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.

随着地理信息系统的进步，非高斯空间数据集越来越大，越来越多样化。本研究为快速灵活的非高斯回归开发了一个通用框架，特别是用于空间/时空建模。开发的模型称为成分扭曲变形加性混合模型（CAMM），结合了添加剂混合模型（AMM）和成分扭曲变形的高斯过程，以建模各种非高斯连续数据，包括空间效应和其他影响。所提出的 CAMM 的一个特定优点是它不需要与现有 AMM 不同的数据分布的明确假设。蒙特卡罗实验显示了 CAMM 对非高斯数据建模的估计精度和计算效率，包括肥尾和/或偏斜分布。最后，该模型应用于犯罪数据，以检查回归分析和预测的经验表现。结果表明，CAMM 提供了直观合理的系数估计，并且在预测精度方面优于 AMM。经验证，CAMM是一种快速且灵活的模型，可以涵盖各种非高斯数据建模。