Statistical Modelling 11 (2011), 49–69
P-spline ANOVA-type interaction models for spatio-temporal smoothing
Dae-Jin Lee
Department of Statistics,
Universidad Carlos III de Madrid,
Av. Universidad, 30
E–28911 Leganés, Madrid
Spain
eMail: dae-jin.lee@uc3m.es
María Durbán
Department of Statistics,
Universidad Carlos III de Madrid
Spain
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
(P-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.
Keywords:
ANOVA decomposition; mixed models; Penalized splines; spatio-temporal data
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