A Pseudo Maximum Likelihood Approach to Multilevel Modelling of Survey Data

Abstract

An application of the pseudo maximum likelihood method to estimation of a multilevel linear model fitted to the dependent observations coming from a finite population is demonstrated. The proposed approach provides a closed form solution for estimating of the model parameters. It is computationally simpler than the iterative procedures suggested in the literature (e.g., the iterative probability weighted least squares method of Pfeffermann et al. (Pfeffermann, D., Skinner, C.J., Holmes, D.J., Goldstein, H., Rasbash, J. (1998). Weighting for unequal selection probabilities in multilevel models. Journal of Royal Statistical Society B 60:23–40)). Issues related to model and sample design hierarchies and their impact on estimation are discussed. A problem of weighting at different levels is addressed. A small simulation study showed that the proposed procedure is efficient even for small within group sample sizes.

Keywords:

• Finite population inference
• Hierarchical linear modelling
• Probability sampling
• Variance components estimation
• Weighting

Acknowledgments

The authors thank Professor J. N. K. Rao and Harold Mantel for their useful comments. S. N. Rai's research was supported in part by the Cancer Center Support Grant (CA 21765) and by the American Lebanese Syrian Associated Charities (ALSAC).