SPATIAL REGRESSION METHODS IN DENDROCLIMATOLOGY - A REVIEW AND COMPARISON OF 2 TECHNIQUES

We review and compare two alternative spatial regression methods used in dendroclimatology to reconstruct climate from tree rings. These met hods are orthogonal spatial regression (OSR) and canonical regression (CR). Both the OSR and CR methods have a common foundation in least-sq uares theory and converge to the same solution when all p candidate tr ee-ring predictors of climate are forced into the model. However, the performance of OSR and CR may differ when only subsets p' < p predicto rs are used. Theory cannot predict how either method is likely to perf orm when best-subset selection is applied, especially with regards to reconstruction accuracy. Consequently, empirical comparisons of OSR an d CR are made using three tree-ring and climate networks from western Europe and eastern North America that have been used in previous dendr oclimatic studies. These comparisons rely on a suite of regression mod el verification statistics to validate the accuracy of the climatic re constructions produced by the best-subset models. The results indicate little real difference between OSR and CR, with each performing equal ly good or bad depending on the amount of recoverable climatic informa tion in the tree rings. Canonical regression may perform slightly bett er in high signal-to-noise cases; conversely, OSR may perform slightly better when the signal-to-noise ratio is low. None of these apparent differences are large enough to select one method in preference to the other, however, and many more comparisons would be needed to determin e if such indications are generally valid.