FORWARD SELECTION OF EXPLANATORY VARIABLES

TLDR

Classical forward selection suffers from inflated Type I error rates and overestimation of explained variance. Correcting these issues promises to enhance the reliability of forward selection for ecological modeling. The authors introduce a two‑step method that first applies a global test of all predictors, then proceeds with forward selection only if significant, using both an alpha threshold and an adjusted R² criterion to stop and reject variables, and validate the approach with simulations and a Bryce Canyon ecological case study.

Abstract

This paper proposes a new way of using forward selection of explanatory variables in regression or canonical redundancy analysis. The classical forward selection method presents two problems: a highly inflated Type I error and an overestimation of the amount of explained variance. Correcting these problems will greatly improve the performance of this very useful method in ecological modeling. To prevent the first problem, we propose a two‐step procedure. First, a global test using all explanatory variables is carried out. If, and only if, the global test is significant, one can proceed with forward selection. To prevent overestimation of the explained variance, the forward selection has to be carried out with two stopping criteria: (1) the usual alpha significance level and (2) the adjusted coefficient of multiple determination ( ) calculated using all explanatory variables. When forward selection identifies a variable that brings one or the other criterion over the fixed threshold, that variable is rejected, and the procedure is stopped. This improved method is validated by simulations involving univariate and multivariate response data. An ecological example is presented using data from the Bryce Canyon National Park, Utah, USA.