Appendix B. An algorithm for computing ensemble streamflow
reconstructions by recursive forward selection
Multiple linear regression, and choosing predictors by forward
selection, is the conventional method of creating a tree-ring model
for the reconstruction of pre-instrumental climate and hydrology.
From a pool of tree-ring chronologies, the regression algorithm
sequentially adds predictors to the model, minimizing correlation
among predictors while maximizing the extent to which they
account for variance in the dependent variable (predictand) measured
by the statistic R2. By removing the chosen predictors from
the pool, and maintaining a fixed sequence of predictor variables,
the algorithm is relatively fast and efficient. There is no guarantee,
however, that the model built by forward selection is the best set
of ‘n’ predictors from a pool of size ‘N’, since once predictors are
selected, only models including those predictors are tested. There
may be other models that are almost as good, or even better,
according to a criterion such as the R2 adjusted (degraded) by the
degrees of freedom.