Optimization for Calibration of Survey Weights under a Large Number of Conflicting Constraints
针对调查数据校准中大量冲突约束导致无可行解的问题，提出优化框架和快速计算方法，在受限空间中选出最接近满足所有约束的稳定校准权数，并提供诊断信息。
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.