Latent Curve Detrending for Disaggregating Between-Person Effect and Within-Person Effect

Cross-level covariance approach to the disaggregation of between-person effect and within-person effect.

“…The key idea of centering and detrending using oberved variables is that the total variation of a time-varying variable is decomposed into two orthogonal portions—a time-invariant between-person component and a time-varying within-person component— by making a residual (Hori & Miyazaki, 2022). In person-mean centering, a time-varying predictor X ti is decomposed into the person mean trueX¯·i (the time-invariant between-person component) and its orthogonal complement Xti−trueX¯·i (the time-varying within-person component).…”

“…The latent centering can easily be extended to detrending. Figure 1B presents the latent detrending model (Hori & Miyazaki, 2022). Both latent centering and detrending models produce a latent residual εtiX by subtracting the time-invariant between-person components from the raw variable (i.e., εtiX=Xti−IiX for the latent centering; εtiX=Xti−IiX−λtSiX for the latent detrending).…”

“…2 After detrending is performed, the estimated individual coefficients and the residual are included in a (multilevel) regression model to estimate the between-person and within-person effects (Curran & Bauer, 2011;Wang & Maxwell, 2015). 3 The key idea of centering and detrending using oberved variables is that the total variation of a time-varying variable is decomposed into two orthogonal portions-a time-invariant between-person component and a time-varying within-person component-by making a residual (Hori & Miyazaki, 2022). In person-mean centering, a time-varying predictor X ti is decomposed into the person mean X Ái (the time-invariant betweenperson component) and its orthogonal complement X ti À X Ái (the time-varying within-person component).…”

“…In their method, a time-varying predictor is regressed on a time variable for each person to remove the effect of trends in the predictor (i.e., detrending) (first step), and the intercept estimate and the residual from the first step are put back into the outcome model to estimate the between-person and within-person effects (second step). After this seminal work of Curran & Bauer (2011), the disaggregation of the between- and within-person effects attracted researchers’ attention during the last decade (e.g., Curran et al, 2012; Hoffman, 2015; Hoffman & Stawski, 2009; Hori & Miyazaki, 2022; Wang & Maxwell, 2015).…”

The importance of change communication and state motivation when adapting to changes

“…Including more measurements of time-varying covariates would also facilitate building more complex models that enable disaggregating between-person and within-person effects of predictors. Since five or more waves of measurements are recommended to ensure precise estimates of predictor effects for simple linear trajectories (Hori & Miyazaki, 2022, it can be safely assumed that less than five measurements will probably not be enough when modeling complex trajectories like adaption processes. At the same time, researchers need to consider the task duration and burden for the participants.…”