Extraction of Continuous and Discrete Spatial Heterogeneities: Fusion Model of Spatially Varying Coefficient Model and Sparse Modelling

Abstract

Geospatial phenomena often have spatial heterogeneity, which is caused by differences in the data generation process from place to place. There are two types of spatial heterogeneity: continuous and discrete, and there has been much discussion about how to analyze one type of spatial heterogeneity. Although geospatial phenomena can have both types of spatial heterogeneities, previous studies have not sufficiently discussed how to consider these two different types of spatial heterogeneity simultaneously and how to detect them separately, which may lead to biased estimates and the wrong interpretation of geospatial phenomena. This study proposes a new approach for the analysis of spatial data with both heterogeneities by combining the eigenvector spatial filtering-based spatially varying coefficient (ESF-SVC) model, which assumes the continuous spatial heterogeneity and generalized lasso (GL) estimation, which assumes discrete spatial heterogeneity and proposes the ESF-GL-SVC model. The performance of ESF-GL-SVC was evaluated through experiments based on a Monte Carlo simulation and confirms that the ESF-GL-SVC showed better performance in estimating coefficients with both types of spatial heterogeneity than the previous two models. The application of the apartment rent data showed that the ESF-GL-SVC outputs the result with the smallest BIC value, and the estimated coefficients depict continuous and discrete spatial heterogeneity in the dataset. Reasonable coefficients were estimated using the ESF-GL-SVC, although some coefficients by ESF-SVC were not.

Multiscale Continuous and Discrete Spatial Heterogeneity Analysis: The Development of a Local Model Combining Eigenvector Spatial Filters and Generalized Lasso Penalties

“…Hence, continuous and discrete spatial processes jointly shape the housing market, and both need to be considered in the analysis. In this regard, Inoue and Den (2022) combined ESF‐SVC and GL to develop the ESF‐GL‐SVC model, which extracts continuous and discrete spatial heterogeneity within the same modeling framework. However, ESF‐SVC‐GL inherits the limitations of the ESF‐SVC in that it ignores local scales of continuous spatial variations, leading to biased estimates and incorrect interpretations.…”