Multiscale spatially varying coefficient modelling using a Geographical Gaussian Process GAM
Multiscale spatially varying coefficient modelling using a Geographical Gaussian Process GAM
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DOI：
10.1080/13658816.2023.2270285
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发表时间：
2023-10
影响因子：
5.7
通讯作者：
A. Comber;Paul Harris;C. Brunsdon
中科院分区：
文献类型：
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作者：
A. Comber;Paul Harris;C. Brunsdon
摘要提出了一种基于地理高斯过程GAM （GGP-GAM）的空间变系数（SVC）回归方法：高斯过程样条在观测点参数化的广义加性模型（GAM）。将GGP-GAM应用于具有不同程度空间异质性的多个模拟系数数据集，并在一系列拟合指标下优于SVC品牌领导者多尺度地理加权回归（MGWR）。然后将两者应用于英国脱欧案例研究并进行比较，MGWR略优于GGP-GAM。讨论了两种方法的理论框架和实现：GWR模型校准多个模型，而GAMs提供完整的单一模型；GAMs可以自动惩罚局部共线性；基于gwr的方法在计算上要求更高；MGWR仍然只适用于高斯响应；MGWR带宽是空间异质性的直观指标。还讨论了GGP-GAM的校准和调整，并确定了未来工作的领域，包括创建一个用户友好的软件包来支持模型创建和系数映射，并促进与备选SVC模型的比较。最后观察到GGP-GAMs有潜力克服一些长期以来对基于gwr的回归方法的保留意见，并在更广泛的社区中提高对SVCs的认识。
Abstract This paper proposes a novel spatially varying coefficient (SVC) regression through a Geographical Gaussian Process GAM (GGP-GAM): a Generalized Additive Model (GAM) with Gaussian Process (GP) splines parameterised at observation locations. A GGP-GAM was applied to multiple simulated coefficient datasets exhibiting varying degrees of spatial heterogeneity and out-performed the SVC brand-leader, Multiscale Geographically Weighted Regression (MGWR), under a range of fit metrics. Both were then applied to a Brexit case study and compared, with MGWR marginally out-performing GGP-GAM. The theoretical frameworks and implementation of both approaches are discussed: GWR models calibrate multiple models whereas GAMs provide a full single model; GAMs can automatically penalise local collinearity; GWR-based approaches are computationally more demanding; MGWR is still only for Gaussian responses; MGWR bandwidths are intuitive indicators of spatial heterogeneity. GGP-GAM calibration and tuning are also discussed and areas of future work are identified, including the creation of a user-friendly package to support model creation and coefficient mapping, and to facilitate ease of comparison with alternate SVC models. A final observation that GGP-GAMs have the potential to overcome some of the long-standing reservations about GWR-based regression methods and to elevate the perception of SVCs amongst the broader community.