Model-Assisted Analyses of Cluster-Randomized Experiments
本文从设计角度评估了整群随机实验中三种回归估计量及其稳健标准误，指出基于群均值的回归估计加权平均处理效应，基于个体数据的回归效率次优，而基于群总和的回归在群数多时更一致高效，并强调协变量对提升效率的关键作用。
Abstract Cluster-randomized experiments are widely used due to their logistical convenience and policy relevance. To analyse them properly, we must address the fact that the treatment is assigned at the cluster level instead of the individual level. Standard analytic strategies are regressions based on individual data, cluster averages and cluster totals, which differ when the cluster sizes vary. These methods are often motivated by models with strong and unverifiable assumptions, and the choice among them can be subjective. Without any outcome modelling assumption, we evaluate these regression estimators and the associated robust standard errors from the design-based perspective where only the treatment assignment itself is random and controlled by the experimenter. We demonstrate that regression based on cluster averages targets a weighted average treatment effect, regression based on individual data is suboptimal in terms of efficiency and regression based on cluster totals is consistent and more efficient with a large number of clusters. We highlight the critical role of covariates in improving estimation efficiency and illustrate the efficiency gain via both simulation studies and data analysis. The asymptotic analysis also reveals the efficiency-robustness trade-off by comparing the properties of various estimators using data at different levels with and without covariate adjustment. Moreover, we show that the robust standard errors are convenient approximations to the true asymptotic standard errors under the design-based perspective. Our theory holds even when the outcome models are misspecified, so it is model-assisted rather than model-based. We also extend the theory to a wider class of weighted average treatment effects.