No abstract

This article introduces a new SAS procedure written by the authors that analyzes longitudinal data (developmental trajectories) Patterson et al. 1998;Patterson and Yoerger 1997;Sampson and Laub 1993). This article demonstrates a new SAS procedure, called TRAJ, developed by the authors for estimating developmental trajectories. The procedure is based on a semiparametric, group-based modeling strategy. Technically, the model is a mixture of probability distributions that are suitably specified to describe the data to be analyzed. The approach is intended to complement two well-established methods for analyzing developmental trajectories-hierarchical modeling (Bryk and Raudenbush 1987, 1992;Goldstein 1995) and latent growth curve modeling (Meredith and Tisak 1990;Muthen 1989;Willett and Sayer 1994). In hierarchical modeling, individual variation in developmental trajectories, which are commonly called growth curves, are captured by a random coefficients modeling strategy.

A developmental trajectory describes the course of a behavior over age or time. A group-based method for identifying distinctive groups of individual trajectories within the population and for profiling the characteristics of group members is demonstrated. Such clusters might include groups of "increasers." "decreasers," and "no changers." Suitably defined probability distributions are used to handle 3 data types-count, binary, and psychometric scale data. Four capabilities are demonstrated: (a) the capability to identify rather than assume distinctive groups of trajectories, (b) the capability to estimate the proportion of the population following each such trajectory group, (c) the capability to relate group membership probability to individual characteristics and circumstances, and (d) the capability to use the group membership probabilities for various other purposes such as creating profiles of group members.Over the past decade, major advances have been made in methodology for analyzing individual-level developmental trajectories. The two main branches of methodology are hierarchical modeling (Bryk &

Group-based trajectory models are increasingly being applied in clinical research to map the developmental course of symptoms and assess heterogeneity in response to clinical interventions. In this review, we provide a nontechnical overview of group-based trajectory and growth mixture modeling alongside a sampling of how these models have been applied in clinical research. We discuss the challenges associated with the application of both types of group-based models and propose a set of preliminary guidelines for applied researchers to follow when reporting model results. Future directions in group-based modeling applications are discussed, including the use of trajectory models to facilitate causal inference when random assignment to treatment condition is not possible.

This study used data from 6 sites and 3 countries to examine the developmental course of physical aggression in childhood and to analyze its linkage to violent and nonviolent offending outcomes in adolescence. The results indicate that among boys there is continuity in problem behavior from childhood to adolescence and that such continuity is especially acute when early problem behavior takes the form of physical aggression. Chronic physical aggression during the elementary school years specifically increases the risk for continued physical violence as well as other nonviolent forms of delinquency during adolescence. However, this conclusion is reserved primarily for boys, because the results indicate no clear linkage between childhood physical aggression and adolescent offending among female samples despite notable similarities across male and female samples in the developmental course of physical aggression in childhood.Children's behavior problems have long been considered precursors of juvenile delinquency and adult criminality (Carpenter, 1851;Horn, 1989; Roosevelt, 1909). The development of these behavior problems during the elementary school years was the object of intensive investigations over the last quarter of the 20th century. A number of large-scale longitudinal studies in different industrialized countries used repeated measurements over many years to trace the development of behavior problems. These studies followed older pioneering longitudinal studies that were retrospective (e.g., Robins, 1966) or that had limited their prospective assessments to one time point during childhood and one or two time points during adolescence and adulthood (e.g., Lefkowitz, Eron, Walder, & Huesmann, 1977; West & Harrington, 1973).Having reviewed this long-lived literature, the U.S. National Research Council's Panel on Understanding and Preventing Violence concluded, " [I] NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript to become violent teenagers and adults" (Reiss & Roth, 1993, p, 358). There is indeed ample evidence that, at least for boys, childhood disruptive or troublesome behavior is one of the best predictors of adolescent and adult criminality, including violent offending (e.g., Farrington, 1994;Fergusson & Horwood, 1995;Huesmann, Eron, Lefkowitz, & Walder, 1984;Moffitt, 1990;Pulkkinen & Tremblay, 1992;Stattin & Magnusson, 1989;Tremblay, Pihl, Vitaro, & Dobkin, 1994). However, Nagin and Tremblay (1999) and Tremblay (2000) pointed out that extant research generally does not distinguish physical from nonphysical aggression or violence. Thus, it is only possible to conclude that disruptive or troublesome behavior during childhood predicts later delinquent behavior, not that physical aggression during childhood per se is a distinct risk factor for physical violence in adolescence or adulthood.A determination of whether physical aggression is a distinct risk factor for later physical violence is important for both conceptual and practical reasons. Conceptually, the nature of ...