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


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

《Full Text》 檔名

  1. 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【Center for Survey Research, RCHSS, Academic Sinica. (2014). SRDA: Taiwan Higher Education Database. Retrieved from】
  2. 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.】
  3. 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】
  4. 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.】
  5. 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.】
» More
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