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While spatially varying coefficient (SVC) modeling is popular in appliedscience, its computational burden is substantial. This is especially true if amultiscale property of SVC is considered. Given this background, this studydevelops a Moran's eigenvector-based spatially varying coefficients (M-SVC)modeling approach that estimates multiscale SVCs computationally efficiently.This estimation is accelerated through a (i) rank reduction, (ii)pre-compression, and (iii) sequential likelihood maximization. Steps (i) and(ii) eliminate the sample size N from the likelihood function; after thesesteps, the likelihood maximization cost is independent of N. Step (iii) furtheraccelerates the likelihood maximization so that multiscale SVCs can beestimated even if the number of SVCs, K, is large. The M-SVC approach iscompared with geographically weighted regression (GWR) through Monte Carlosimulation experiments. These simulation results show that our approach is farfaster than GWR when N is large, despite numerically estimating 2K parameterswhile GWR numerically estimates only 1 parameter. Then, the proposed approachis applied to a land price analysis as an illustration. The developed SVCestimation approach is implemented in the R package "spmoran."

Spatially varying coefficient modeling for large datasets: Eliminating N from spatial regressions