A computational scheme for fitting smoothing spline ANOVA models to
large data sets with a (near) tensor product design is proposed. Such data sets
are common in spatial-temporal analyses. The proposed scheme uses the
backfitting algorithm to take advantage of the tensor product design to save
both computational memory and time. Several ways to further speed up the
backfitting algorithm, such as collapsing component functions and successive
over-relaxation, are discussed. An iterative imputation procedure is used to
handle the cases of near tensor product designs. An application to a global
historical surface air temperature data set, which motivated this work, is used
to illustrate the scheme proposed.