Disaggregating Associations of Between-Person Differences in Change over Time from Associations of Within-Person Fluctuation in Longitudinal Data

In longitudinal models with time-varying predictors, the need to distinguish their within-person (WP) relations of time-specific residuals from their between-person (BP) relations of individual means is relatively well-known. In contrast, the need to further distinguish their BP relations of individual time slopes has received much less attention. This article addresses the deleterious impact that ignoring effects of individual time slopes in time-varying predictors can have on the recovery of BP intercept and WP residual relations in commonly used variants of longitudinal models. Using simulation methods and analyses of example data, this problem is demonstrated within univariate longitudinal models (i.e., multilevel or mixed-effects models using observed predictors), as well as in multivariate longitudinal models (i.e., structural equation models using latent predictors, including those for cross-lagged relations). Recommendations are provided for how to avoid conflating the BP and WP associations of longitudinal variables in practice.