Estimating variance components by using survey data

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Multilevel modelling of complex survey data (2006, background): “Longford (1995a, b, 1996), Graubard and Korn (1996), Korn and Graubard (2003), Pfeffermann et al. (1998) and others have discussed the use of sampling weights to rectify this problem in the context of two-level linear (or linear mixed) models, particularly random-intercept models.”
Introduction to Variance Estimation (2008, unknown): “Chapter 1 contains a quick review of standard methods of variance estimation, complete with references (up to the page numbers) from the sampling staple textbook by Cochran (1977). This is very handy for the teachers among us, although references to a more recent sampling text, such as that of Sarnd”
General Multi-Level Modeling with Sampling Weights (2006, methodology): “However, that estimator becomes biased for small cluster sample sizes even with SRS as noted in Korn and Graubard (2003), where as the MPML estimator is consistent even for small cluster sample sizes.”