WiBB: an integrated method for quantifying the relative importance of predictive variables

A fundamental goal of scientific research is to identify the underlying variables that govern crucial processes of a system. This is especially difficult in ecology, which is intrinsically rich in candidate predictors. An efficient statistical procedure to evaluate the relative importance of predictors in regression models is highly desirable. However, previous studies criticised the most universally applicable method, by pointing out the low discriminating power of the importance index in simulated datasets. Here we proposed a new index, WiBB, which integrates the merits of several existing methods. WiBB combines a model-weighting method from information theory (Wi), a standardised regression coefficient method measured by β* (B), and bootstrap resampling technique (B). We applied the WiBB in simulated datasets with known correlation structures, for both linear models (LM) and generalized linear models (GLM), to evaluate its performance. We also applied it to an empirical dataset of a plant genus Mimulus to select bioclimatic predictors of species' presence across the landscape. Results in the simulated datasets showed that the bootstrap resampling technique significantly improved the discriminant ability by correctly sorting the orders of relative importance of predictors. The WiBB method outperformed the β* and the relative sum of weights (SWi, a standardised version of sum of weights) methods in scenarios with small and large sample sizes, respectively. When testing WiBB in the empirical dataset with GLM, it sensibly identified four important predictors with high credibility out of six candidates in modelling geographical distributions of 71 Mimulus species. This integrated index has great advantages in evaluating predictor importance and hence reducing the dimensionality of data, without losing interpretive power. The simplicity of calculation of the new metric over more sophisticated statistical procedures makes it a handy method in the statistical toolbox.