Statistical tests for spatial nonstationarity based on the geographically weighted regression model
Statistical tests for spatial nonstationarity based on the geographically weighted regression model
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DOI：
10.1068/a3162
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发表时间：
2000-01-01
影响因子：
4.2
通讯作者：
Zhang, WX
中科院分区：
文献类型：
--
作者：
Leung, Y;Mei, CL;Zhang, WX
地理加权回归（GWR）是一种通过校准多元回归模型来探索空间非平稳性的方法，该模型允许空间中不同点存在不同的关系。然而，正式的空间非平稳性测试程序尚未开发自成立以来的模型。在本文中，作者主要集中在与此模型相关的统计检验方法的发展。提出了检验GWR模型拟合优度和检验模型参数变异的统计量，并研究了它们的近似分布。这项工作使得有可能测试空间非平稳性在一个传统的统计方式。为了证实理论的论点，一些模拟运行，以探讨空间非平稳性的统计和结果是令人鼓舞的。为了简化模型，还制定了一个逐步选择重要自变量的程序。最后，研究了基于GWR模型的预测问题，并建立了因变量在新位置处真值的置信区间。该研究为基于GWR模型的空间非平稳性形式化分析奠定了基础。
Geographically weighted regression (GWR) is a way of exploring spatial nonstationarity by calibrating a multiple regression model which allows different relationships to exist at different points in space. Nevertheless, formal testing procedures for spatial nonstationarity have not been developed since the inception of the model. In this paper the authors focus mainly on the development of statistical testing methods relating to this model. Some appropriate statistics for testing the goodness of fit of the GWR model and for testing variation of the parameters in the model are proposed and their approximated distributions are investigated. The work makes it possible to test spatial nonstationarity in a conventional statistical manner. To substantiate the theoretical arguments, some simulations are run to examine the power of the statistics for exploring spatial nonstationarity and the results are encouraging. To streamline the model, a stepwise procedure for choosing important independent variables is also formulated. In the last section, a prediction problem based on the GWR model is studied, and a confidence interval for the true value of the dependent variable at a new location is also established. The study paves the path for formal analysis of spatial nonstationarity on the basis of the GWR model.