This paper deals with making inference on parameters of a two-level model matching the design hierarchy of a two-stage sample. In a pioneering paper, Scott and Smith (Journal of the American Statistical Association, 1969, 64, 830–840) proposed a Bayesian model based or prediction approach to estimating a finite population mean under two-stage cluster sampling. We provide a brief account of their pioneering work. We review two methods for the analysis of two-level models based on matching two-stage samples. Those methods are based on pseudo maximum likelihood and pseudo composite likelihood taking account of design weights. We then propose a new method for analysis of two-level models based on a normal approximation to the estimated cluster effects and taking account of design weights. This method does not require cluster sizes to be constants or unrelated to cluster effects. We evaluate the relative performance of the three methods in a simulation study. Finally, we apply the methods to real data obtained from 2011 Nepal Demographic and Health Survey (NDHS).

中文翻译：

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基于两阶段信息抽样和关联两水平模型的聚类调查数据分析

本文涉及对与两级样本的设计层次相匹配的两级模型的参数进行推断。在一篇开创性的论文中，Scott 和 Smith ( Journal of the American Statistical Association , 1969, 64, 830–840) 提出了一种基于贝叶斯模型或预测方法来估计两阶段整群抽样下的有限总体均值。我们简要介绍了他们的开创性工作。我们回顾了两种基于匹配两阶段样本的两级模型分析方法。这些方法基于考虑到设计权重的伪最大似然和伪复合似然。然后，我们提出了一种基于对估计集群效应的正态近似并考虑设计权重的两级模型分析新方法。此方法不要求簇大小为常量或与簇效应无关。我们在模拟研究中评估了这三种方法的相对性能。最后，我们将这些方法应用于从 2011 年尼泊尔人口与健康调查 (NDHS) 获得的真实数据。