——即经设计校正的后验方差与基于模型的后验方差之比——作为逐参数诊断工具，用以识别哪些统计量具有调查敏感性。闭式分解表明：固定效应的敏感性取决于识别变异存在于群组之间还是群组内部，而随机效应的敏感性则由层次收缩机制决定。这些结果催生了一个计算-分类-校正工作流程，该流程为贝叶斯估计增加的计算开销可忽略不计。在涵盖54种场景、10,800次层次逻辑回归复现的模拟实验中，选择性校正使调查敏感参数达到87-88%的覆盖概率——与全面校正效果相当——同时使受保护参数保持接近名义水平的覆盖概率（全面校正会将其压缩至20-21%）。采用1.2的阈值可实现零误报，其分离比约为4:1。应用于2019年全国早期保育与教育调查（6,785家机构，51个州）时，该诊断框架从54个参数中精准标记出1个需要校正的参数；若采用全面校正，将导致最宽剩余区间的宽度缩减至原始宽度的4.3%。整个处理流程在0.03秒内完成，实现了基于设计与基于模型的调查推断方法的有效衔接。