As with the advancement of geographical information systems, non-Gaussian spatial data sets are getting larger and more diverse. 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. A specific advantage of the proposed CAMM is that it requires no explicit assumption of data distribution unlike existing AMMs. 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 model is applied to crime data to examine the empirical performance of the regression analysis and prediction. The result shows that CAMM provides intuitively reasonable coefficient estimates and outperforms AMM in terms of prediction accuracy. CAMM is verified to be a fast and flexible model that potentially covers a wide variety of non-Gaussian data modeling. The proposed approach is implemented in an R package spmoran.
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