Model estimation and model testing
All models will be estimated in Mplus 8.4 [The main hypothesis will be evaluated for each outcome variable by comparing Models A-D using the Bayesian information criterion (BIC). When comparing models, lower BIC indicates better relative model fit; a BIC difference of greater than 10 indicates very strong evidence against the model with the largest BIC [To assess power for this analysis, we conducted a Monte Carlo simulation using Model D. The model included two groups (intervention and comparison), latent intercepts and slopes for both groups, and three continuous indicators (e.g., parcels) at both pretest and posttest. We specified population values of .70 for all standardized factor loadings and a mean difference of .50 between the latent slopes of the two groups. We assumed a sample size of 288, with 144 in each group. Under these assumptions and using 1,000 replications and a robust maximum likelihood estimator, the power estimate for the group difference in latent slopes was .88.