AI 中文总结
该研究针对分类后分层场景，构造了逻辑回归等效权重的频率论调查加权框架，证明其具有良好的有限样本估计与方差估计性能，并通过实证研究展示了其应用价值。
AI 中文摘要
回归模型的等效权重为基于设计和基于模型的调查推断提供了桥梁。我们开发了一种用于分类后 stratification（后分层）下逻辑回归等效权重的频率论调查加权框架。由于基于逻辑模型的总体估计量在观测结果中是非线性的，我们通过局部一阶表示定义等效权重，每个权重由总体估计量关于对应观测结果的缩放导数给出。该构造根据拟合的逻辑模型和总体单元结构产生显式闭式表达式。我们在有限单元超总体框架下，建立了有效样本量比的收敛性、所得加权估计量的渐近线性性，以及一致的插件方差估计量。模拟结果检验了总体恢复、回归性能、有效样本量和渐近方差近似的有限样本行为。结果表明，在考虑的设置中，逻辑等效加权提供了有竞争力的有限样本点估计和近似有效的插件方差估计，有效样本量与其他基于模型的加权方法相比具有竞争力。对“家庭与儿童福祉未来研究”的应用说明了所提出权重和方差估计量在实证调查场景中的构造与使用。我们强调逻辑等效加权与近期关于非线性多层回归和后分层的局部等效权重研究之间的关系，同时重点关注权重的频率论解释、其调查加权性质及其在推断中的应用。
英文摘要
Equivalent weights from regression models provide a bridge between design-based and model- based survey inference. We develop a frequentist survey-weighting framework for logistic regres- sion equivalent weights under categorical poststratification. Because the logistic model-based population estimator is nonlinear in the observed outcomes, we define equivalent weights through a local first-order representation, with each weight given by the scaled derivative of the popula- tion estimator with respect to the corresponding observed outcome. This construction yields an explicit closed-form expression in terms of the fitted logistic model and population cell structure. We establish convergence of the effective sample size ratio, asymptotic linearity of the resulting weighted estimator, and a consistent plug-in variance estimator under a finite-cell superpop- ulation framework. Simulation results examine population recovery, regression performance, effective sample size, and the finite-sample behavior of the asymptotic variance approximation. The results show that logistic equivalent weighting provides competitive finite-sample point esti- mation and approximately valid plug-in variance estimation, effective sample size is competitive with alternative model-based weighting in the settings considered. An application to the Fu- ture of Families and Child Wellbeing Study illustrates the construction and use of the proposed weights and variance estimator in an empirical survey setting. We emphasize the relationship between logistic equivalent weighting and recent work on locally equivalent weights for non- linear multilevel regression and poststratification, while focusing specifically on the frequentist interpretation of the weights, their survey-weight properties, and their use for inference.
Comments49 pages
