Survey data are often collected under multistage sampling designs where units are binned to clusters that are sampled in a first stage. The unit-indexed population variables of interest are typically dependent within cluster. We propose a Fully Bayesian method that constructs an exact likelihood for the observed sample to incorporate unit-level marginal sampling weights for performing unbiased inference for population parameters while simultaneously accounting for the dependence induced by sampling clusters of units to produce correct uncertainty quantification. Our approach parameterizes cluster-indexed random effects in both a marginal model for the response and a conditional model for published, unit-level sampling weights. We compare our method to plug-in Bayesian and frequentist alternatives in a simulation study and demonstrate that our method most closely achieves correct uncertainty quantification for model parameters, including the generating variances for cluster-indexed random effects. We demonstrate our method in two applications with NHANES data.
翻译:在多阶段抽样设计中,往往收集调查数据,单位被捆绑到第一阶段抽样的组群中。单位指数人口变量通常取决于组群。我们建议采用全巴伊西亚方法,根据这种方法,观察的抽样组将单位一级的边际抽样权重纳入对人口参数进行公正无偏的推断的单位一级边际抽样权重,同时计算单位抽样组群引起的依赖性,以得出正确的不确定性量化。我们的方法在反应的边际模型和公布的单位级抽样权重的有条件模型中将群集指数随机效应参数化。我们在模拟研究中将我们的方法与插塞贝伊西亚和常客替代方法进行比较,并表明我们的方法最接近于模型参数的准确不确定性量化,包括产生集成指数随机效应的差异。我们用NHANES数据在两个应用中展示了我们的方法。我们用NHAES数据在两个应用中展示了我们的方法。