Flexible Spatio-temporal smoothing with array methods

In recent years, spatio-temporal modelling has become a challenging area of research in many fields (e.g. epidemiology, environmental studies, and disease mapping). However, most of the models developed are constrained by the large amount of data available. Smoothing methods present very attractive and flexible modelling tools for this type of data set. In the context of environmental studies, where data often present a strong seasonal trend, and the interaction of spatial and temporal processes may be strong, the size of the regression basis needed to capture the temporal trend is large and, as a consequence, the estimation of the spatio-temporal interaction is computationally intensive. We propose the use of Penalized Splines as mixed models for smoothing spatio-temporal data. The array properties of the regression bases allow us to fit Smooth-ANOVA-type models, imposing identifiability constraints over the coefficients. These models are fitted taking advantage of the array structure of the space-time interaction and the use of the GLAM (generalized linear array methods) algorithms. We illustrate the methodology with the analysis of real environmental problems.