空间多观测样本的地理加权回归模型

Geographically Weighted Regression for Spatial Data with Replicates

地理加权回归(GWR)以及GWR改进模型无法处理空间点上多个观测样本的情况,本文对GWR进行了拓展,构建了一种可以处理多观测样本的地理加权回归模型(MRGWR)。MRGWR在估计回归系数时,充分利用了回归关系在邻近点上具有相似性的特点,对邻近空间点的观测样本施加不同权重。通过数值实验评估了MRGWR的估计性能,并与普通最小二乘回归和GWR模型进行了比较。采用MRGWR模型探究了物理海洋学中海洋中尺度涡旋热反馈问题,揭示了北太平洋中尺度海面净热通量异常对中尺度海面温度(SST)异常的响应关系。研究结果表明,中尺度海面净热通量异常对中尺度SST异常的响应关系存在显著的季节和空间变化。

The paper extends the classical GWR and constants a multiple replicates geographically weighted regression(MRGWR)that is able to handle an arbitrary number of replicates at each individual location.MRGWR adequately utilizes the similarity of regression relationships at neighboring locations when estimating regression coefficients,and imposes different weights on the replicates at neighboring locations.Moreover,it can directly handle the case of arbitrary number of replicates at each location.Numerical experiments are conducted to estimate the performance of the proposed model and to compare with ordinary least squares regression(OLSR)and GWR models.Furthermore,MRGWR is applied to resolving an important scientific problem in oceanography,i.e.,the ocean mesoscale eddy thermal feedback,revealing the seasonal and spatial variations in the response relationship between mesoscale sea surface heat flux anomalies and mesoscale sea surface temperature(SST)anomalies in the North Pacific.