Modelling, Fitting, and Prediction with Non-Gaussian Spatial and Spatio-Temporal Data using FRK

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.