发表机构
Michigan State University（密歇根州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究揭示多水平中介分析中合并估计量的聚合失真机制，提出权重不匹配与非线性分解、设计标准化诊断，并通过模拟和ECLS-K:2011数据验证。核心贡献在于阐明失真取决于设计且常用构造可能夸大失真。
AI 中文摘要
研究者通常使用单水平系数乘积估计量来总结聚类数据中的中介效应。我们展示了这种合并分析估计的是什么，以及为什么目标取决于设计。合并的a路径按处理的组内-组间方差组成加权。合并的b路径使用不同的权重，基于在对处理和协变量进行残差化后剩余的介体方差。由于这些权重通常不同，合并的间接效应可能不同于组内和组间间接效应的水平尊重组合。我们推导了合并的概率极限，并将这一差异分解为非线性项和权重不匹配项。相等的b路径消除失真，但相等的a路径不能。允许两个权重变化给出具有鞍点几何、尖锐角界和零失真前沿的双线性曲面。我们还定义了设计标准化的间接效应和实用诊断。模拟验证了这些恒等式，并表明常见的先分解、聚类加权构造可能夸大表面失真。在ECLS-K:2011示例中，有8,363名儿童分布在753所基线学校，组内权重分别为0.723和0.896，差异为-0.173（95%自助法置信区间[-0.193, -0.151]）。传统构造产生的绝对失真量是恒等式一致构造的1.76倍。恒等式一致的AD区间包含零。因此，该应用显示了不等权重和对构造的敏感性，而非非零总体失真的证据。
英文摘要
Researchers often summarize mediation in clustered data with a single-level product-of-coefficients estimator. We show what this pooled analysis estimates and why the target depends on the design. The pooled a-path is weighted by the within-between variance composition of the treatment. The pooled b-path uses a different weight, based on the mediator variance that remains after residualizing on treatment and covariates. Because these weights generally differ, the pooled indirect effect can differ from a level-respecting combination of the within- and between-level indirect effects. We derive the pooled probability limit and split this difference into a nonlinearity term and a weight-mismatch term. Equal b-paths remove the distortion, but equal a-paths do not. Allowing the two weights to vary gives a bilinear surface with saddle geometry, sharp corner bounds, and a zero-distortion frontier. We also define a design-standardized indirect effect and practical diagnostics. Simulations verify the identities and show that a common decompose-first, cluster-weighted construction can overstate apparent distortion. In an ECLS-K:2011 illustration with 8,363 children in 753 baseline schools, the within-level weights were 0.723 and 0.896, a difference of -0.173 (95% bootstrap CI [-0.193, -0.151]). The conventional construction produced 1.76 times the absolute distortion of the identity-consistent construction. The identity-consistent AD interval included zero. Thus, the application shows unequal weighting and sensitivity to construction, not evidence of nonzero population distortion.
Comments40 pages, 6 figures
