Longitudinal design considerations to optimize power to detect variances and covariances among rates of change: simulation results based on actual longitudinal studies.

We investigated the power to detect variances and covariances in rates of change in the context of existing longitudinal studies using linear bivariate growth curve models. Power was estimated by means of Monte Carlo simulations. Our findings show that typical longitudinal study designs have substantial power to detect both variances and covariances among rates of change in a variety of cognitive, physical functioning, and mental health outcomes. We performed simulations to investigate the interplay among number and spacing of occasions, total duration of the study, effect size, and error variance on power and required sample size. The relation between growth rate reliability (GRR) and effect size to the sample size required to detect power greater than or equal to .80 was nonlinear, with rapidly decreasing sample sizes needed as GRR increases. The results presented here stand in contrast to previous simulation results and recommendations (Hertzog, Lindenberger, Ghisletta, & von Oertzen, 2006; Hertzog, von Oertzen, Ghisletta, & Lindenberger, 2008; von Oertzen, Ghisletta, & Lindenberger, 2010), which are limited due to confounds between study length and number of waves, error variance with growth curve reliability, and parameter values that are largely out of bounds of actual study values. Power to detect change is generally low in the early phases (i.e., first years) of longitudinal studies but can substantially increase if the design is optimized. We recommend additional assessments, including embedded intensive measurement designs, to improve power in the early phases of long-term longitudinal studies.