The analysis proceeded in three stages. First, we estimated prevalence for binary outcomes and means/standard deviations for continuous outcomes among Blacks and Whites for each wave of the study. Second, we estimated multivariate random effects models, modeling log odds and/or mean differences in each substance use outcome between Blacks and Whites at each wave of the study, accounting for the correlation within person in substance use across time while estimating between group variance. Third, we estimated difference-in-difference random effects models to test whether the association between race/ethnicity and substance use changed across the four waves of the study. For example, we tested whether the difference in any past 30-day smoking between Blacks and Whites became larger, smaller, or did not change from Wave 1 to Wave 2, Wave 2 to Wave 3, Wave 3 to Wave 4, Wave 1 to Wave 4. We implemented this difference-indifference approach by creating model constraint parameters in MPLUS that estimated the difference in estimates of effect across waves, and tested whether these parameters were significantly different from 0 (0 would indicate no difference in
