  Raking is widely used in categorical data modeling and 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 the solution subspaces
via basis functions or 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, with the capability
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
Wellbeing study and demonstrate that model-based approaches significantly
improve inferential reliability and substantive findings as a unified survey
inference framework.

Methodology;Computation