  While spatially varying coefficient (SVC) modeling is popular in applied
science, its computational burden is substantial. This is especially true if a
multiscale property of SVC is considered. Given this background, this study
develops 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 these
steps, the likelihood maximization cost is independent of N. Step (iii) further
accelerates the likelihood maximization so that multiscale SVCs can be
estimated even if the number of SVCs, K, is large. The M-SVC approach is
compared with geographically weighted regression (GWR) through Monte Carlo
simulation experiments. These simulation results show that our approach is far
faster than GWR when N is large, despite numerically estimating 2K parameters
while GWR numerically estimates only 1 parameter. Then, the proposed approach
is applied to a land price analysis as an illustration. The developed SVC
estimation approach is implemented in the R package "spmoran."
