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| 基于超总体模型的设计效应分解 | |
| 引用本文： | 徐映梅 杨延飞. 基于超总体模型的设计效应分解[J]. 统计研究, 2019, 36(5): 100-119. DOI: 10.19343/j.cnki.11-1302/c.2019.05.008 |
| 作者姓名： | 徐映梅 杨延飞 |
| 作者单位： | 中南财经政法大学统计与数学学院;中南财经政法大学大数据研究院;中南财经政法大学;中国人民解放军空军预警学院 |
| 摘 要： | 本文基于超总体模型研究抽样调查中设计效应的计算问题。首先以随机效应模型为基础,明确了简单随机、二阶段、不等概率和分层抽样对应的超总体模型,进而通过所给模型推导出分层、类集、加权单因素设计效应和多因素组合设计效应的计算公式并给出了对应估计量,公式表明:多因素同时存在的组合设计效应等于对应单因素设计效应的乘积。最后,对设计效应的理论值、估计值和真实值之间的关系进行了蒙特卡洛仿真,并利用相对偏倚、相对均方误进行了评价。本文的研究对复杂抽样设计中正确计算、使用设计效应具有指导意义。 |
| 关 键 词： | 设计效应 超总体模型 类集效应 加权效应 |
Decomposition of Design Effects based on Super-population Models |
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| Xu Yingmei , Yang Yanfei. Decomposition of Design Effects based on Super-population Models[J]. Statistical Research, 2019, 36(5): 100-119. DOI: 10.19343/j.cnki.11-1302/c.2019.05.008 | |
| Authors: | Xu Yingmei & Yang Yanfei |
| Abstract: | This paper studies the calculation of Design Effects in the sample surveys based on the super-population model. Firstly, taking the random effect model as a basis, the study clarifies the super-population models corresponding to SRS, two-stage sampling, unequal probability sampling and stratified sampling. Furthermore, through these Super-population Models, the formulas of the design effects of simple factors such as stratification, clustering and weighting，and the formulas of the combined design effects of multi-factors are derived with the corresponding estimators. The formulas show that the combined design effects of multiple factors is equal to the product of the design effect of a simple factor. Finally, the Monte Carlo simulation is conducted on the relationship between the theoretical value, the estimated value and the true value of the design effects, and their relative bias and relative mean square errors are evaluated. This research is of a guiding significance for the correct calculation and the application of the design effects in the complicated sampling. |
| Keywords: | Design Effect Super-population Model Clustering Effect Weighting Effect Combination effect. |
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