Multiple regression and inference in ecology and conservation biology: further comments on identifying important predictor variables

Ecologists and conservation biologists frequently use multiple regression (MR) to try to identify factors influencing response variables such as species richness or occurrence. Many frequently used regression methods may generate spurious results due to multicollinearity. Mac Nally (2000, Biodiversity and Conservation 9: 655-671) argued that there are actually two kinds of MR modelling: (1) seeking the best predictive model; and (2) isolating amounts of variance attributable to each predictor variable. The former has attracted most attention with a plethora of criteria (measures of model fit penalized for model complexity - number of parameters) and Bayes-factor-based methods having been proposed, while the latter has been little considered, although hierarchical methods seem promising (e. g. hierarchical partitioning). If the two approaches agree on which predictor variables to retain, then it is more likely that meaningful predictor variables (of those considered) have been found. There has been a problem in that, while hierarchical partitioning allowed the ranking of predictor variables by amounts of independent explanatory power, there was no (statistical) way to decide which variables to retain. A solution using randomization of the data matrix coupled with hierarchical partitioning is presented, as is an ecological example.