Balancing Spatial and Non-Spatial Variation in Varying Coefficient Modeling: A Remedy for Spurious Correlation

Abstract

This study discusses the importance of balancing spatial and non-spatial variation in spatial regression modeling. Unlike spatially varying coefficients (SVC) modeling, which is popular in spatial statistics, non-spatially varying coefficients (NVC) modeling has largely been unexplored in spatial fields. Nevertheless, as we will explain, consideration of non-spatial variation is needed not only to improve model accuracy but also to reduce spurious correlation among varying coefficients, which is a major problem in SVC modeling. We consider a Moran eigenvector approach modeling spatially and non-spatially varying coefficients (S&NVC). A Monte Carlo simulation experiment comparing our S&NVC model with existing SVC models suggests both modeling accuracy and computational efficiency for our approach. Beyond that, somewhat surprisingly, our approach identifies true and spurious correlations among coefficients nearly perfectly, even when usual SVC models suffer from severe spurious correlations. It implies that S&NVC model should be used even when the analysis purpose is modeling SVCs. Finally, our S&NVC model is employed to analyze a residential land price data set. Its results suggest existence of both spatial and non-spatial variation in regression coefficients in practice. The S&NVC model is now implemented in the R package spmoran.