Spatial heterogeneity automatic detection and estimation
Spatial heterogeneity automatic detection and estimation
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DOI：
10.1016/j.csda.2022.107667
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发表时间：
2020-12
期刊：
影响因子：
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通讯作者：
Xin Wang;Zhengyuan Zhu-;Haozhe Zhang
中科院分区：
文献类型：
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作者：
Xin Wang;Zhengyuan Zhu-;Haozhe Zhang
空间回归被广泛用于因变量和解释协变量之间的关系建模。通常，线性关系在空间上变化，使得一些协变量对响应具有位置特定的影响。一个基本问题是如何检测模型中的系统性变化，并确定哪些位置共享共同的回归系数，哪些位置不共享。只有正确的模型结构才能保证系数的无偏估计和有效的推断。提出了一种新的方法，称为空间异质性自动检测和估计（SHADE），自动和同时子组和估计协变量效应的空间回归模型。SHADE对所有观测值对采用一类空间加权融合类型惩罚，使用空间信息构造特定于位置的权重，将系数聚类到子组中。在一定的规律性条件下，阴影被证明是能够识别真实的模型结构的概率接近1和估计回归系数一致。提出了一种交替方向乘子法（ADMM）来计算SHADE。在数值研究中，通过使用不同的权重选择和比较它们的精度来证明SHADE的经验性能。结果表明，空间信息可以增强子群结构分析在具有挑战性的情况下，当回归系数之间的空间变异很小或重复测量的数量很小。最后，阴影被应用到寻找自然资源调查和土地覆盖数据层之间的关系，以确定空间上可解释的群体。
Spatial regression is widely used for modeling the relationship between a dependent variable and explanatory covariates. Oftentimes, the linear relationships vary across space, such that some covariates have location-specific effects on the response. One fundamental question is how to detect the systematic variation in the model and identify which locations share common regression coefficients and which do not. Only a correct model structure can assure unbiased estimation of coefficients and valid inferences. A new procedure is proposed, called Spatial Heterogeneity Automatic Detection and Estimation (SHADE), for automatically and simultaneously subgrouping and estimating covariate effects for spatial regression models. The SHADE employs a class of spatially-weighted fusion type penalty on all pairs of observations, with location-specific weight constructed using spatial information, to cluster coefficients into subgroups. Under certain regularity conditions, the SHADE is shown to be able to identify the true model structure with probability approaching one and estimate regression coefficients consistently. An alternating direction method of multiplier algorithm (ADMM) is developed to compute the SHADE. In numerical studies, the empirical performance of the SHADE is demonstrated by using different choices of weights and comparing their accuracy. The results suggest that spatial information can enhance subgroup structure analysis in challenging situations when the spatial variation among regression coefficients is small or the number of repeated measures is small. Finally, the SHADE is applied to find the relationship between a natural resource survey and a land cover data layer to identify spatially interpretable groups.