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.
翻译:随着地理信息系统的发展,非圭亚那空间数据正在变得越来越广泛和多样化。考虑到这一背景,本研究报告为快速和灵活的非圭亚那非圭亚那回归,特别是空间/SPatote-时间模型开发了一个总体框架,特别是空间/SPatote-时间模型;开发了一种模型,称为构成扭曲的添加性混合模型(CAMM),结合了一种添加型混合模型(AMM)和构成扭曲型高萨进程,以模拟广泛的非圭亚那连续数据,包括空间影响和其他影响;拟议的CAMM的具体优势并不要求明确假设数据分布不同于现有AMM的情况,而要求通过有限的可能性最大化来快速估算,平衡模型的准确性和复杂性;蒙特卡洛实验显示CAM的估算准确性和计算效率,用以模拟非Gaussian数据,包括脂肪的成型和/或偏斜分布;最后,拟议方法适用于犯罪数据,以审查回归分析和预测的经验性业绩;拟议方法在Spmorran软件包中实施。见如何执行CAMMMMM的详情,见 https://gimobran.commura.com/mal.com。