Bayes-Raking: Bayesian Finite Population Inference with Known Margins

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.