Non-Gaussian spatial and spatial-temporal data are becoming increasingly prevalent, and their analysis is needed in a variety of disciplines, such as those involving small-area demographics or global satellite remote sensing. FRK is an R package for spatial/spatio-temporal modelling and prediction with very large data sets that, to date, has only supported linear process models and Gaussian data models. In this paper, we describe a major upgrade to FRK that allows for non-Gaussian data to be analysed in a generalised linear mixed model framework. The existing functionality of FRK is retained with this advance into non-linear, non-Gaussian models; in particular, it allows for automatic basis-function construction, it can handle both point-referenced and areal data simultaneously, and it can predict process values at any spatial support from these data. These vastly more general spatial and spatio-temporal models are fitted using the Laplace approximation via the software TMB. This new version of FRK also allows for the use of a large number of basis functions when modelling the spatial process, and is thus often able to achieve more accurate predictions than previous versions of the package in a Gaussian setting. We demonstrate innovative features in this new version of FRK, highlight its ease of use, and compare it to alternative packages using both simulated and real data sets.
翻译:非高加索空间和时空数据日益普遍,需要在许多学科,例如涉及小地区人口统计或全球卫星遥感的学科中进行分析。FRK是一个空间/空间时空建模和预测的R包,空间/空间时空建模和预测使用非常庞大的数据集,迄今为止,这些数据只支持线性进程模型和高斯数据模型。在本文中,我们描述了对FRK的重大升级,允许在一个通用的线性混合模型框架内分析非高加索数据。FRK的现有功能随着这一进步而保留为非线性、非伽西文模型;特别是,它允许自动构建基础功能,它能够同时处理点参照和数据,它能够根据这些数据的任何空间支持预测过程值。这些广得多的空间和时空-时空模型通过软件TMB安装Laplace近似模型。FRK的新版本还允许在模拟空间进程和非伽西南模型时使用大量的基础功能;因此,它可以同时进行自动基础功能构造,可以同时同时处理点参照点参照点标值和数据,从而能够更精确地使用其以前的版本。