After testing the model fit for each substance on the overall sample, we examined the covariance equivalence of the model across genders, across ethnic groups, and across the treatment and control group by using multiple group analyses. Because of the large sample size, the change in comparative fit index (Δ CFI) was used to assess the significance of the difference between the multiple group “constrained” models, in which correlations and regression paths were assumed to be equivalent in the two groups, and the multiple group “unconstrained” models, in which correlations and regression paths were not assumed to be identical in the two groups. According to Cheung and Rensvold (2002), Δ CFI of 0.01 or greater indicates a significant difference between the two models.
