P -spline ANOVA-type interaction models for spatio-temporal smoothing

Abstract

In recent years, spatial and spatio-temporal modelling have become an important area of research in many fields (epidemiology, environmental studies, disease mapping, etc.). However, most of the models developed are constrained by the large amounts of data available. We propose the use of penalized splines ( -splines) in a mixed model framework for smoothing spatio-temporal data. Our approach allows the consideration of interaction terms which can be decomposed as a sum of smooth functions similarly as an analysis of variance decomposition. The properties of the bases used for regression allow the use of algorithms that can handle large amount of data. We show that on imposing the same constraints as in a factorial design it is possible to avoid identifiability problems. We illustrate the methodology for Europe ozone levels in the period 1999–2005.