A Weighted Estimating Equations Approach to Inference for Two-level Models from Survey Data

Multi-level models are extensively used for analyzing survey data with design hierarchy matching the model hierarchy. We propose a weighted estimating equations (WEE) approach for two-level models that leads to design-model consistent estimators of model parameters even when the within-cluster sample sizes are small, provided the number of sample clusters is large. A unified approach based on weighted log composite likelihood that can handle generalized linear multi-level model is also proposed. Results of a small simulation study demonstrate superior performance of the proposed WEE method relative to existing methods under informative sampling within clusters.