推荐信对大学录取的不同影响：观察性研究中亚组效应的近似平衡权重
Varying impacts of letters of recommendation on college admissions: Approximate balancing weights for subgroup effects in observational studies
摘要：
在2016-17年招生周期的一个试点项目中，加州大学伯克利分校邀请了许多新生入学申请人提交推荐信。我们使用这个试点作为提交推荐信对后续录取的影响的观察性研究的基础，目的是估计影响如何在预定义的亚组之间变化。然而，在观察性研究中理解这种变化具有挑战性，因为估计的影响反映了实际处理效应变化和各组间协变量平衡的差异。为了解决这个问题，我们开发了平衡权重，直接优化“局部平衡”的亚组内，同时保持治疗和控制单位之间的全局协变量平衡。然后，我们表明，这种方法具有双重表示形式的逆倾向得分加权与分层倾向得分模型。在加州大学伯克利分校的试点研究中，我们提出的方法产生了良好的局部和全局平衡，不像更传统的加权方法，无法平衡子组内的协变量。我们发现，推荐信的影响随着预测的录取概率的增加而增加，代表性不足的少数民族申请人的差异的混合证据。
英文摘要：
In a pilot program during the 2016-17 admissions cycle, the University of California, Berkeley invited many applicants for freshman admission to submit letters of recommendation. We use this pilot as the basis for an observational study of the impact of submitting letters of recommendation on subsequent admission, with the goal of estimating how impacts vary across pre-defined subgroups. Understanding this variation is challenging in observational studies, however, because estimated impacts reflect both actual treatment effect variation and differences in covariate balance across groups. To address this, we develop balancing weights that directly optimize for ``local balance'' within subgroups while maintaining global covariate balance between treated and control units. We then show that this approach has a dual representation as a form of inverse propensity score weighting with a hierarchical propensity score model. In the UC Berkeley pilot study, our proposed approach yields excellent local and global balance, unlike more traditional weighting methods, which fail to balance covariates within subgroups. We find that the impact of letters of recommendation increases with the predicted probability of admission, with mixed evidence of differences for under-represented minority applicants.
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