  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 dataset. 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.
