共線性對檢測調節效用的影響

Abstract

調節複廻歸已廣泛應用於兩連續式變數交互作用分析，而兩變數和其交互相乘項間的 共線性對檢測的影響，自然地成為重要議題。本文試圖探索變數間相關程度對檢測調節 效用的可能正面幫助，藉以釐清普遍以為共線性對調節複廻歸分析百害而無一利的誤 解。針對簡單雙變數及三變數交互作用模式的理論解析和數據驗證，所獲結果有助於改 變學者對變數間高度相關現象的憎惡，更提昇調節效用研究方法的實用價值。

Due to extensive applicability and computational ease, moderated multiple regression (MMR) has been widely employed to analyze interaction effects between two continuous predictor variables. Accordingly, considerable attention has been drawn toward the supposed multicollinearity problem between predictor variables and their cross-product term. This article attempts to clarify the misconception of multicollinearity in MMR studies. The counter-intuitive yet beneficial effects of multicollinearity on the ability to detect moderator relationships are explored. Comprehensive treatments and numerical investigations are presented for the simplest interaction model and more complex three-predictor setting. The obtained results provide critical insight that not only avoids misleading interpretation but also yields better understanding of the impact of intercorrelation among predictor variables on MMR analyses.