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Hierarchical Bayes small area estimation under a spatial model with application to health survey data

机译：空间模型下的贝叶斯小面积估计及其在健康调查数据中的应用

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In this paper we study small area estimation using area level models. We first consider the Fay-Herriot model (Fay and Herriot 1979) for the case of smoothed known sampling variances and the You-Chapman model (You and Chapman 2006) for the case of sampling variance modeling. Then we consider hierarchical Bayes (HB) spatial models that extend the Fay-Herriot and You-Chapman models by capturing both the geographically unstructured heterogeneity and spatial correlation effects among areas for local smoothing. The proposed models are implemented using the Gibbs sampling method for fully Bayesian inference. We apply the proposed models to the analysis of health survey data and make comparisons among the HB model-based estimates and direct design-based estimates. Our results have shown that the HB model-based estimates perform much better than the direct estimates. In addition, the proposed area level spatial models achieve smaller CVs than the Fay-Herriot and You-Chapman models, particularly for the areas with three or more neighbouring areas. Bayesian model comparison and model fit analysis are also presented.
机译：在本文中，我们研究使用面积模型的小面积估计。对于平滑的已知采样方差，我们首先考虑Fay-Herriot模型（Fay和Herriot 1979），对于采样方差建模，我们首先考虑You-Chapman模型（You和Chapman 2006）。然后，我们考虑通过捕获地理上非结构化的异质性和区域之间的空间相关效应来进行局部平滑，从而扩展了Fay-Herriot和You-Chapman模型的分层贝叶斯（HB）空间模型。所提出的模型是使用Gibbs采样方法实现的，以进行完全贝叶斯推理。我们将提出的模型应用于健康调查数据的分析，并在基于HB模型的估计值和基于直接设计的估计值之间进行比较。我们的结果表明，基于HB模型的估计比直接估计要好得多。此外，与Fay-Herriot和You-Chapman模型相比，拟议的区域级空间模型实现的CV较小，特别是对于具有三个或更多相邻区域的区域。还提出了贝叶斯模型比较和模型拟合分析。

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