Utility of a slopes difference test for probing longitudinal multilevel aptitude treatment interactions: a simulation.

To determine which interventions work best for which students, precision education researchers can examine aptitude-treatment interactions (ATI) or skill-by-treatment interactions (STI) using longitudinal multilevel modeling. Probing techniques like the slopes difference test fit an ATI or STI framework, but power for using slopes difference tests in longitudinal multilevel modeling is unknown. The current study used simulation to determine which design factors influence the power of slopes difference tests. Design factors included effect size, number of waves, number of clusters, participants per cluster, proportion of assignment to the treatment group, and intraclass correlation. Of these factors, effect size, number of waves, number of clusters, and participants per cluster were the strongest determinants of power, model convergence, and rates of singularity. Slopes difference tests had greater power in longitudinal multilevel modeling than where it is originally utilized: multiple regression.