Non-Gaussian spatial and spatio-temporal data are becoming increasingly prevalent, and their analysis is needed in a variety of disciplines. 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. These vastly more general spatial and spatio-temporal models are fitted using the Laplace approximation via the software TMB. The existing functionality of FRK is retained with this advance into 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. 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:在本文中,我们描述FRK的一项重大升级,允许在一般的线性混合模型框架内分析非Gausian数据。这些广泛得多的空间和时空模型在各种学科中都需要分析。FRK是一个用于空间/时空空间/空间建模和预测的R套套件,该套套件具有非常大的数据集,迄今为止只支持线性进程模型和Gaussian数据模型。在本文中,我们描述FRK的一项重大升级,允许在一般的线性混合模型框架内对非Gausian数据进行分析。这些广泛得多的空间和时空模型通过TMB软件使用Laplace近似。FRK的现有功能随着这一进步被保留在非Gausian模型中;特别是它允许自动的基功能构建,它能够同时处理点参照和数据,它可以在这些数据的任何空间支持下预测进程值。FRK的新版本还允许在模拟过程的模型中使用大量的基础功能,因此,因此往往能够比以前版本的套件更加精确地预测,同时使用FRC的模型设置。