Statistica Sinica 26 (2016), 569-587 doi:http://dx.doi.org/10.5705/ss.2013.383
Abstract: Multi-level models provide a convenient framework for analyzing data from survey samples with hierarchical structures. Inferential procedures that take account of survey design features are well established for single-level (or marginal) models. However, methods that are valid for general multi-level models are somewhat limited. This paper presents a unified method for two-level models, based on a weighted composite likelihood approach, that takes account of design features and provides valid inferences even for small sample sizes within level 2 units. The proposed method has broad applicability and is straightforward to implement. Empirical studies have demonstrated that the method performs well in estimating the model parameters. Moreover, this research has an important implication: it provides a particular scenario to showcase the unique merit of the composite likelihood method where the likelihood method would not work.
Key words and phrases: Complex sampling design, composite likelihood, design-based inference, multi-level model, super-population model, variance estimation.