Balancing spatial and non-spatial variation in varying coefficient modeling: a remedy for spurious correlation
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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 first develop a Moran eigenvector approach estimating spatially and non-spatially varying coefficients (S NVC). While the computational burden can be prohibitive, even for moderate samples, we lighten this cost by applying a pre-conditioning estimation approach. A Monte Carlo simulation experiment comparing our S NVC model with existing SVC models suggests both estimation accuracy and computational efficiency for our approach. Beyond that, somewhat surprisingly, our approach estimates identify 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 estimating SVCs. Finally, our S NVC model is employed to analyze a residential land price dataset. Its results suggest existence of both spatial and non-spatial variation in regression coefficients in practice. The S NVC model is implemented in the R package spmoran.
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