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
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