Large-scale statistical surveys seldom use simple random sampling. Two fundamental approaches (design- and model-based) exist to incorporate complexities such as stratification, clustering and/or unequal probabilities of selection into the survey analysis. The debate about design- vs. model-based analysis has a long history and currently centers around the role of design-based sampling weights in model-based analyses. This thesis begins by investigating three different published proposals on how to insert the sampling weights into linear mixed-effects (LME) models. This component, which focuses on how the sampling weights are inserted into LME models, derives the three methods from a common starting place and emphasizes the unique decisions that distinguish the different approaches. The second component of this thesis compares the methods in a simulation study that varies the types of informative sampling and model misspecification. The goal of this component is to characterize when it is appropriate to include sampling weights into a model-based analysis, as well as which kinds of sampling and modeling errors weights can correct. Finally, the lessons from the first two components are extended to the Grade of Membership (GoM) model, a hierarchical Bayesian mixed-membership model whose variance components do not map well to the dependencies induced by complex sampling designs. The GoM model is modified to include a polytomous logistic mixed-effects regression prior to reflect the sampling design. A new type of weighting, called weighting based on the estimated parameter is developed and explored through a simulation study.
|School:||Carnegie Mellon University|
|School Location:||United States -- Pennsylvania|
|Source:||DAI-B 69/08, Dissertation Abstracts International|
|Keywords:||Grade of Membership model, Linear mixed-effects model, Sampling weights, Survey sampling|
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