Geographically and Temporally Weighted Quantile Regression Analysis Based on Multibandwidth Local Polynomial

The geographically and temporally weighted regression method based on weighted least squares estimation achieves optimal estimates under the assumption of Gauss-Markov independent identical distributions. However, these conditions cannot be always satisfied. If there are outliers or heavy-tailed distributions in the data, the least squares estimates may be significantly biased. On the other hand, quantile regression is less affected by outliers and is more robust than least squares regression, which can be applied in a broader range of applications under more relaxed conditions. More importantly, the least squares regression model only focuses on the mean of the response, while quantile regression explores the global distribution of the response variable (e.g., quantiles of the response variable) and can obtain richer information. In this paper, we propose the geographically and temporally weighted quantile regression model based on the local polynomial estimation. This model allows for different optimal bandwidths for different explanatory variables and use a two-step estimation method to obtain the estimates of the coefficients. To illustrate the superiority of the proposed method, we compare the proposed method with the geographically and temporally weighted least squares regression through numerical simulations. The simulation results show that the mean square error and the mean absolute error of the coefficient estimates for the proposed quantile regression model are both smaller than those of the least squares regression model. For example, at the 0.75 quantile, the mean square error and mean absolute error of the coefficient estimates based on the least squares regression are 10 times and 4 times those based on the quantile regression, respectively. This indicates that our proposed method is robust and can explore the global distribution of the response variable compared to the least squares regression model. Finally, to illustrate the practical ability of the method, we apply it to the data of Shanghai's commercial residential neighborhoods from 2017 to 2021 to investigate the effects of different factors on residential prices at different quantiles (e.g., high house prices, medium house prices, and low house prices). The results show that the explanatory variables have different effects on house prices at different quantiles. The spatial and temporal distributions of the coefficients of the variables differ significantly among high house prices, medium house prices, and low house prices, and the optimal bandwidths for different explanatory variables also differ. Compared to the MGTWR based on least squares regression, the quantile regression model proposed in this paper is more robust with the presence of outliers. After removing 1% of extreme values, the change in the mean absolute error of the fitting based on the quantile regression model is 1% smaller than that based on the least squares regression model. Additionally, the quantile regression model can explore the factors affecting the different price levels of the housing such as the high house prices, medium house prices, and low house prices. © 2024 Science Press. All rights reserved.