Spatial modeling with spatially varying coefficient processes
Spatial modeling with spatially varying coefficient processes
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DOI：
10.1198/016214503000170
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发表时间：
2003-06-01
影响因子：
3.7
通讯作者：
Banerjee, S
中科院分区：
文献类型：
--
作者：
Gelfand, AE;Kim, HJ;Banerjee, S
在许多应用中，目标是建立回归模型，以在响应空间相关的假设下解释感兴趣区域上的响应变量。在几乎所有这项工作中，回归系数都被假设为在该区域内恒定。然而，在某些应用中，系数预计会在地方或次区域层面有所不同。这里我们重点关注当地的案例。尽管对系数的空间表面进行参数化建模是可能的，但在这里我们认为将表面视为空间过程的实现更为自然和灵活。我们展示了如何在高斯响应的背景下形式化这种建模，在随机效应和解释残差方面提供有吸引力的解释。我们还提供广义线性模型和时空设置的扩展。我们用一个试图解释（记录）单户住宅售价的数据集来说明静态和动态建模。
In many applications, the objective is to build regression models to explain a response variable over a region of interest under the assumption that the responses are spatially correlated. In nearly all of this work, the regression coefficients are assumed to be constant over the region. However, in some applications, coefficients are expected to vary at the local or subregional level. Here we focus on the local case. Although parametric modeling of the spatial surface for the coefficient is possible, here we argue that it is more natural and flexible to view the surface as a realization from a spatial process. We show how such modeling can be formalized in the context of Gaussian responses providing attractive interpretation in terms of both random effects and explaining residuals. We also offer extensions to generalized linear models and to spatio-temporal setting. We illustrate both static and dynamic modeling with a dataset that attempts to explain (log) selling price of single-family houses.