This study proposes a method for aggregating/synthesizing global and local sub-models for fast and flexible spatial regression modeling. Eigenvector spatial filtering (ESF) was used to model spatially varying coefficients and spatial dependence in the residuals by sub-model, while the generalized product-of-experts method was used to aggregate these sub-models. The major advantages of the proposed method are as follows: (i) it is highly scalable for large samples in terms of accuracy and computational efficiency; (ii) it is easily implemented by estimating sub-models independently first and aggregating/averaging them thereafter; and (iii) likelihood-based inference is available because the marginal likelihood is available in closed-form. The accuracy and computational efficiency of the proposed method are confirmed using Monte Carlo simulation experiments. This method was then applied to residential land price analysis in Japan. The results demonstrate the usefulness of this method for improving the interpretability of spatially varying coefficients. The proposed method is implemented in an R package spmoran (version 0.3.0 or later).

翻译：本研究提出了一种聚合/合成全局与局部子模型的方法，用于实现快速灵活的空间回归建模。采用特征向量空间滤波通过子模型对空间变系数及残差中的空间依赖性进行建模，并利用广义专家乘积方法聚合这些子模型。所提方法的主要优势如下：(i) 在精度与计算效率方面对大规模样本具有高度可扩展性；(ii) 易于实现，可先独立估计子模型，随后进行聚合/平均处理；(iii) 由于边际似然可推导出闭合形式，因此可进行基于似然的推断。通过蒙特卡洛模拟实验验证了所提方法的精度与计算效率，并将其应用于日本住宅用地价格分析。结果表明，该方法在提升空间变系数可解释性方面具有实用价值。所提方法已集成于R语言包spmoran（0.3.0及以上版本）中。