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Regression with empirical variable selection: description of a new method and application to ecological datasets.

机译：选择经验变量进行回归：描述一种新方法并将其应用于生态数据集。

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Despite recent papers on problems associated with full-model and stepwise regression, their use is still common throughout ecological and environmental disciplines. Alternative approaches, including generating multiple models and comparing them post-hoc using techniques such as Akaike's Information Criterion (AIC), are becoming more popular. However, these are problematic when there are numerous independent variables and interpretation is often difficult when competing models contain many different variables and combinations of variables. Here, we detail a new approach, REVS (Regression with Empirical Variable Selection), which uses all-subsets regression to quantify empirical support for every independent variable. A series of models is created; the first containing the variable with most empirical support, the second containing the first variable and the next most-supported, and so on. The comparatively small number of resultant models (n = the number of predictor variables) means that post-hoc comparison is comparatively quick and easy. When tested on a real dataset--habitat and offspring quality in the great tit (Parus major)--the optimal REVS model explained more variance (higher R(2)), was more parsimonious (lower AIC), and had greater significance (lower P values), than full, stepwise or all-subsets models; it also had higher predictive accuracy based on split-sample validation. Testing REVS on ten further datasets suggested that this is typical, with R(2) values being higher than full or stepwise models (mean improvement = 31% and 7%, respectively). Results are ecologically intuitive as even when there are several competing models, they share a set of "core" variables and differ only in presence/absence of one or two additional variables. We conclude that REVS is useful for analysing complex datasets, including those in ecology and environmental disciplines.
机译：尽管最近发表了有关全模型和逐步回归相关问题的论文，但在整个生态和环境学科中仍普遍使用它们。替代方法，包括生成多个模型并使用Akaike的信息标准（AIC）等技术事后进行比较，正在变得越来越流行。但是，当存在许多独立变量时，这些问题就成问题了；当竞争模型包含许多不同变量和变量组合时，通常很难解释。在这里，我们详细介绍了一种新方法REVS（具有经验变量选择的回归），该方法使用全子集回归来量化对每个自变量的经验支持。创建了一系列模型；第一个包含获得最多经验支持的变量，第二个包含第一个变量并获得第二个最受支持的变量，依此类推。结果模型的数量相对较少（n =预测变量的数量）意味着事后比较相对快速，容易。当在真实的数据集上（大山雀（Parus major）的栖息地和后代质量）进行测试时，最优的REVS模型可以解释更多的方差（较高的R（2）），更简约的（较低的AIC）以及更重要的意义（低于完整，逐步或全子集模型；基于分割样本验证，它还具有更高的预测准确性。对另外十个数据集进行REVS测试表明这是典型的，R（2）值高于完整模型或逐步模型（均值改善分别为31％和7％）。结果具有生态直观性，即使存在多个竞争模型，它们也共享一组“核心”变量，并且仅在存在或不存在一个或两个其他变量时有所不同。我们得出结论，REVS可用于分析复杂的数据集，包括生态和环境学科的数据集。

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