To Weight or Not to Weight: Incorporating Sampling Effects into Model-Based Survey Analysis

The two fundamental approaches used to analyze survey data, designand model-based, differ in how they incorporate complexities of the sampling design, such as stratification, clustering and/or unequal probabilities of selection, into the survey analysis. The design-based analysis uses the sampling design as the sole source of the variability, which necessitates the use of survey sampling weights. Model-based analysis includes a model which generated the data in addition to the sampling design, which makes the role of the sampling weights questionable. The goal of this dissertation is to investigate the use of sampling weights in model-based analysis, and to that end, the proposed work has three major components. The first component investigates two current proposals for incorporating sampling weights to robustly estimate mixed-effects models in the presence of model mis-specification and/or informative sampling (Korn and Graubard, 2003; Pfeffermann et al., 1998), comparing their advantages and disadvantages in various situations. The second component addresses the role of sampling weights when the survey design was not formulated according to particular statistical model of substantive interest, and will consider models other than mixed-effects models to see how the work generalizes across model-based techniques. This component will consider using estimating equation methods (Binder and Patak, 1994) as a bridge between model-based and design-based analyses. Both of these components will be explored analytically, through simulation, and by considering examples involving current research questions of interest on large national surveys (such as the National Survey of Child and Adolescent Well-Being and/or the National Long Term Care Survey). As part of the thesis, guidelines regarding the use of sampling weights in model-based analysis will be proposed. The third component of this work will be to develop these recommendations as a set of publishable tutorials that serve to clarify these issues and methodologies for survey analysts.