In spatial regression analysis, a suitable specification of the mean regression model is crucial for unbiased analysis. Also, to enhance statistical efficiency of the mean regression analysis, we need to suitably account for the underlying spatial correlation structure. In this paper, we focus on selection of an appropriate mean model in spatial regression analysis under a general anisotropic nested correlation structure considered in Adegboye et al. (2018). We propose a distribution-free model selection criterion, called the Spatial Information Criterion (SIC), which is an estimate of the weighted mean squared error for predicting the response variable, and relies on assumptions only for the first two moments of the spatial response data. The simulations under the settings of covariate selection reveal that the SIC performs well for covariate selection in the mean model regardless of the correlation structure is nested/non-nested (multi-source or not), isotropic/anisotropic (direction-dependent or not). Also, the SIC accommodates both continuous and count response data. We illustrate the utility of the proposed method by a real data application concerning the predictive regression model for the fine particulate matter (PM_2.5) concentration.

在空间回归分析中，均值回归模型的合适规范对于无偏分析至关重要。同样，为了提高均值回归分析的统计效率，我们需要适当考虑潜在的空间相关性结构。在本文中，我们着重在Adegboye等人考虑的一般各向异性嵌套相关结构下，在空间回归分析中选择合适的均值模型。（2018）。我们提出了一种无分布的模型选择标准，称为空间信息标准（SIC），该标准是对加权均方误差的估计，用于预测响应变量，并且仅依赖于空间响应数据的前两个时刻的假设。在协变量选择设置下的仿真显示，无论相关结构是嵌套/非嵌套（是否有多源），各向同性/各向异性（是否有方向依赖），SIC在均值模型中的协变量选择方面都表现良好。此外，SIC可以容纳连续和计数响应数据。我们通过关于细颗粒物（PM）的预测回归模型的实际数据应用来说明所提出方法的实用性_2.5）浓度。