Balanced Repeated Replication for Stratified Multistage Survey Data under Imputation
插补下分层多阶段调查数据的平衡重复复制AI 解读 ↓
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插补下分层多阶段调查数据的平衡重复复制
- 研究问题
- 调查中大量缺失值经过插补后，如何让平衡重复复制方差估计计入插补变异，同时避免对每个复制样本重新随机插补的成本？
- 方法与思路
- 作者调整 BRR 方差估计：确定性插补下匹配逐份重新插补的结果，随机插补下无需生成额外随机数，并研究一致性。
- 材料陈述的贡献
- 摘要称，调整方法可捕捉插补变异，在一般分层多阶段设计下对平滑统计量和样本分位数具有一致性，并提供模拟及数据例子。
- 阅读关注点
- 应核对插补方式与抽样设计要求、调整项的构造，以及平滑统计量和分位数各自的一致性条件及模拟比较标准。
- 阅读边界
- 依据版本未注明的 OpenAlex 索引摘要；完整插补条件、缺失机制及有限样本误差未说明，不能推广为适用于所有缺失数据或调查设计。
原文摘要
Balanced repeated replication (BRR) is a popular method for variance estimation in surveys. The standard BRR method works by first creating a set of “balanced” pseudoreplicated datasets from the original dataset. For a survey estimator θ, the BRR variance estimator is the average of squared deviations θ(r) – θ, where θ(r) is the same as θ but based on the data in the rth pseudoreplicated dataset only. But when there are a large number of imputed missing values (nonrespondents), treating the imputed values as observed data and applying the standard BRR variance estimation formula does not produce valid variance estimators. Intuitively, the variation due to imputation can be captured by the BRR method if every pseudoreplicated dataset is imputed in exactly the same way as the original dataset is imputed (assuming that the dataset contains flags for nonrespondents). But when a random imputation method (such as random hot deck imputation, random ratio imputation, or random regression imputation) is used, imputing every pseudoreplicated dataset requires the generation of many random variates and is computationally expensive. We propose an adjusted BRR variance estimator that is exactly the same as the BRR variance estimator obtained by imputing every pseudoreplicated dataset when a deterministic imputation method (e.g., ratio or regression imputation) is used. For random imputation methods, the proposed adjustment does not require the generation of additional random variates, but it still captures the variation due to imputation. Under a general stratified multistage sampling design, consistency of the adjusted BRR variance estimators for functions of estimated totals (smooth statistics) or for sample quantiles (nonsmooth statistics) is established. A simulation study shows that the adjusted BRR method works well and is much better than the unadjusted BRR method. An example with real data is also presented.