Pseudo Bayesian Mixed Models under Informative Sampling

Abstract When random effects are correlated with survey sample design variables, the usual approach of employing individual weights (constructed to be inversely proportional unit inclusion probabilities) form a pseudo-likelihood no longer produces asymptotically unbiased inference. We construct weight-exponentiated formulation for distribution that achieves approximately inference generating hyperparameters effects. contrast our frequentist methods rely on numerical integration reveal pseudo Bayesian method both estimation respect sampling and consistency population distribution. Our simulations real data example business establishments demonstrate utility across different modeling formulations designs. This work serves as capstone recent developmental efforts combine traditional approaches paradigm provides bridge two rich but disparate sub-fields.