Time-Varying Effect Sizes for Quadratic Growth Models in Multilevel and Latent Growth Modeling

Multilevel and latent growth modeling analysis (GMA) is often used to compare independent groups in linear random slopes of outcomes over time, particularly in randomized controlled trials. The unstandardized coefficient for the effect of group on the slope from a linear GMA can be transformed into a model-estimated effect size for the group difference at the end of a study. Because effect sizes vary non-linearly in quadratic GMA, the effect size at the end of a study using quadratic GMA cannot be derived from a single coefficient, and cannot be used to estimate effect sizes at intermediate time points with backwards extrapolation. This article formulates equations and associated input commands in Mplus for time-varying effect sizes for quadratic GMA. Illustrative analyses that produced these time-varying effect sizes were presented, and Monte Carlo study found that bias in the effect sizes and their confidence intervals was ignorable.