Putting the individual back into individual growth curves

Scaling of time (age) in latent growth curve (LGC) models has important implications for studies of development. When participants begin a study at different ages, sample means and covariance-based structural equation modeling (SEM) approaches produce biased estimates of the variance of the intercept and the covariance between the Intercept and Slope factors. However, individual data vector-based SEM approaches produce proper estimates of these parameters that are identical to those produced by multilevel modeling (MLM). Scaling of the time variable also raises issues regarding the interpretation of within- and between-persons effects of time that parallel those associated with centering of predictor variables in MLM. A numerical example is used to illustrate these issues, and an Mx script for fitting individual data vector-based LGC models is provided.