多元迴歸的自變數比較與多元共線性之影響：效果量、優勢性與相對權數指標的估計與應用

The Impact of Multicollinearity on the Evaluations of Regressors: Comparisons of Effect Size Index, Dominance Analysis and Relative Weight Analysis in Multiple Regression

迴歸分析雖廣泛應用於社會科學研究，但過度仰賴顯著性檢定與迴歸係數而忽略了效果量與相對重要性的評估，本文除了檢視乘積係數等早期指標，並整理近來提出的優勢分析與相對權數分析，以模擬數據進行增強、壓抑與重疊等不同型態的共線性效果下各種指標的表現差異，並以「華人家庭動態資料庫」2011 年的調查資料，檢驗人口變數與人力資本變數對於 2,325 名臺灣民眾的薪資差異的影響。研究結果指出，多元共線性對於自變數效果量與相對重要性的影響非常明顯，相對權數分析與優勢分析的相對重要性指數的表現最為穩定，其中優勢分析具有相當彈性能夠提供更豐富的變數效果與重要性資訊。最後本文對於各種指標策略進行整理比較，並說明在多元迴歸上的應用策略。

Regression analysis is frequently used in social sciences. However, regression analyses often rely heavily on hypothesis testing and interpretations of regression coefficients. As a result, the effect sizes of regression models as well as the qualities of individual predictors have long been ignored. This paper reviews several indices that can be used to evaluate the effect size and relative importance of predictors, the relative weight analysis (RWA), and the dominance analysis (DA) in multiple regressions. A simulated dataset is used to examine the impacts of mutlicollinearity, including the enhancement, suppression, and redundancy effects, on the evaluation of the effect size and relative importance of predictors. A sample of 2,325 Taiwanese adults selected from the 2011 Panel Study of Family Dynamics (PSFD) are used to demonstrate the use of those indices in predicting the salary differences. Results suggest that the indices based on RWA and DA are recommended for evaluating the relative importance of predictors. In particular, DA has the advantage of flexible procedures for evaluating the different facets of the dominance of predictors. The properties of the recommended index were summarized in the end of the paper.