Putting the individual back into individual growth curves

Scaling of rime (age) in latent growth curve (LGC) models has important imp lications for studies of development. When participants begin a study at di fferent ages, sample means and covariance-based structural equation modelin g (SEM) approaches produce biased estimates of the variance of the intercep t and the covariance between the Intercept and Slope factors. However, indi vidual data vector-based SEM approaches produce proper estimates of these p arameters that are identical to those produced by multilevel modeling (MLM) . Scaling of the time variable also raises issues regarding the interpretat ion of within- and between-persons effects of time that parallel those asso ciated with centering of predictor variables in MLM. A numerical example is used to illustrate these issues, and an Mr script for fitting individual d ata vector-based LGC models is provided.