Theory, Examples & Exercises
Forward selection is a procedure for selecting a subset of explanatory variable from the set of all variables available for constrained ordination (RDA or CCA). The goal is to reduce the number of explanatory variables entering the analysis, while keeping the variation explained by them to maximum. Suitable mostly in case of observational studies, where many (often highly intercorrelated) environmental variables are recorded, to reduce their number (and to simplify the story); not useful for experimental studies with balanced design of treatment application.
The simplified sequence of steps is the following:
The simplest method is forward selection, which is adding explanatory variables one by one; backward selection, in contrary, starts from the full model and deletes variables which the least decreases the total explained variation. Combination of both approaches is forward-backward selection, in which in every step the analysis checks whether some of already included variables cannot be removed to improve the model.
Significance of the variables is one of the possible stopping rules (once the best variable is not significant, the selection is stopped). Alternative stopping rule is reaching the adjusted R2 of the global model (Blanchet et al. 2008): first calculate adjusted variation explained by all explanatory variables (global model); if during the forward selection the adjusted variation explained by selected variables reaches the R2adj of the global model, the selection will be stopped (available in function