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FORWARD SELECTION OF EXPLANATORY VARIABLES

FORWARD SELECTION OF EXPLANATORY VARIABLES 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Ecology Ecological Society of America

FORWARD SELECTION OF EXPLANATORY VARIABLES

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References (43)

Publisher
Ecological Society of America
Copyright
Copyright © 2008 by the Ecological Society of America
Subject
Articles
ISSN
0012-9658
DOI
10.1890/07-0986.1
Publisher site
See Article on Publisher Site

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.

Journal

EcologyEcological Society of America

Published: Sep 1, 2008

Keywords: forward selection ; Moran's eigenvector maps (MEM) ; non-orthogonal explanatory variables ; orthogonal explanatory variables ; principal coordinates of neighbor matrices (PCNM) ; simulation study ; Type I error

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