A cost-effective algorithm for calibrating multiscale geographically weighted regression models

ABSTRACT

The multiscale geographically weighted regression (MGWR) model is a useful extension of the geographically weighted regression (GWR) model. MGWR, however, is a kind of Nadaraya–Watson kernel smoother, which usually leads to inaccurate estimates for the regression function and suffers from the boundary effect. Moreover, the widely used calibration technique for the MGWR with a back-fitting estimator (MGWR-BF) is computationally demanding, preventing it from being applied to large-scale data. To overcome these problems, we proposed a local linear-fitting-based MGWR (MGWR-LL) by introducing a local spatially varying coefficient model in which coefficients of different variables could be characterised as linear functions of spatial coordinates with different degrees of smoothness. Then the model was calibrated with a two-step least-squared estimated algorithm. Both simulated and actual data were implemented to validate the performance of the proposed method. The results consistently showed that the MGWR-LL automatically corrected for the boundary effect and improved the accuracy in most cases, not only in the goodness-of-fit measure but also in reducing the bias of the coefficient estimates. Moreover, the MGWR-LL significantly outperformed the MGWR-BF in computational cost, especially for larger-scale data. These results demonstrated that the proposed method can be a useful tool for the MGWR calibration.

KEYWORDS:

• Multiscale GWR
• back-fitting estimator
• local linear estimator
• spatial nonstationarity
• large-scale data

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data and codes availability statement

The codes and datasets that support the findings of this study are available in https://doi.org/10.6084/m9.figshare.14561820.v1. The toolkit used for comparison in this study is available in their corresponding links as noted in Section 4.1. The actual dataset is available at https://www.kaggle.com/c/zillow-prize-1.

Additional information

Funding

Funding was provided by the Natural Science Foundation of China [Grant No. 41961055, U1811464] and the Outstanding Youth Project of Education Department of Hunan Province [Grant No.19B078].

Notes on contributors

Bo Wu

Bo Wu is a Professor at Jiangxi Normal University. His research interests include spatiotemporal data analysis, and remote sensing image processing.

Jinbiao Yan

Jinbao Yan is a PhD candidate at Jiangxi Normal University. His research interest is spatial statistical analysis.

Hui Lin

Hui Lin is a leading Professor at Jiangxi Normal University, His research interest is virtual geographical environment.