1. Multiscale cooperative optimization in multiscale geographically weighted regression models.
- Author
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Yan, Jinbiao, Wu, Bo, and Zheng, He
- Subjects
- *
GENETIC algorithms , *ESTIMATION bias , *SIGNAL-to-noise ratio , *REGRESSION analysis , *ALGORITHMS , *AUTOCORRELATION (Statistics) - Abstract
AbstractScale in multiscale geographically weighted regression (MGWR) directly impacts the accuracy of coefficient estimates and shapes the comprehensive evaluation of the intensity of spatially non-stationary relationships. Presently, MGWR primarily utilizes back-fitting for sequentially optimizing multiple scales (MGWR-BF). However, the set of individual optima obtained through sequential optimization may not necessarily represent the global optimum. To address this issue, this paper proposes a multi-scale cooperative optimization within MGWR (MGWR-GA) model. Specifically, MGWR-GA employs a genetic algorithm to simultaneously input potential scale combinations, each comprising P scales. Subsequently, it introduces a dedicated overall estimation algorithm designed for these P scales, ultimately determining the optimal scale combinations based on the AICc. Simulation experiments have shown that, at least for global stationarity, the scales obtained by MGWR-GA approximate the true values across twelve different test environments. Additionally, the coefficient estimation bias of MGWR-GA is lower than that of MGWR-BF, especially in low signal-to-noise ratio settings. Empirical experiments further confirm the effectiveness of MGWR-GA in identifying both globally stationary and locally non-stationary scales. Furthermore, MGWR-GA outperforms MGWR-BF in terms of goodness-of-fit, adjusted goodness-of-fit, AICc and spatial autocorrelation of residuals. These findings indicate that MGWR-GA can serve as a valuable tool for modeling spatially non-stationary relationships. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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