DOI: 10.5061/dryad.xsj3tx9g1
title: WiBB: An integrated method for quantifying the relative importance of predictive variables

description: This dataset contains simulated datasets, empirical data, and R scripts
 described in the paper: “Li, Q. and Kou, X. (2021) WiBB: An integrated
 method for quantifying the relative importance of predictive variables.
 Ecography (DOI: 10.1111/ecog.05651)”. A fundamental goal of scientific
 research is to identify the underlying variables that govern crucial
 processes of a system. Here we proposed a new index, WiBB, which
 integrates the merits of several existing methods: a model-weighting
 method from information theory (Wi), a standardized regression coefficient
 method measured by ß* (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 two other methods, relative sum
 of wight (SWi), and standardized beta (ß*), to evaluate their performance
 in comparison with the WiBB method on ranking predictor importances under
 various scenarios. We also applied it to an empirical dataset in a plant
 genus Mimulus to select bioclimatic predictors of species’ presence across
 the landscape. Results in the simulated datasets showed that the WiBB
 method outperformed the ß* and SWi methods in scenarios with small and
 large sample sizes, respectively, and that the bootstrap resampling
 technique significantly improved the discriminant ability. When testing
 WiBB in the empirical dataset with GLM, it sensibly identified four
 important predictors with high credibility out of six candidates in
 modeling 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.
description: To simulate independent datasets (size = 1000), we adopted
 Galipaud et al.’s approach (2014) with custom modifications of the
 <em>data.simulation</em> function, which used the multiple
 normal distribution function <em>rmvnorm</em> in R package
 <em>mvtnorm</em>(v1.0-5, Genz et al. 2016). Each dataset was
 simulated with a preset correlation structure between a response variable
 (<em>y</em>) and four
 predictors(<em>x<sub>1</sub>, x<sub>2</sub>,
 x<sub>3</sub>, x<sub>4</sub></em>). The
 first three (genuine) predictors were set to be strongly, moderately, and
 weakly correlated with the response variable, respectively (denoted by
 large, medium, small Pearson correlation coefficients,
 <em>r</em>), while the correlation between the response and
 the last (spurious) predictor was set to be zero. We simulated datasets
 with three levels of differences of correlation coefficients of
 consecutive predictors, where <em>∆r</em> = 0.1, 0.2, 0.3,
 respectively. These three levels of <em>∆r</em> resulted in
 three correlation structures between the response and four predictors:
 (0.3, 0.2, 0.1, 0.0), (0.6, 0.4, 0.2, 0.0), and (0.8, 0.6, 0.3, 0.0),
 respectively. We repeated the simulation procedure 200 times for each of
 three preset correlation structures (600 datasets in total), for LM
 fitting later. For GLM fitting, we modified the simulation procedures with
 additional steps, in which we converted the continuous response into
 binary data <em>O</em> (e.g., occurrence data having 0 for
 absence and 1 for presence). We tested the <em>WiBB</em>
 method, along with two other methods, relative sum of wight
 (<em>SWi</em>), and standardized beta
 (<em>ß</em>*), to evaluate the ability to correctly rank
 predictor importances under various scenarios. The empirical dataset of 71
 <em>Mimulus</em> species was collected by their occurrence
 coordinates and correponding values extracted from climatic layers from
 WorldClim dataset (www.worldclim.org), and we applied the
 <em>WiBB</em> method to infer important predictors for their
 geographical distributions.
description: The README file contains an explanation of simulated and
 empirical datasets and R scripts for analyses. Information on how the
 datasets were simulated or compiled, and how different methods were
 applied and compared can be found in the associated manuscript referenced
 above.