Identification of Trajectories
To maximize meaningful comparisons, we selected a four-class model for each measure. For most cases, this was the best-fitting model in terms of model fit and class interpretability and size (see for fit indices). Model fit was evaluated with information criteria fit indices (Bayesian information criterion [Schwartz, 1978
]; Akaike’s information criterion [Akaike, 1987
]). also presents entropy values, which represent precision of classification based on posterior probability values (Muthén & Muthén, 1998-2004
); an entropy value close to 1.0 indicates clear classification (little overlap among trajectories).
Model Fit for Five Indices of Alcohol Involvement
Figures through show the developmental courses for alcohol use disorder, alcohol dependence, alcohol consequences, alcohol quantity–frequency, and heavy drinking, respectively. Group membership was characterized by the following courses: nondrinking or nonproblematic drinking, which ranged from 45% to 74%; developmentally limited, which decreased over time, ranging from 8% to 26%; later onset, which increased over time, ranging from 2% to 19%; and chronic (this course also often exhibited a decrease over time; however, it was the most chronic of all courses), which ranged from 3% to 22%.
Figure 1 Latent class growth analysis model for alcohol use disorder (AUD) at Waves 1–6, weighted by estimated class probabilities. N = 377. Later Ons. = later onset; NonDx = nondrinking or nonproblematic drinking; Dev Limited = developmentally limited. (more ...)
Figure 5 Mixture model for heavy drinking at Waves 1–6, weighted by estimated class probabilities. N = 377. Heavy drinking was scored as 0 = didn’t drink 5 or more drinks at a single sitting in the past 30 days, 2 = once during the past 30 days (more ...)
Comparison of Trajectories
To compare agreement between class membership for each measure, respondents were first assigned to classes on the basis of their most likely group membership (unweighted by probability of class membership), and then contingency tables were created for each pairwise comparison (10 in all).3
Agreement between indices, assessed by Cohen’s kappa (Cohen, 1960
), ranged from κ
= .26 to κ
= .54 (see below the diagonal in ). These represent moderate levels of agreement (Goodman & Kruskal, 1954
). Ancillary analyses examined hand-calculated kappa estimates that were weighted by probability of group membership, which were very similar in magnitude (κ
= .21 to κ
= .48; see above the diagonal in ). Note that these “weighted” kappas are not weighted kappas as the term is traditionally used in the literature to describe a kappa variant that takes into account gradation in level of disagreement (Cohen, 1968
). Rather, they are unweighted kappas for estimates that were weighted by probability of group membership.
Comparison of Trajectories Using Cohen’s Kappa
One concern is that the association between any two measures is actually driven by the nonproblem groups. We recomputed the kappas after eliminating those two groups from the comparison (see ). On average, the magnitude of the kappas was reduced by about two thirds (Mdn = 66%), suggesting that, overall, different patterns among users account for the majority, but not all, of the concordance between the indices. Inspection of specific pairs indicated substantial variability after eliminating nonusers (39% to 94% of the original value of the kappa remained after removing nonusers); however, there was no specific pattern suggesting that nonusers account for concordance among certain constructs.
Comparison of Trajectories Using Cohen’s Kappa After Removing Nonusers
Given that presenting each of the 10 pairwise contingency tables would be cumbersome, we also present a summary figure (see ) documenting the location of trajectory agreement (i.e., along the diagonal) and disagreement (i.e., off-diagonal cells). To determine the particular combinations of courses that most contribute to agreement between two trajectories, the cell chi-square statistics for each cell were plotted with bar graphs for each of the 10 comparisons. Corresponding courses were observed at a rate greater than what would be expected by chance (i.e., agreement along the diagonal). Associations between AUD and other indices were lower than those between any other comparison. This may be due to the larger negative slope and higher initial value of the developmentally limited course for AUD than for the other indices.
Figure 6 Summary of trajectory agreement represented by cell chi-square statistics for each of the five alcohol measures. Dark bars reflect values that are greater than would be expected by chance, and light bars indicate values that are lower than would be expected (more ...)
Correspondingly, disagreement along the off diagonal was considerable, although the chronic course was occasionally associated with the developmentally limited and later-onset courses. Although the chronic course tended to decline over time for some of the alcohol indices (AUD, alcohol dependence, alcohol consequences), this would not explain why it was associated with the developmentally limited course for other alcohol indices or why it was at times associated with the later-onset course.
Finally, we examined third-variable prediction of group membership for each of the indices. Predictors (sex, family history of alcoholism, conduct disorder symptom count, novelty seeking, lifetime diagnosis with a DSM–III
depression or anxiety disorder, presence of suicidal thoughts in lifetime, and affect-regulation reasons for drinking) were treated as exogenous to class membership. Continuous measures (conduct disorder symptom count, novelty seeking, and reasons for drinking) were standardized to provide a more meaningful metric for odds ratios. A multinomial logistic regression procedure was used (Agresti, 1990
). Five comparisons of interest were examined: the three drinking groups versus the nondrinking group (consistent with the literature) and developmentally limited versus chronic (begin at the same point but diverge) and later onset versus chronic (begin at different points but converge). All models were run in Mplus, which allows for parameters to be weighted by probability of group membership. For the five psychosocial predictors, sex and family history were controlled.
In , we present odds ratios for each measure of alcohol involvement and each of the seven predictors. Relative to the nondrinking/nonproblematic drinking group, likelihood of membership in the chronic group was generally predicted by all etiological predictors, although considerably less so for family history of alcoholism, depression/anxiety, and suicidal thoughts. In general, likelihood of belonging to the developmentally limited class was significantly predicted by greater conduct disorder, novelty seeking, and reasons for drinking. Likelihood of belonging to the later onset class was positively predicted by greater reasons for drinking and, for measures of more problematic drinking (AUD, alcohol dependence, alcohol consequences), greater conduct disorder. There were few differences between the chronic group and the developmentally limited and later-onset groups. Those who remitted from the problematic alcohol involvement measures were less likely to exhibit conduct disorder or endorse affect-regulation reasons for drinking than were those who continued their drinking. In addition, those who increased their alcohol involvement over young adulthood were more likely to exhibit conduct disorder (for the consumption measures) or endorse novelty seeking (particularly for the problematic measures). In sum, with a few exceptions, prediction tended to be relatively consistent across measures of alcohol involvement, despite the differences in trajectory structure and membership and the low-to-moderate agreement among trajectories.
Odds Ratios and Significance Values for Univariate Prediction of Trajectories for Five Pairwise Comparisons Across Each Measure of Alcohol Involvement, for Seven Predictor Variables