效果迴歸分析

Abstract

在因果關係中定義何謂直接效果(direct effect)與全部效果(total effect)長期以來都是在錯誤方式下訂定的。我們這篇文章發現在迴歸模型中，一個解釋變數在對反應變數的影響所造成的直接(direct)、間接(indirect)及全部(total)效果不僅發生在迴歸函數的斜率參數上，同時也反映在截距項上。這表示說不管討論何種效果都應該以迴歸的型式來呈現。在我們建立了三種迴歸型態的效果迴歸後，我們也建立了效果迴歸參數的統計推論方法。對這些方法我們也進行模擬分析以研究它們的有效性並予呈現。

Specification of direct and total effects have been mistreated for years that will mislead to incorrect conclusion about statistical inferences about indirect effect. We prove that for detection of presence of mediation, it requires only to test the association between the predictor and mediator giving the reason that how Baron and Kenny (1986)’s three steps of tests has low power. We also provide theoretical proofs for the observation of Hayes (2009) for absence of total effect but there is indirect effect and the observation of Palmatier et al. (2009) for total effect containing no indirect effect. With regression function being formulated in terms of distributional parameters of variables of response, predictor and mediator, we allow to quantify the information of mediation existed in their joint distribution to be removed to specify unambiguous direct effect and total effects. One important discovery is that the mediation causes not only affect the regression slope parameters but also the regression intercept. So, instead of limited use of slope type effects, we introduce regression setup direct, indirect and total effects expanding to the scope of effect prediction. Statistical inferences for these effect regressions are introduced and evaluated.