论文标题
群集随机化实验中概率 - 比例到大小的取样的好处
The Benefits of Probability-Proportional-to-Size Sampling in Cluster-Randomized Experiments
论文作者
论文摘要
在一个集群的实验中，将治疗分配给各个利益单位的集群 - 房屋，教室，村庄等 - 而不是单位本身。每个集群中采样的群集数量和采样的单位数通常受预算约束的限制。在Neyman-Rubin潜在结果模型下，对簇随机实验的先前分析已经假定了一个简单的簇样本样本。在此假设下的人口平均治疗效果（PATE）的估计量通常会偏向于潜在结果的位置变化。我们证明，通过对概率与群集中的单元数成正比进行抽样簇，Horvitz-Thompson估计器（HT）与位置移位不变，并且无偏见。我们得出HT的标准误差，并讨论如何估计这些标准误差。我们还表明，当样品与每个层中的群集大小成比例地绘制样品时，分层随机样品的结果成立。我们使用基于从实验的数据来证明了该采样方案的功效，该实验测量了阿富汗国家团结计划的功效。
In a cluster-randomized experiment, treatment is assigned to clusters of individual units of interest--households, classrooms, villages, etc.--instead of the units themselves. The number of clusters sampled and the number of units sampled within each cluster is typically restricted by a budget constraint. Previous analysis of cluster randomized experiments under the Neyman-Rubin potential outcomes model of response have assumed a simple random sample of clusters. Estimators of the population average treatment effect (PATE) under this assumption are often either biased or not invariant to location shifts of potential outcomes. We demonstrate that, by sampling clusters with probability proportional to the number of units within a cluster, the Horvitz-Thompson estimator (HT) is invariant to location shifts and unbiasedly estimates PATE. We derive standard errors of HT and discuss how to estimate these standard errors. We also show that results hold for stratified random samples when samples are drawn proportionally to cluster size within each stratum. We demonstrate the efficacy of this sampling scheme using a simulation based on data from an experiment measuring the efficacy of the National Solidarity Programme in Afghanistan.
