The geographically weighted regression (GWR) is an essential tool for estimating the spatial variation of relationships between dependent and independent variables in geographical contexts. However, GWR suffers from the problem that classical linear regressions, which compose the GWR model, are more prone to be underfitting, especially for significant volume and complex nonlinear data, causing inferior comparative performance. Nevertheless, some advanced models, such as the decision tree and the support vector machine, can learn features from complex data more effectively while they cannot provide explainable quantification for the spatial variation of localized relationships. To address the above issues, we propose a geographically gradient boosting weighted regression model, GWRBoost, that applies the localized additive model and gradient boosting optimization method to alleviate underfitting problems and retains explainable quantification capability for spatially-varying relationships between geographically located variables. Furthermore, we formulate the computation method of the Akaike information score for the proposed model to conduct the comparative analysis with the classic GWR algorithm. Simulation experiments and the empirical case study are applied to prove the efficient performance and practical value of GWRBoost. The results show that our proposed model can reduce the RMSE by 18.3% in parameter estimation accuracy and AICc by 67.3% in the goodness of fit.
翻译:地理加权回归(GWR)是估算地域背景中依赖性和独立变量之间关系的空间差异的基本工具。然而,GWR遇到的问题是,构成GWR模型的古典线性回归(古典线性回归(古典线性回归)(古典线性回归)(古典线性回归)(古典线性回归(古典线性回归)(古典线性回归)(古典线性非线性数据)更容易不适应,特别是大量和复杂的非线性数据,造成较低的比较性能。然而,一些先进的模型,如决策树和辅助矢量机等,可以更有效地从复杂数据中学习特征,而不能为本地关系的空间差异提供可解释的量化。为了解决上述问题,我们提出了一种地理梯度推增加权回归模型(GWRBoost),采用本地化添加模型和梯度推进优化法(梯度优化法),以缓解不适应的问题,并保留用于地理位置变量之间空间变化关系的可解释的量化能力。此外,我们为拟议的模型制定了Akaik信息评分法的计算方法,以便与典型的GWRWSBoost进行比较分析。模拟实验和实验,以证明GWWSBost的高效率和实用价值。结果的模型可以减少RMSE的18.3%的准确性能。