AI 中文总结
针对大规模教育评估中亚组成绩估计受样本量限制的问题，本研究提出SABDB方法，经模拟和PISA 2018数据验证，其覆盖率接近名义水平，优于校准错误的HBSAE模型。
AI 中文摘要
大规模教育评估会抑制样本量低于最小阈值的亚组成绩估计，例如美国国家教育进展评估（NAEP）设定的62的规则，这对历史上代表性不足的群体影响尤为严重。本研究提出小区域贝叶斯动态借用（SABDB），这是一种单元级小区域估计方法，为每个回归系数分配其自身的区域间方差，从而使跨区域借用适应每个系数的异质性。我们在模拟研究和实证案例研究中，将SABDB与单元级分层贝叶斯小区域估计（HBSAE）模型进行比较。模拟研究模拟了NAEP八年级数学评估，案例研究使用了PISA 2018数据集。在两项研究中，SABDB实现了接近名义水平的覆盖率，而HBSAE的区间较窄但校准严重错误。
英文摘要
Large-scale assessments suppress subgroup achievement estimates below minimum sample size thresholds, such as the National Assessment of Educational Progress (NAEP) rule of 62, disproportionately affecting historically underrepresented groups. This study introduces Small Area Bayesian Dynamic Borrowing (SABDB), a unit-level small area estimation method assigning each regression coefficient its own between-area variance, so cross-area borrowing adapts to each coefficient's heterogeneity. We compare SABDB against the unit-level Hierarchical Bayesian Small Area Estimation (HBSAE) model in a simulation study and an empirical case study. The simulation mimics the NAEP eighth-grade mathematics assessment, and the case study uses the PISA 2018 dataset. Across both studies, SABDB achieved near-nominal coverage, whereas HBSAE's intervals were narrow but severely miscalibrated.
