Parameter estimation and inference from complex survey samples typically focuses on global model parameters whose estimators have asymptotic properties, such as from fixed effects regression models. The central challenge is to both mitigate bias induced from potentially unbalanced samples and to incorporate adjustments for differences in effective sample size to get correct variance and interval estimates. We present a motivating example of Bayesian inference for a multi-level or mixed effects model in which estimates of both the local parameters (e.g. group level random effects) and the global parameters need to be adjusted for the complex sampling design. We evaluate the limitations of the survey-weighted pseudo-posterior and an existing automated post-processing method to improve the uncertainty quantification. We propose modifications to the automated process and demonstrate their improvements for multi-level models via a simulation study and a motivating example from the National Survey on Drug Use and Health. Reproduction examples are available from the authors and the updated R package is available via github:https://github.com/RyanHornby/csSampling

翻译：基于复杂调查样本的参数估计与推断通常聚焦于全局模型参数，其估计量具有渐近性质（如固定效应回归模型）。核心挑战在于既要减轻潜在不平衡样本所引发的偏差，又要纳入有效样本量差异的调整以获取正确的方差和区间估计。我们以贝叶斯推断为动机，探讨了一个多层次或混合效应模型的应用实例——其中局部参数（如组级随机效应）与全局参数的估计均需针对复杂抽样设计进行调整。我们评估了调查加权伪后验方法及现有自动后处理技术在改进不确定性量化方面的局限性，并提出了针对自动后处理流程的改进方案。通过模拟研究及来自《全国药物使用与健康调查》的实证案例，验证了这些改进对多层次模型的有效性。复制示例可向作者索取，更新后的R包可通过github获取：https://github.com/RyanHornby/csSampling