Sub-Model Aggregation for Scalable Eigenvector Spatial Filtering: Application to Spatially Varying Coefficient Modeling

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.