A Weighted Composite Likelihood Approach to Inference for Two-level Models from Survey Data

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J.N.K. Rao, F. Verret and M.A. Hidiroglou1


Multi-level models are extensively used for analyzing survey data with the design hierarchy matching the model hierarchy. We propose a unified approach, based on a design-weighted log composite likelihood, for two-level models that leads to design-model consistent estimators of the model parameters even when the within cluster sample sizes are small provided the number of sample clusters is large. This method can handle both linear and generalized linear two-level models and it requires level 2 and level 1 inclusion probabilities and level 1 joint inclusion probabilities, where level 2 represents a cluster and level 1 an element within a cluster. Results of a simulation study demonstrating superior performance of the proposed method relative to existing methods under informative sampling are also reported.

Key Words

Composite likelihood, Inclusion probabilities, Informative sampling, Multi-level models.

Table of content

1 Introduction

2 Two-level models: past work

3 Design-weighted estimating equations

4 Weighted log composite likelihood: a unified approach

5 Simulation study

6 Concluding remarks






1J.N.K. Rao, School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada, K1S 5B6, jrao@math.carleton.ca. F. Verret, Statistics Canada, 15 B, R.-H.-Coats Building, Ottawa, Ontario, Canada, K1A 0T6, francois.verret@statcan.gc.ca. M.A. Hidiroglou, Statistics Canada, 16 D, R.-H.-Coats Building, Ottawa, Ontario, Canada, K1A 0T6, mike.hidiroglou@statcan.gc.ca.

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