基于IGGⅢ的地理加权回归模型研究
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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R~2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 R~2. 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.
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 R~2. 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.
引文
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[15] 李广超,李如仁,卢月明,等.利用主成分分析法及地理加权回归模型分析AOD数据[J].测绘通报,2018(4):50-56.
[2] 覃文忠,王建梅,刘妙龙.混合地理加权回归模型算法研究[J].武汉大学学报(信息科学版),2007,32(2):115-119.
[3] HUANG B,WU B,BARRY M.Geographically and temporally weighted regression for modeling spatio-temporal variation in house prices[J].International Journal of Geographical Information Science,2010,24(3):383-401.
[4] 杨毅.顾及时空非平稳性的地理加权回归方法研究[D].武汉:武汉大学,2016.
[5] 赵阳阳,刘纪平,徐胜华,等.一种基于半监督学习的地理加权回归方法[J].测绘学报,2017,46(1):123-129.
[6] 吴森森,地理时空神经网络加权回归理论与方法研究[D].杭州:浙江大学,2018.
[7] 卢月明,王亮,仇阿根,等.一种基于主成分分析的时空地理加权回归方法[J].测绘科学技术学报,2017,34(6):654-658.
[8] ZHANG H G,MEI C L.Local least absolute deviation estimation of spatially varying coefficient models:robust geographically weighted regression approaches[J].International Journal of Geographical Information Science,2011,25(9):1467-1489.
[9] FARBER S,ANTONIO P.A systematic investigation of cross-validation in GWR model estimation:empirical analysis and Monte Carlo simulations[J].Journal of Geographical Systems,2007,9(4):371-396.
[10] HUBER P J.Robust estimation of a location parameter[M]//Breakthroughs in Statistics.New York:Springer,1992:492-518.
[11] 周江文.经典误差理论与抗差估计[J].测绘学报,1989,18(2):115-120.
[12] 陈西强,黄张裕.抗差估计的选权迭代法分析与比较[J].测绘工程,2010,19(4):14-17.
[13] 龚循强,李志林.稳健加权总体最小二乘法.稳健加权总体最小二乘法[J].测绘学报,2014,43(9):888-894.
[14] 王潜心,徐天河,许国昌.粗差检测与抗差估计相结合的方法在动态相对定位中的应用[J].武汉大学学报(信息科学版),2011,36(4):476-480.
[15] 李广超,李如仁,卢月明,等.利用主成分分析法及地理加权回归模型分析AOD数据[J].测绘通报,2018(4):50-56.