Analyzing Developmental Trajectories with Mixture Models: A Second Generation of Models and Software

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A developmental trajectory describes the course of a behavior over age or time. This project builds upon prior NSF funded research (SES-9511412) that developed a semi-parametric, group-based approach for identifying distinctive groups of individual trajectories within the population of interest, and also produced "canned" SAS-based software for estimation of the trajectory models. This project will extend the research in several important ways. First, the univariate trajectory models and software will be extended to include a random effect component. The software also will be expanded to incorporate a previously developed non-parametric trajectory model. Second, a next generation of joint trajectory models will be developed. Work to date has focused on developing group-based models appropriate for analyzing the developmental course of a single behavior. A key goal of this research is to generalize univariate trajectory models to allow the joint estimation of trajectories of two distinct but related behaviors, for example, physical aggression in childhood and violent delinquency in adolescence. Here again the capacity for joint trajectory estimation will be incorporated into the already available software package. Third, alternative measures for evaluating model goodness of fit will be explored. Such measures are intended to complement the Bayesian Information Criterion (BIC) as a basis for model selection.This methodological research program is motivated by substantive problems from criminology, developmental psychology, and psychiatry, such as co-morbidity and heterotypic continuity. Co-morbidity refers to the contemporaneous occurrence of two or more undesirable conditions such as physical aggression and hyperactivity during childhood. Heterotypic continuity refers to the inter-temporal manifestation of a latent individual trait in different but analogous behavioral forms. For example, a latent propensity for violence may reveal itself as kicking and biting siblings during early childhood, gang fighting during adolescence, and spouse abuse during adulthood. The form and target of the aggression is different but the constant is physical violence. Because of the changing form of the manifestation, use of the same measurement scale at different stages of life is inappropriate for capturing such a tendency. The themes of co-morbidity and heterotypic continuity will be explored in analyses of major prospective longitudinal data sets from around the world.