  This study develops a spatial additive mixed modeling (AMM) approach
estimating spatial and non-spatial effects from large samples, such as millions
of observations. Although fast AMM approaches are already well-established,
they are restrictive in that they assume an known spatial dependence structure.
To overcome this limitation, this study develops a fast AMM with the estimation
of spatial structure in residuals and regression coefficients together with
non-spatial effects. We rely on a Moran coefficient-based approach to estimate
the spatial structure. The proposed approach pre-compresses large matrices
whose size grows with respect to the sample size N before the model estimation;
thus, the computational complexity for the estimation is independent of the
sample size. Furthermore, the pre-compression is done through a block-wise
procedure that makes the memory consumption independent of N. Eventually, the
spatial AMM is memory-free and fast even for millions of observations. The
developed approach is compared to alternatives through Monte Carlo simulation
experiments. The result confirms the accuracy and computational efficiency of
the developed approach. The developed approaches are implemented in an R
package spmoran.
