追蹤資料分析中隨時間變動解釋變項平減之研究
作者:
溫福星(東吳大學國際經營與貿易學系)
卷期：60卷第1期
日期：2015年3月
頁碼：73-97
DOI：10.6209/JORIES.2015.60(1).03
摘要：
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。
關鍵詞：追蹤資料、組平減、等價、隨機截距模型、總平減
《詳全文》
參考文獻：
- 中央研究院人社中心調查研究專題中心（2014）。學術調查研究資料庫：台灣高等教育資料庫。取自https://srda.sinica.edu.tw/group/scigview/3/10【Center for Survey Research, RCHSS, Academic Sinica. (2014). SRDA: Taiwan Higher Education Database. Retrieved from https://srda.sinica.edu.tw/group/scigview/3/10】
- 巫博瀚、陸偉明、賴英娟（2012）。台灣青少年快樂發展之縱貫性研究：二階層線性成長模式的發現。中華輔導與諮商學報，34，1-18。【Wu, P.-H., Luh, W.-M., & Lai, Y.-C. (2012). A longitudinal study of teenagers’ development of happiness in Taiwan: An analysis of hierarchical linear growth model. Chinese Journal of Guidance and Counseling, 34, 1-18.】
- 李靜芳、溫福星（2008）。階層線性模式於追蹤研究之應用－以子宮切除婦女之術後初期症狀困擾為例。護理雜誌，55（4），63-72。doi:10.6224/JN.55.4.63【Lee, C.-F., & Wen, F.-H. (2008). Applying the hierarchical linear model in longitudinal studies: An example of symptom distress in women who had undergone a hysterectomy. The Journal of Nursing, 55(4), 63-72. doi:10. 6224/JN.55.4.63】
- 周玉慧（2011）。夫妻間衝突因應策略之類型變遷及其長期影響。中華心理學刊，53（2），229- 253。【Jou, Y.-H. (2011). Longitudinal transmission and longitudinal effects of conflict-coping strategies styles on Taiwanese married couples’ martial quality. Chinese Journal of Psychology, 53(2), 229-253.】
- 林清山（1992）。心理與教育統計學。臺北市：東華。【Lin, C.-S. (1992). Statistics for psychology and education. Taipei, Taiwan: Tung Hua.】
» 展開更多
- 中央研究院人社中心調查研究專題中心（2014）。學術調查研究資料庫：台灣高等教育資料庫。取自https://srda.sinica.edu.tw/group/scigview/3/10【Center for Survey Research, RCHSS, Academic Sinica. (2014). SRDA: Taiwan Higher Education Database. Retrieved from https://srda.sinica.edu.tw/group/scigview/3/10】
- 巫博瀚、陸偉明、賴英娟（2012）。台灣青少年快樂發展之縱貫性研究：二階層線性成長模式的發現。中華輔導與諮商學報，34，1-18。【Wu, P.-H., Luh, W.-M., & Lai, Y.-C. (2012). A longitudinal study of teenagers’ development of happiness in Taiwan: An analysis of hierarchical linear growth model. Chinese Journal of Guidance and Counseling, 34, 1-18.】
- 李靜芳、溫福星（2008）。階層線性模式於追蹤研究之應用－以子宮切除婦女之術後初期症狀困擾為例。護理雜誌，55（4），63-72。doi:10.6224/JN.55.4.63【Lee, C.-F., & Wen, F.-H. (2008). Applying the hierarchical linear model in longitudinal studies: An example of symptom distress in women who had undergone a hysterectomy. The Journal of Nursing, 55(4), 63-72. doi:10. 6224/JN.55.4.63】
- 周玉慧（2011）。夫妻間衝突因應策略之類型變遷及其長期影響。中華心理學刊，53（2），229- 253。【Jou, Y.-H. (2011). Longitudinal transmission and longitudinal effects of conflict-coping strategies styles on Taiwanese married couples’ martial quality. Chinese Journal of Psychology, 53(2), 229-253.】
- 林清山（1992）。心理與教育統計學。臺北市：東華。【Lin, C.-S. (1992). Statistics for psychology and education. Taipei, Taiwan: Tung Hua.】
- 張苙雲（2003）。台灣教育長期追蹤資料庫：第一波（2001）國中學生問卷。取自http://srda. sinica.edu.tw/group/sciitem/2/113【Chang, L.-Y. (2003). Taiwan Education Panel Survey: Users’ guide and the first wave (2001) student questionnaire for junior high school. Retrieved from http://srda.sinica.edu.tw/group/sciitem/2/113】
- 楊惠卿（2010）。頭頸癌患者健康控制信念、因應方式與身心社會調適關聯之縱貫性研究（未出版博士論文）。國立臺灣師範大學，臺北市。【Yang, H.-C. (2010). The relationship among health locus of control, way of coping, and bio-psyal-social adaptation effect on the head and neck cancer patient: A longitudinal study (Unpublished doctoral dissertation). National Taiwan Normal University, Taipei, Taiwan.】
- 溫福星、邱皓政（2009）。多層次模型方法論：階層線性模式的關鍵議題與試解。臺大管理論叢，19（2），263-293。doi:10.6226/NTURM2009.19.2.263【Wen, F.-H., & Chiou, H.-J. (2009). Methodology of multilevel modeling: The key issues and their solutions of hierarchical linear modeling. NTU Management Review, 19(2), 263-293. doi:10.6226/NTURM2009.19.2.263】
- 蕭佳純（2011）。TEPS資料庫中學業成就與相關影響因素之縱貫性研究。教育政策論壇，14（3），119-154。【Hsiao, C.-C. (2011). A longitudinal study of students’ academic achievements and associated factors by using the empirical data of TEPS. Educational Policy Forum, 14(3), 119-154.】
- 蕭佳純、董旭英（2011）。TEPS資料庫中國中生心理健康情形之縱貫性分析。諮商輔導學報，23，75-97。【Hsiao, C.-C., & Tung, Y.-Y. (2011). Apply hierarchical linear modeling in the longitudinal study: In the casa of mental health. Journal of Counseling & Guidance, 23, 75-97.】
- 謝雨生、周玉慧（2012）。每下愈況或漸入佳境？夫妻婚姻品質之變化與相互影響性。台灣社會學，23（2），101-154。【Hsieh, Y.-S., & Jou, Y.-H. (2012). Worse or better? Trajectories of marital quality and their mutual influence among Taiwanese married couples. Taiwanese Sociology, 23(2), 101-154.】
- Allison, P. D. (2005). Fixed effects regression methods for longitudinal data using SAS. Cary, NC: SAS Institute.
- Bolger, N., & Laurenceau, J. P. (2013). Intensive longitudinal methods: An introduction to diary and experience sampling research. New York, NY: Guilford.
- Edwards, J., & Lambert, L. (2007). Methods for integrating moderation and mediation: A general analytical framework using moderated path analysis. Psychological Methods, 12(1), 1-22.
- Fitzmaurice, M., Laird, M., & Ware, H. (2011). Applied longitudinal analysis (2nd ed.). Hoboken, NJ: John Wiley & Sons.
- Heck, R. H., & Thomas, S. L. (2009). An introduction to multilevel modeling techniques (2nd ed.). New York, NY: Lawrence Erlbaum Associates.
- Hofmann, D., & Gavin, M. (1998). Centering decisions in hierarchical linear models: Implications for research in organizations. Journal of Management, 24(5), 623-641. doi:10.1016/S0149-2063 (99)8077-4
- Kenny, D. A., Bolger, N., & Kashy, D. (2002). Traditional methods for estimating multilevel models. In D. S. Moskowitz & S. L. Hershberger (Eds.), Modeling intraindividual variability in repeated measures data: Methods and applications (pp. 1-24). Mahwah, NJ: Lawrence Erlbaum Associates.
- Kreft, I., & de Leeuw, J. (1998). Introducing to multilevel modeling. London, UK: Sage. doi:10.4135/ 9781849209366
- Kreft, I., de Leeuw, J., & Aiken, L. (1995). The effect of different forms of centering in hierarchical linear models. Multivariate Behavioral Research, 30(1), 1-21. doi:10.1207/s15327906mbr3001_1
- Likert, R. (1932). A technique for the measurement of attitudes. Archives of Psychology, 22(140), 1-55.
- Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (3rd ed.). New York, NY: McGraw-Hill.
- Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Thousand Oaks, CA: Sage.
- Singer, D. J., & Willett, B. J. (2003). Applied longitudinal data analysis. New York, NY: Oxford University Press.
- Twisk, J. W. R. (2003). Applied longitudinal data analysis for epidemiology. Cambridge, UK: Cambridge University Press.
- Wallace, D., & Green, S. B. (2002). Analysis of repeated measures designs with linear mixed models. In D. S. Moskowitz & S. L. Hershberger (Eds.), Modeling intraindividual variability with repeated measures data: Methods and applications (pp. 103-134). Mahwah, NJ: Lawrence Erlbaum Associates.
| 中文APA引文格式 | 溫福星(2015)。追蹤資料分析中隨時間變動解釋變項平減之研究。教育科學研究期刊，60(1)，73-97。doi:10.6209/JORIES.2015.60(1).03
|
|---|
| APA Format | Wen, F.-H. (2015). Centering on the Time-Varying Independent Variables in Longitudinal Data Analysis. Journal of Research in Education Sciences, 60(1), 73-97. doi:10.6209/JORIES.2015.60(1).03
|
|---|
Journal directory listing - Volume 60 (2015) - Journal of Research in Education Sciences【60(1)】March
Centering on the Time-Varying Independent Variables in Longitudinal Data Analysis
Author:
Fur-Hsing Wen(Department of International Business, Soochow University)
Vol.&No.：Vol. 60, No. 1
Date：March 2015
Pages：73-97
DOI：10.6209/JORIES.2015.60(1).03
Abstract：
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.
Keywords：longitudinal data, grand-mean centering, equivalence, random intercepts model, group-mean centering