分层抽样用于模型辅助估计的替代性结果
Stratified Sampling for Model-Assisted Estimation with Surrogate Outcomes
AI总结：
本文提出分层抽样方法，用于模型辅助估计中替代性结果的高效利用，通过优化分配规则提升估计效率。
摘要：
在许多随机试验中，诸如文章或开放式回答等结果必须作为初步步骤手动评分以影响分析，这一过程成本高昂且限制性。模型辅助估计提供了一种将由机器学习或大语言模型生成的替代性结果与人工编码子集结合的方法，但通常的实现使用简单随机抽样，因此忽略了替代性预测误差中的系统性变化。我们通过引入分层抽样来扩展这一框架，以更有效地分配人工编码努力。我们推导了分层模型辅助估计量的精确方差，刻画了分层在提高精度时的条件，以及识别了一个奈曼型最优分配规则，该规则对残差方差较大的分层进行超采样。我们通过全面的模拟研究评估了我们的方法，以评估有限样本性能。总体而言，我们发现当替代性预测误差表现出结构化偏差或异方差性时，分层方法在效率上始终优于传统方法。我们还提出了两个实证应用，一个使用教育随机对照试验的数据，另一个使用大规模观察数据集，以说明如何利用ChatGPT生成的替代性结果来实施这些方法。总体而言，这一框架提供了一种基于设计的实用方法，以利用替代性结果并战略性地分配人工编码努力，以获得无偏估计，提高效率。虽然受到文本作为数据应用的启发，该方法适用于任何结果测量成本高昂或不可行的场景，并可用于组间比较或估计单组的均值。
英文摘要：
In many randomized trials, outcomes such as essays or open-ended responses must be manually scored as a preliminary step to impact analysis, a process that is costly and limiting. Model-assisted estimation offers a way to combine surrogate outcomes generated by machine learning or large language models with a human-coded subset, yet typical implementations use simple random sampling and therefore overlook systematic variation in surrogate prediction error. We extend this framework by incorporating stratified sampling to more efficiently allocate human coding effort. We derive the exact variance of the stratified model-assisted estimator, characterize conditions under which stratification improves precision, and identify a Neyman-type optimal allocation rule that oversamples strata with larger residual variance. We evaluate our methods through a comprehensive simulation study to assess finite-sample performance. Overall, we find stratification consistently improves efficiency when surrogate prediction errors exhibit structured bias or heteroskedasticity. We also present two empirical applications, one using data from an education RCT and one using a large observational corpus, to illustrate how these methods can be implemented in practice using ChatGPT-generated surrogate outcomes. Overall, this framework provides a practical design-based approach for leveraging surrogate outcomes and strategically allocating human coding effort to obtain unbiased estimates with greater efficiency. While motivated by text-as-data applications, the methodology applies broadly to any setting where outcome measurement is costly or prohibitive, and can be applied to comparisons across groups or estimating the mean of a single group.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
