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

Longitudinal designs afford the opportunity to examine the many different ways in which variables can be related over time, which can be both a blessing and a curse. Much has been written about the need to distinguish between-person relations of individual mean differences from within-person relations of time-specific residuals for time-varying predictors. The present work expands on this topic by describing the need to further distinguish between-person relations among individual slopes for change over time. Using simulation methods, 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). The discussion presents recommendations for practice, along with caveats and concerns regarding related longitudinal models for lead-lag effects.