When applying the hierarchical model in a multigroup context, both the unconstrained model (in which criterion loadings and thresholds were estimated separately for each group) and the constrained model (in which group means for multi-substance dependence varied among groups, while holding constant the criterion loadings and thresholds) fit the data well, as indicated by low RMSEA and high CFI and TLI. The difference in CFI between the constrained and unconstrained models was 0.002 (which is less than the recommended maximum difference cut-off of 0.01 for establishing measurement invariance [38]). Therefore, we conclude that mean differences in the multi-substance dependence latent trait adequately describe criterion-level differences between the groups and proceed with interpreting the results of the constrained model.
