This paper partially solves the problem of defining design-consistent model-assisted estimators for regression and variance-component parameters within parametric models based on complex survey data. There are several well-known papers in this area (Binder 1983, Pfeffermann et al. 1998, Korn and Graubard 2003, Rabe-Hesketh and Skrondal 2006) and some less-known but also potentially important papers (Rao et al. 2013, Feder et al. 2000), but the problem of design-consistent estimation of variance-component parameters in surveys has not previously been solved in a practically effective way.
The main contribution of the paper is to provide an EM-based solution to the design-based estimation of superpopulation variance components in important mixed-effect models based on complex surveys. The method is illustrated, and evaluated for consistency via simulation, both in two-way ANOVA and in random-intercept logistic-regression settings.