Uncertainty Quantification for Multi-level Models Using the Survey-Weighted Pseudo-Posterior

Parameter estimation and inference from complex survey samples typically focuses on global model parameters whose estimators have asymptotic properties, such as from fixed effects regression models. We present a motivating example of Bayesian inference for a multi-level or mixed effects model in which both the local parameters (e.g. group level random effects) and the global parameters may need to be adjusted for the complex sampling design. We evaluate the limitations of the survey-weighted pseudo-posterior and an existing automated post-processing method to incorporate the complex survey sample design for a wide variety of Bayesian models. We propose modifications to the automated process and demonstrate their improvements for multi-level models via a simulation study and a motivating example from the National Survey on Drug Use and Health. Reproduction examples are available from the authors and the updated R package is available via github:https://github.com/RyanHornby/csSampling