Bayesian hierarchical weighting adjustment and survey inference

Abstract: We combine Bayesian prediction and weighted inference as a unified approach to survey inference. The general principles of Bayesian analysis imply that models for survey outcomes should be conditional on all variables that affect the probability of inclusion. We incorporate the weighting variables under the framework of multilevel regression and poststratification, as a byproduct generating model-based weights after smoothing. We investigate deep interactions and introduce structured prior distributions for smoothing and stability of estimates. The computation is done via Stan and implemented in the open source R package "rstanarm" ready for public use. Simulation studies illustrate that model-based prediction and weighting inference outperform classical weighting. We apply the proposal to the New York Longitudinal Study of Wellbeing. The new approach generates robust weights and increases efficiency for finite population inference, especially for subsets of the population.