Disaggregating Within-Person and Between-Person Effects in the Presence of Linear Time Trends in Time-Varying Predictors: Structural Equation Modeling Approach
Educational researchers are often interested in phenomena that unfold over time within a person and at the same time, relationships between their characteristics that are stable over time. Since variables in a longitudinal study reflect both within- and between-person effects, researchers need to disaggregate them to understand the phenomenon of interest correctly. Although the person-mean centering technique has been believed as the gold standard of the disaggregation method, recent studies found that the centering did not work when there was a trend in the predictor. Hence, they proposed some detrending techniques to remove the systematic change; however, they were only applicable to multilevel models. Therefore, this dissertation develops novel detrending methods based on structural equation modeling (SEM). It also establishes the links between centering and detrending by reviewing a broad range of literature. The proposed SEM-based detrending methods are compared to the existing centering and detrending methods through a series of Monte Carlo simulations. The results indicate that (a) model misspecification for the time-varying predictors or outcomes leads to large bias of and standard error, (b) statistical properties of estimates of the within- and between-person effects are mostly determined by the type of between-person predictors (i.e., observed or latent), and (c) for unbiased estimation of the effects, models with latent between-person predictors require nonzero growth factor variances, while those with observed predictors at the between level need either nonzero or zero variance, depending on the parameter. As concluding remarks, some practical recommendations are provided based on the findings of the present study.