Observed versus predicted age-trends in frequency of alcohol, marijuana, and cigarette use. Predicted = implied by univariate latent growth curve models. Observed = calculated from observed data. For alcohol use, 2 = 1-2 days per year, and 5 = 1-2 days per month. For cigarette and marijuana use, 0 = Never, 1 = less than once per week, and 2 = 1-2 days per week.