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.
"Backfitting in smoothing spline ANOVA." Ann. Statist. 26 (5) 1733 - 1759, October 1998. https://doi.org/10.1214/aos/1024691355