Effect Size for a Multilevel Model Random Slope Effect: Change in Variance Accounted for with Likelihood-based versus Variance Partition Measures

Applied educational researchers may be interested in exploring random slope effects in multilevel models, such as when examining individual growth trajectories with longitudinal data. Random slopes are effects for which the slope of an individual-level coefficient varies depending on group membership, however these effects can be difficult to interpret. The change in variance accounted for is often used as an effect size measure and could be appropriate for helping to interpret a random slope effect. Two methods for computing variance accounted for include likelihood-based methods and variance partition methods. It is unclear how results from these two methods compare to each other when used to compute a measure of change in variance accounted for with a random slope effect. The present study fills this gap through a simulation study comparing these two methods under various conditions. Results indicate that the value of variance accounted for may differ depending on the type of measure used, and that applied researchers should consider reporting values for both measures