Residualized Relative Importance Analysis
指出标准相对重要性分析不适用于交互或高阶效应(如二次、三次项),提出三种方差分解策略:层级F检验、约束相对重要性分析和残差化相对重要性分析,并用实例说明其应用。
The current article notes that the standard application of relative importance analyses is not appropriate when examining the relative importance of interactive or other higher order effects (e.g., quadratic, cubic). Although there is a growing demand for strategies that could be used to decompose the predicted variance in regression models containing such effects, there has been no formal, systematic discussion of whether it is appropriate to use relative importance statistics in such decompositions, and if it is appropriate, how to go about doing so. The purpose of this article is to address this gap in the literature by describing three different yet related strategies for decomposing variance in higher-order multiple regression models—hierarchical F tests (a between-sets test), constrained relative importance analysis (a within-sets test), and residualized relative importance analysis (a between- and within-sets test). Using a previously published data set, we illustrate the different types of inferences these three strategies permit researchers to draw. We conclude with recommendations for researchers seeking to decompose the predicted variance in regression models testing higher order effects.