AI 中文总结
研究样本调查中数值变量粗化问题，提出通过将观察响应视为潜在变量粗化表现，用调查加权伪似然方法联合建模，经方差分解传播不确定性，经模拟研究和实际应用验证方法性能及相关性。
AI 中文摘要
样本调查中自我报告的数值变量经常会出现粗化，因为受访者倾向于报告四舍五入或堆积的值而非确切的基础数量。虽然统计文献提供了各种基于模型的解决方案，但官方统计和公共卫生监测通常需要在复杂抽样设计下对有限总体指标进行基于设计的推断。本文引入了一个通用框架，通过将观察到的响应视为潜在变量的粗化表现，通过调查加权伪似然方法对粗化程度增加的报告机制与潜在分布进行联合建模来弥合这一差距。拟合模型用于生成潜在值的后验预测复制，应用标准的基于设计的估计量，通过明确的方差分解正式传播额外的不确定性。模拟研究评估了该方法在各种错误设定和抽样场景下的有限样本性能和稳健性。最后，通过应用于意大利PASSI监测系统的行为数据证明了其实际相关性，说明了粗化如何以不同方式影响不同的函数，如均值、分位数和基于阈值的患病率指标。
英文摘要
Self-reported numerical variables in sample surveys are frequently subject to coarsening, as respondents tend to report rounded or heaped values rather than the exact underlying quantity. While the statistical literature offers various model-based solutions, official statistics and public health surveillance routinely require design-based inference on finite-population indicators under complex sampling designs. This paper introduces a general framework that bridges this gap by treating the observed response as a coarsened manifestation of a latent variable, modeling reporting regimes of increasing coarseness jointly with the latent distribution via a survey-weighted pseudo-likelihood approach. The fitted model is used to generate posterior predictive replicates of the latent values, to which standard design-based estimators are applied, formally propagating the additional uncertainty through an explicit variance decomposition. Simulation studies assess the finite-sample performance and robustness of the proposed method under various misspecification and sampling scenarios. Finally, its practical relevance is demonstrated through an application to behavioural data from the Italian PASSI surveillance system, illustrating how coarsening affects different functionals, such as means, quantiles, and threshold-based prevalence indicators in heterogeneous ways.
