基于IGGⅢ的地理加权回归模型研究

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。

Research on geographically weighted regression based on IGGⅢ

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.