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As with the advancement of geographical information systems, non-Gaussianspatial data sets are getting larger and more diverse. This study develops ageneral framework for fast and flexible non-Gaussian regression, especially forspatial/spatiotemporal modeling. The developed model, termed thecompositionally-warped additive mixed model (CAMM), combines an additive mixedmodel (AMM) and the compositionally-warped Gaussian process to model a widevariety of non-Gaussian continuous data including spatial and other effects. Aspecific advantage of the proposed CAMM is that it requires no explicitassumption of data distribution unlike existing AMMs. Monte Carlo experimentsshow the estimation accuracy and computational efficiency of CAMM for modelingnon-Gaussian data including fat-tailed and/or skewed distributions. Finally,the model is applied to crime data to examine the empirical performance of theregression analysis and prediction. The result shows that CAMM providesintuitively reasonable coefficient estimates and outperforms AMM in terms ofprediction accuracy. CAMM is verified to be a fast and flexible model thatpotentially covers a wide variety of non-Gaussian data modeling. The proposedapproach is implemented in an R package spmoran.

Compositionally-warped additive mixed modeling for a wide variety of non-Gaussian spatial data