Bayes-Raking: Bayesian Finite Population Inference with Known Margins

Abstract

Abstract Raking is widely used for categorical data modeling and calibration in survey practice but faced with methodological and computational challenges. We develop a Bayesian paradigm for raking by incorporating the marginal constraints as a prior distribution via two main strategies: (1) constructing solution subspaces via basis functions or the projection matrix and (2) modeling soft constraints. The proposed Bayes-raking estimation integrates the models for the margins, the sample selection and response mechanism, and the outcome as a systematic framework to propagate all sources of uncertainty. Computation is done via Stan, and codes are ready for public use. Simulation studies show that Bayes-raking can perform as well as raking with large samples and outperform in terms of validity and efficiency gains, especially with a sparse contingency table or dependent raking factors. We apply the new method to the longitudinal study of well-being study and demonstrate that model-based approaches significantly improve inferential reliability and substantive findings as a unified survey inference framework.