  As with the advancement of geographical information systems, non-Gaussian
spatial data is getting larger and more diverse. Considering this background,
this study develops a general framework for fast and flexible non-Gaussian
regression, especially for spatial/spatiotemporal modeling. The developed
model, termed the compositionally-warped additive mixed model (CAMM), combines
an additive mixed model (AMM) and the compositionally-warped Gaussian process
to model a wide variety of non-Gaussian continuous data including spatial and
other effects. Specific advantages of the proposed CAMM requires no explicit
assumption of data distribution unlike existing AMMs, and fast estimation
through a restricted likelihood maximization balancing the modeling accuracy
and complexity. Monte Carlo experiments show the estimation accuracy and
computational efficiency of CAMM for modeling non-Gaussian data including
fat-tailed and/or skewed distributions. Finally, the proposed approach is
applied to crime data to examine the empirical performance of the regression
analysis and prediction. The proposed approach is implemented in an R package
spmoran. See details on how to implement CAMM, see
https://github.com/dmuraka/spmoran.
