追蹤資料分析中隨時間變動解釋變項平減之研究 Centering on the Time-Varying Independent Variables in Longitudinal Data Analysis - 溫福星 Fur-Hsing Wen (National Taiwan Normal University, 2015)
利用多層次模式或是階層線性模式進行重複觀測資料的分析，如果個體層次解釋變項包含隨時間變動解釋變項時，在個體層次方程式對它不平減或是總平減所獲得的迴歸係數是一個偏誤的結果，因為這個隨時間變動的解釋變項具有追蹤與橫斷面的資料特性，對個體層次結果變項的影響可以拆解為互斥的組間迴歸係數與組內迴歸係數，因此，必須利用組平減並將組平均數置回截距項方程式方能獲得正確的估計結果。但在不平減、總平減與組平減三種方法下都加上組平均數置回截距項方程式，在隨機截距模型下則會獲得等價的估計結果。本研究整理出這些平減方法之間的統計關係，並利用實徵資料示範分析各種模式，說明之間的差異與等價關係，最後提出研究的結論與建議。 When analyzing repeated measures by using multilevel modeling (MLM) or hierarchical linear modeling (HLM), if the individual-level independent variables include a time-varying variable and it is modeled as uncentered or grand-mean centered in a level-one equation, then this regression coefficient is a biased estimate. Because repeated measures data comprise longitudinal and cross-sectional parts, the total effect of the time-varying independent variable on the individual outcomes can be decomposed into within- and between-subject regression coefficients. Therefore, the optimal approach is to use group-mean centered in a level-one equation and group means replaced in the intercept equation. In some cases (e.g., the random intercepts model), the three methods, namely uncentered, grand-mean centered, and group-mean centered time-varying variable approaches with group means replacement, are equivalent in MLM and HLM. We adopted a statistical model and empirical data analysis to determine the equivalent relationships and differences among the three centered methods and present a conclusion and recommendations.