Simultaneous coefficient penalization and model selection in geographically weighted regression: the geographically weighted lasso
Simultaneous coefficient penalization and model selection in geographically weighted regression: the geographically weighted lasso
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DOI：
10.1068/a40256
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发表时间：
2009-03-01
影响因子：
4.2
通讯作者：
Wheeler, David C.
中科院分区：
文献类型：
--
作者：
Wheeler, David C.
在空间分析领域，一些研究人员对局部变量之间的关系建模的兴趣导致了具有空间变化系数的回归模型的发展。其中一个被广泛应用的模型是地理加权回归（GWR）。在GWR的应用中，回归系数的空间模式的边际推断往往是感兴趣的，因为是，不太典型的，预测和估计的响应变量。实证研究和模拟研究表明，解释变量的局部相关性可能导致GWR中的估计回归系数强相关，因此，对变量之间的关系进行推断是有问题的。作者介绍了一种惩罚形式的GWR，称为“地理加权套索”（GWL），它增加了一个约束的估计回归系数的大小，以限制影响的因果变量相关性。GWL还通过在研究区域的某些位置潜在地将某些估计的回归系数收缩为零来执行局部模型选择。两个版本的GWL介绍：一个旨在提高预测的响应变量，和一个更面向约束回归系数的推断。将GWL应用于模拟数据集和真实的数据集的结果表明，该方法在存在共线性的情况下稳定回归系数，并且产生比GWR和GWR的另一个约束版本地理加权岭回归更低的响应变量的预测和估计误差。
In the field of spatial analysis, the interest of some researchers in modeling relationships between variables locally has led to the development of regression models with spatially varying coefficients. One such model that has been widely applied is geographically weighted regression (GWR). In the application of GWR, marginal inference on the spatial pattern of regression coefficients is often of interest, as is, less typically, prediction and estimation of the response variable. Empirical research and simulation studies have demonstrated that local correlation in explanatory variables can lead to estimated regression coefficients in GWR that are strongly correlated and, hence, problematic for inference on relationships between variables. The author introduces a penalized form of GWR, called the 'geographically weighted lasso' (GWL) which adds a constraint on the magnitude of the estimated regression coefficients to limit the effects of explanatory-variable correlation. The GWL also performs local model selection by potentially shrinking some of the estimated regression coefficients to zero in some locations of the study area. Two versions of the GWL are introduced: one designed to improve prediction of the response variable, and one more oriented toward constraining regression coefficients for inference. The results of applying the GWL to simulated and real datasets show that this method stabilizes regression coefficients in the presence of collinearity and produces lower prediction and estimation error of the response variable than does GWR and another constrained version of GWR-geographically weighted ridge regression.