Accounting for standard errors of measurement when modeling change

Modeling within-person change over time and between-person differences in change over time is a primary goal in prevention science. When modeling change in an observed score over time with multilevel or structural equation modeling approaches, each observed score counts toward the estimation of model parameters equally. However, observed scores can differ in terms of their precision—both within and across participants. We propose an approach to weight observed scores by their level of precision, which is estimated as the inverse of their standard error of measurement in the context of item response modeling. Thus, scores with lower standard errors of measurement have greater weight, and scores with higher standard errors of measurement are down weighted. We discuss the weighting approaches and illustrate how to apply this approach with commonly available software. We then compare this approach to modeling change without weighting based on standard errors of measurement.