基于IGGⅢ的地理加权回归模型研究  

Research on geographically weighted regression based on IGGⅢ

作　　者：于志英 张福浩[1] 仇阿根[1] 赵阳阳[1] YU Zhiying;ZHANG Fuhao;QIU Agen;ZHAO Yangyang(Chinese Academy of Surveying and Mapping, Beijing 100830, China)

机构地区：[1]中国测绘科学研究院

出　　处：《测绘通报》2019年第7期23-27,共5页Bulletin of Surveying and Mapping

基　　金：国家基础测绘科技项目(2018KJ0104);国家重点研发计划(2018YFC0807000)

摘　　要：针对离群值存在时地理加权回归模型拟合效果较差的问题,本文提出了基于IGGⅢ的地理加权回归方法。核心是采用IGGⅢ方案中的权函数计算权重矩阵,将权因子用于地理加权回归参数估计模型。利用模拟数据和真实数据与GWR、ACV-GWR进行对比试验,以MSE、MAE和R2作为指标对结果进行评价。模拟试验结果显示,IGGⅢ-GWR比GWR性能分别提升了51.14%、23.77%、28.4%,比ACV-GWR分别提升了49.96%、22.57%、27.1%;真实试验结果显示,IGGⅢ-GWR比GWR性能分别提升了12.65%、7.44%、0.37%,比ACV-GWR分别提升了11.85%、6.96%、0.34%。试验结果表明,基于IGGⅢ的地理加权回归可提高模型的抗差能力,拟合效果更好。Aiming at the problem that the geographically weighted regression model has poor fitting effect when the outliers exist, a geographically weighted regression method based on IGGⅢ is proposed. The core is to use the weight function in the IGGⅢ scheme to calculate the weight matrix, and the weight factor is used in the geo-weighted regression parameter estimation model. The simulation data and the real data are used for the test, compared with GWR and ACV-GWR, and the results were evaluated by MSE, MAE and R2. The simulation results show that the performance of IGGⅢ-GWR is increased by 51.14%, 23.77% and 28.4% than GWR, increased by 49.96%, 22.57% and 27.1% than ACV-GWR. The actual experimental results show that IGGⅢ-GWR is 12.65%, 7.44% and 0.37% higher than GWR, respectively, and 11.85%, 6.96% and 0.34% higher than ACV-GWR. The experimental results show that the IGGⅢ-GWR can improve the robustness and fitting effect of GWR.

关 键 词：IGGⅢ 地理加权回归 参数估计 抗差估计 空气质量分析 

分 类 号：P208[天文地球—地图制图学与地理信息工程]