Inference in Multiscale Geographically Weighted Regression
Inference in Multiscale Geographically Weighted Regression
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DOI：
10.1111/gean.12189
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发表时间：
2020-01-01
影响因子：
3.6
通讯作者：
Wolf, Levi John
中科院分区：
文献类型：
--
作者：
Yu, Hanchen;Fotheringham, A. Stewart;Wolf, Levi John
最近的一篇论文大大扩展了著名的地理加权回归(GWR)框架，允许对模型中的每个协变量分别推导GWR中的带宽或平滑因子-该框架称为多尺度GWR(MGWR)。然而，MGWR框架的一个局限性是，到目前为止，不可能对当地参数估计进行推断。在形式上，所谓的“HAT矩阵”，即将观测到的响应向量投影到预测的响应向量，在GWR中可用，但在MGWR中不可用。本文通过将广义加性模型重构为广义加性模型，将这一框架扩展到广义加性模型，然后推导出广义加性模型中局部参数的标准误差，从而解决了这一局限性。此外，我们还演示了如何获得MGWR模型的总体拟合度和模型中每个协变量的有效参数个数。这一统计量对于比较MGWR、GWR和传统全球模型之间的模型拟合以及调整多个假设检验至关重要。我们用模拟数据集和真实数据集演示了对MGWR框架的这些改进，并提供了到MGWR的新软件(MGWR1.0)的链接，其中包括这里描述的MGWR的新推理框架。
A recent paper expands the well-known geographically weighted regression (GWR) framework significantly by allowing the bandwidth or smoothing factor in GWR to be derived separately for each covariate in the model-a framework referred to as multiscale GWR (MGWR). However, one limitation of the MGWR framework is that, until now, no inference about the local parameter estimates was possible. Formally, the so-called "hat matrix," which projects the observed response vector into the predicted response vector, was available in GWR but not in MGWR. This paper addresses this limitation by reframing GWR as a Generalized Additive Model, extending this framework to MGWR and then deriving standard errors for the local parameters in MGWR. In addition, we also demonstrate how the effective number of parameters can be obtained for the overall fit of an MGWR model and for each of the covariates within the model. This statistic is essential for comparing model fit between MGWR, GWR, and traditional global models, as well as for adjusting multiple hypothesis tests. We demonstrate these advances to the MGWR framework with both a simulated data set and a real-world data set and provide a link to new software for MGWR (MGWR1.0) which includes the novel inferential framework for MGWR described here.