Guo Xin, Fu Qiang
School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland, Australia.
Department of Sociology, The University of British Columbia, Vancouver, British Columbia, Canada.
Sociol Methods Res. 2024 Aug;53(3):1319-1349. doi: 10.1177/00491241221113877. Epub 2022 Aug 8.
Grouped and right-censored (GRC) counts have been used in a wide range of attitudinal and behavioural surveys yet they cannot be readily analyzed or assessed by conventional statistical models. This study develops a unified regression framework for the design and optimality of GRC counts in surveys. To process infinitely many grouping schemes for the optimum design, we propose a new two-stage algorithm, the Fisher Information Maximizer (FIM), which utilizes estimates from generalized linear models to find a global optimal grouping scheme among all possible -group schemes. After we define, decompose, and calculate different types of regressor-specific design errors, our analyses from both simulation and empirical examples suggest that: 1) the optimum design of GRC counts is able to reduce the grouping error to zero, 2) the performance of modified Poisson estimators using GRC counts can be comparable to that of Poisson regression, and 3) the optimum design is usually able to achieve the same estimation efficiency with a smaller sample size.
分组和右删失（GRC）计数已在广泛的态度和行为调查中使用，但传统统计模型无法轻易对其进行分析或评估。本研究为调查中GRC计数的设计和最优性建立了一个统一的回归框架。为了处理无限多个分组方案以实现最优设计，我们提出了一种新的两阶段算法，即Fisher信息最大化器（FIM），它利用广义线性模型的估计值在所有可能的g分组方案中找到全局最优分组方案。在我们定义、分解并计算了不同类型的特定回归变量设计误差后，我们从模拟和实证例子中得到的分析表明：1）GRC计数的最优设计能够将分组误差降至零；2）使用GRC计数的修正泊松估计器的性能可与泊松回归相媲美；3）最优设计通常能够以较小的样本量实现相同的估计效率。
