Fully Bayesian Estimation Under Dependent and Informative Cluster Sampling

Abstract Survey data are often collected under multistage sampling designs where units binned to clusters that sampled in a first stage. The unit-indexed population variables of interest typically dependent within cluster. We propose Fully Bayesian method constructs an exact likelihood for the observed sample incorporate unit-level marginal weights performing unbiased inference parameters while simultaneously accounting dependence induced by produce correct uncertainty quantification. Our approach parameterizes cluster-indexed random effects both model response and conditional published, weights. compare our plug-in frequentist alternatives simulation study demonstrate most closely achieves quantification parameters, including generating variances effects. application with NHANES data. KEY WORDS: Inclusion probabilities; Mixed-effects linear model; NHANES; Primary stage unit; Sampling weights; sampling.