Hyper-local geographically weighted regression: extending GWR through local model selection and local bandwidth optimization
Hyper-local geographically weighted regression: extending GWR through local model selection and local bandwidth optimization
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DOI：
10.5311/josis.2018.17.422
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发表时间：
2018-01-01
影响因子：
1.4
通讯作者：
Harris, Paul
中科院分区：
文献类型：
--
作者：
Comber, Alexis;Wang, Yunqiang;Harris, Paul
地理加权回归 (GWR) 本质上是一种探索性技术，用于检查数据关系中的过程非平稳性。本文开发并应用了超本地 GWR，进一步扩展了此类研究。超本地 GWR 同时优化本地模型选择（协变量包含在每个本地回归中）和本地内核带宽规范（本地应包含多少数据）。这些是使用模型拟合度来评估的。超局部 GWR 方法评估每个位置的不同内核带宽，并选择最简约的局部回归模型。通过允许模型和带宽局部变化，该方法扩展并完善了标准 GWR 下的一刀切的“全地图模型”和“恒定带宽校准”。结果为局部回归提供了另一种、补充性和更细致的解释。通过案例研究对中国北方流域 689 个地点收集的土壤全氮 (STN) 和土壤全磷 (STP) 数据进行建模来说明该方法。该分析比较了 STN 和 STP 的线性回归、标准 GWR 和超局部 GWR 模型，并强调了不同位置的协变量通过不同的 GWR 方法和带宽的空间变化被识别为 STN 和 STP 的显着预测因子。超局部 GWR 结果表明，STN 过程比通过 GWR 标准应用发现的过程更加不稳定和局部化。相比之下，两种 GWR 方法之间的 STP 结果更具证实性（即相似），为观察到的中等非平稳关系的性质提供了额外的保证。也就是说，标准 GWR 可能会低估局部空间异质性强烈存在的情况（如 STN 案例研究中），而可能会高估存在空间同质性的情况（如 STP 案例研究中）。讨论了超本地 GWR 的总体优势，特别是在 GWR 最初研究目标的背景下。超局部方法提供了与标准 GWR 发现的局部回归建模相反的有用视图。在存在空间非平稳性的情况下，超局部 GWR 提供比标准 GWR 分析更细致的定位指示，并且可用于建议进一步分析和调查的方向。建议进一步开展一些工作。
Geographically weighted regression (GWR) is an inherently exploratory technique for examining process non-stationarity in data relationships. This paper develops and applies a hyper-local GWR which extends such investigations further. The hyper-local GWR simultaneously optimizes both local model selection (which covariates to include in each local regression) and local kernel bandwidth specification (how much data should be included locally). These are evaluated using a measure of model fit. The hyper-local GWR approach evaluates different kernel bandwidths at each location and selects the most parsimonious local regression model. By allowing models and bandwidths to vary locally, this approach extends and refines the one-size-fits-all "whole map model" and "constant bandwidth calibration" under standard GWR. The results provide an alternative, complementary and more nuanced interpretation of localized regression. The method is illustrated using a case study modeling soil total nitrogen (STN) and soil total phosphorus (STP) from data collected at 689 locations in a watershed in Northern China. The analysis compares linear regression, standard GWR, and hyper-local GWR models of STN and STP and highlights the different locations at which covariates are identified as significant predictors of STN and STP by the different GWR approaches and the spatial variation in bandwidths. The hyper-local GWR results indicate that the STN processes are more non-stationary and localized than found via a standard application of GWR. By contrast, the results for STP are more confirmatory (i.e., similar) between the two GWR approaches providing extra assurance about the nature of the moderate non-stationary relationships observed. That is, a standard GWR may underestimate localized spatial heterogeneity where it is strongly present (as in the STN case study) and may overestimate it where spatial homogeneity is present (as in the STP case study). The overall benefits of hyper-local GWR are discussed, particularly in the context of the original investigative aims of GWR. A hyper-local approach provides a useful counter view of local regression modeling to that found with standard GWR. Where spatial non-stationarity exists, the hyper-local GWR provides a more spatially nuanced indication of the localization than a standard GWR analysis and can be used to suggest the direction of further analyses and investigations. Some areas of further work are suggested.