Gelfand Alan E, Kim Hyon-Jung, Sirmans C F, Banerjee Sudipto
Institute of Statistics and Decision Sciences, Duke University, Durham, NC 27708-0251.
Department of Mathematical Sciences, University of Oulu, Finland.
J Am Stat Assoc. 2003;98(462):387-396. doi: 10.1198/016214503000170. Epub 2011 Dec 31.
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.
在许多应用中，目标是构建回归模型，以便在响应具有空间相关性的假设下，解释感兴趣区域内的一个响应变量。在几乎所有此类工作中，回归系数在该区域内被假定为常数。然而，在某些应用中，系数预计会在局部或子区域层面发生变化。在此我们关注局部情况。虽然对系数的空间曲面进行参数建模是可行的，但我们认为将该曲面视为空间过程的一个实现会更自然且更灵活。我们展示了在高斯响应的背景下如何将这种建模形式化，这在随机效应和解释残差方面都提供了有吸引力的解释。我们还将其扩展到广义线性模型和时空设置。我们用一个试图解释单户住宅（对数）销售价格的数据集说明了静态和动态建模。
