When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no longer produces asymptotically unbiased inference. We construct a weight-exponentiated formulation for the random effects distribution that achieves unbiased inference for generating hyperparameters of the random effects. We contrast our approach with frequentist methods that rely on numerical integration to reveal that only the Bayesian method achieves both unbiased estimation with respect to the sampling design distribution and consistency with respect to the population generating distribution. Our simulations and real data example for a survey of business establishments demonstrate the utility of our approach across different modeling formulations and sampling designs. This work serves as a capstone for recent developmental efforts that combine traditional survey estimation approaches with the Bayesian modeling paradigm and provides a bridge across the two rich but disparate sub-fields.
翻译:当随机效应与抽样设计变量相关时,通常采用个别调查权重(被认为与单位调查包含的概率成反比)来形成假象的概率,不再产生无症状的不带偏见的推断。我们为随机效应分布设计了一个加权光化配方,这种随机效应分布可以得出不带偏见的推论,产生随机效应的超参数。我们将我们的方法与依赖数字集成的常客方法作对比,以表明只有巴伊西亚方法在抽样设计分布和人口分布方面实现无偏见的估计。我们用于调查商业机构的模拟和真实数据实例显示了我们在不同模型配方和抽样设计方面的做法的效用。这项工作是近期发展努力的顶点,将传统的调查估计方法与巴伊西亚模型化模式相结合,并提供跨越两个丰富但互不相容的子领域的桥梁。