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.

中文翻译：

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WiBB：一种用于量化预测变量相对重要性的综合方法

科学研究的一个基本目标是确定控制系统关键过程的潜在变量。这在生态学中尤其困难，生态学本质上具有丰富的候选预测因子。非常需要一种有效的统计程序来评估回归模型中预测变量的相对重要性。然而，先前的研究通过指出模拟数据集中重要性指数的低辨别力来批评最普遍适用的方法。在这里，我们提出了一个新的指标WiBB，它综合了几种现有方法的优点。WiBB结合了来自信息论 ( Wi )的模型加权方法，这是一种由β * (B ) 和自举重采样技术 ( B )。我们在具有已知相关结构的模拟数据集中应用WiBB，用于线性模型 (LM) 和广义线性模型 (GLM)，以评估其性能。我们还将其应用于植物属植物Mimulus的经验数据集，以选择物种在整个景观中存在的生物气候预测因子。模拟数据集中的结果表明，自举重采样技术通过正确排序预测变量的相对重要性的顺序，显着提高了判别能力。该WiBB方法优于β *和权重的相对总和（SWI，权重总和的标准化版本）方法分别适用于小样本和大样本的场景。在使用 GLM测试经验数据集中的WiBB时，它在对 71种蠹属物种的地理分布建模的六个候选中明智地确定了四个具有高可信度的重要预测因子。这种综合指标在评估预测因子重要性方面具有很大的优势，从而降低了数据的维数，同时又不失去解释力。通过更复杂的统计程序计算新指标的简单性使其成为统计工具箱中的一种方便的方法。