Optimization for Calibration of Survey Weights under a Large Number of Conflicting Constraints

In the analysis of survey data, sampling weights are needed for consistent estimation of the population; however, weights are typically modified through a process termed “calibration” to increase their efficiency and stability by ensuring weighted sums of auxiliary variables match a collection of controls. It is often the case that no single set of weights can be found that simultaneously incorporates all of these controls. Together they induce a large number of constraints and restrictions that don’t produce a feasible solution space. We present an optimization framework and an accompanying fast computational methodology to address this issue of constraint achievement or selection within a restricted space that will produce a stabilized set of calibrated weights. Our approach comes closest to the simultaneous achievement of a large number of conflicting constraints, while providing diagnostics about which constraints may not be exactly met. Our motivating example is the post-stratification for the National Survey on Drug Use and Health. We also make connections to covariate balancing approaches for observational studies. Computations were performed in R and code is provided in the supplementary material.

在调查数据分析场景中，为实现总体的一致估计，需使用抽样权重（sampling weights）；但通常会通过一种被称为"校准（calibration）"的流程对权重进行修正：通过确保辅助变量的加权和与一系列控制量相匹配，以此提升权重的效率与稳定性。但往往无法找到一组权重，能够同时纳入所有上述控制量。这些控制量共同催生了大量约束条件，却无法构成可行解空间。为此，我们提出了一种优化框架与配套的快速计算方法，用于在受限空间内解决约束达成或选择问题，以生成一组稳定的校准权重。我们的方法能够最大限度地同时满足大量存在冲突的约束条件，同时可输出诊断结果，指明哪些约束无法被精确满足。我们的示例动机源自美国全国药物使用与健康调查（National Survey on Drug Use and Health）的事后分层（post-stratification）分析。我们还将该方法与观察性研究中的协变量平衡（covariate balancing）方法建立了关联。所有计算均通过R语言完成，相关代码已在补充材料中提供。