Effect of Parameterization on Statistical Power and Effect Size Estimation in Latent Growth Modeling

The difference between groups in their random slopes is frequently examined in latent growth modeling to evaluate treatment efficacy. However, when end centering is used for model parameterization with a randomized design, the difference in the random intercepts is the model-estimated mean difference between the groups at the end of the study, which has the same expected value as the product of the coefficient for the slope difference and study duration. A Monte Carlo study found that (a) the statistical power to detect the treatment effect was greater when determined from the intercept instead of the slope difference, and (b) the standard error of the model-estimated mean difference was smaller when obtained from the intercept difference. Investigators may reduce Type II errors by comparing groups in random intercepts instead of random slopes to test treatment effects, and should therefore conduct power assessments using end centering to detect each difference.