重複測量、階層線性模型與一般迴歸模型在有遺失值的長期資料下之檢定力比較

Power comparison about repeated measures, hierarchical linear model and regression model in analyzing longitudinal data with missing values

薛惠娟(Hui-Chuan Hsueh)

指導教授 ： 施葦

國立臺北大學/商學院/統計學系/碩士(2010年)

摘要

階層線性模型(HLM)與重複測量(RM)皆可以應用長期資料的分析上，惟有缺失資料時，重複測量可使用之資料量將減少，而階層線性模型則不會。2006年，學者Hua Fang討論了階層線性模型與重複測量在完整資料下的比較。因此，我們想要進一步了解，如果資料具有遺失值，哪一種模型是較佳的選擇？同時，加入了傳統迴歸模型(OLS)一起比較。我們利用模擬的方式分別以MCAR_IT及MCAR缺失型態產生資料，再使用階層線性模型、刪除遺失值的重複測量、插補遺失值的重複測量及一般迴歸模型等方法進行分析，比較各種方法的型I誤差機率及檢定力來判斷模型的優劣，歸納出各方法較適用之情況。結果發現，插補對重複測量並無效果，故對有遺失值之長期資料，利用HLM來分析是最佳的選擇。

關鍵字

階層線性模型 ； 重複測量 ； 缺失資料 ； 長期資料 ； 檢定力

並列摘要

Hierarchical Linear Model (HLM) and Repeated Measures (RM) can be used to analyze the longitudinal data. The data which can be used in RM will be fewer than that in HLM when there are missing values. Hua Fang (2006) compared HLM with RM when the data is complete. In this paper, we discuss the power of HLM vs. RM when there are missing values. Moreover, the traditional regression model is also included in the comparison. This research simulate data by different missing types, MCAR and MCAR_IT, and use HLM, RM with deleting missing values, RM with imputing missing values and regression model to perform the analysis. Probability of Type I error and powers are to be discussed and suggest are proposed in selecting model methods. This research concludes that the imputation is not helpful in RM ana HLM is a better method in analyzing longitudinal data with missing values.

並列關鍵字

Hierarchical Linear Model ； Repeated Measure ； Missing Value ； Longitudinal data ； Power

參考文獻

2. Bliese, P. D. & Hanges P. J. (2004).Being both too liberal and too conservative: The Perils of treating Grouped Data as though they were independent. Organizational Research Methods, Vol.7, No.4, 400-417.

3. Bryk, A. S. & Raudenbush, S. W. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Newbury Park, CA: Sage.

4. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed ).Hillsdale, NJ: Eribaum..

6. Luke, D. (2004). Multilevel modeling. Newbury Park, CA: Sage.

7. Robinson, W. S. (1950). Ecological correlations and the behavior of individuals. American Sociological Rivew,15(3),351-357