With the presence of unequal sampling in a multilevel model, the weight inflated estimators for variance components can be biased even though the use of survey weights results in design consistent estimators of the parameters. In this thesis I will carry out a simulation study to examine the performance of current existing methods and I will examine the resampling method for correcting bias of estimators of variance components of a multilevel model with covariates. This study will be based on these three papers: "Weighting for Unequal Selection Probabilities in Multilevel Models" by D. Pfeffermann , C. J. Skinner, D.J. Holmes, H. Goldstein, and J. Rasbash (1998), Journal of the Royal Statistical Society Series B (Statistical Methodology), Vol. 60, No. 1, 23-40; "Design Consistent Estimators for a Mixed Linear Model on Survey Data" by Rong Huang and Mike Hidiroglou (2003), Business Survey Methods Division, Statistics Canada, Ottawa, Ontario K1Y 0A6; and "A resampling approach to estimate variance components of multilevel models" by Zilin Wang and Mary Thompson (2008), working paper.
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