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Abstract:
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Recent work developed model-based approaches for regression parameter estimation in complex sample designs by interacting covariates of interest and probabilities of inclusion (Elliott 2007, 2008). An alternative approach develops nonparametric regression estimators of means as a function of inclusion probabilities (Zheng and Little 2003, 2005). This work brings together elements of these approaches, modeling each sampled outcome as a mixture regression on covariates, where the mixing fractions are a function of the probability of selection. This allows for a data-driven trade-off in robustness and efficiency, accounting for model misspecification as well as skewness and overdispersion in the residual errors. We consider both finite normal mixture models (McLachlan and Peel 2000) and Bayesian density estimation via extensions to Dirichlet process mixture models (Dunson et al. 2007).
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