论文标题
通过将二元匹配与不平衡优化融合二元匹配来更好的实验设计
Better Experimental Design by Hybridizing Binary Matching with Imbalance Optimization
论文作者
论文摘要
我们提出了一种新的实验设计程序，该程序将一组实验单元划分为两组，以最大程度地减少估计添加剂治疗效果的误差。一个问题是在实验设计阶段最小化误差是两组之间的大协变量失衡。另一个问题是设计在响应模型中的鲁棒性。我们在提出的设计中解决了这两个问题：我们首先使用最佳的非面积匹配将受试者对成对，从而使我们的估计量鲁棒至复杂的非线性响应模型。我们的创新是保持匹配对的现存，在每个匹配对中的协变量差异，然后使用Krieger等人的贪婪开关启发式。 （2019年）或对这些差异的重读。在一个均匀分布的协变量的情况下，后一个步骤大大将协变量不平衡减少了$ o_p（n^{ - 4}）$的速率不平衡。此费率受益于贪婪的开关启发式启发式，即$ o_p（n^{ - 3}）$以及匹配速率，即$ o_p（n^{ - 1}）$。此外，我们所得的设计被证明与匹配一样随机，对未观察到的协变量是可靠的。与以前的设计相比，当响应模型是非线性并至少在响应模型是线性时，我们的方法在治疗效应估计器的平均平方误差方面表现出显着改善。我们的设计过程是在CRAN上可用的称为Greedyexperimentimenty Design的开源R软件包中找到的方法。
We present a new experimental design procedure that divides a set of experimental units into two groups in order to minimize error in estimating an additive treatment effect. One concern is minimizing error at the experimental design stage is large covariate imbalance between the two groups. Another concern is robustness of design to misspecification in response models. We address both concerns in our proposed design: we first place subjects into pairs using optimal nonbipartite matching, making our estimator robust to complicated non-linear response models. Our innovation is to keep the matched pairs extant, take differences of the covariate values within each matched pair and then we use the greedy switching heuristic of Krieger et al. (2019) or rerandomization on these differences. This latter step greatly reduce covariate imbalance to the rate $O_p(n^{-4})$ in the case of one covariate that are uniformly distributed. This rate benefits from the greedy switching heuristic which is $O_p(n^{-3})$ and the rate of matching which is $O_p(n^{-1})$. Further, our resultant designs are shown to be as random as matching which is robust to unobserved covariates. When compared to previous designs, our approach exhibits significant improvement in the mean squared error of the treatment effect estimator when the response model is nonlinear and performs at least as well when it the response model is linear. Our design procedure is found as a method in the open source R package available on CRAN called GreedyExperimentalDesign.
