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.

This article is a follow-up to Jones, Nagin, and Roeder (2001), which described an SAS procedure for estimating group-based trajectory models. Group-based trajectory is a specialized application of finite mixture modeling and is designed to identify clusters of individuals following similar progressions of some behavior or outcome over age or time. This article has two purposes. One is to summarize extensions of the methodology and of the SAS procedure that have been developed since Jones et al. The other is to illustrate how group-based trajectory modeling lends itself to presentation of findings in the form of easily understood graphical and tabular data summaries.

Group-based trajectory models are used to investigate population differences in the developmental courses of behaviors or outcomes. This note introduces a new Stata command, traj, for fitting to longitudinal data finite (discrete) mixture models designed to identify clusters of individuals following similar progressions of some behavior or outcome over age or time. Normal, Censored normal, Poisson, Zero-inflated Poisson, and Logistic distributions are supported.

Identifying and monitoring multiple disease biomarkers and other clinically important factors affecting the course of a disease, behavior or health status is of great clinical relevance. Yet conventional statistical practice generally falls far short of taking full advantage of the information available in multivariate longitudinal data for tracking the course of the outcome of interest. We demonstrate a method called multi-trajectory modeling that is designed to overcome this limitation. The method is a generalization of group-based trajectory modeling. Group-based trajectory modeling is designed to identify clusters of individuals who are following similar trajectories of a single indicator of interest such as post-operative fever or body mass index. Multi-trajectory modeling identifies latent clusters of individuals following similar trajectories across multiple indicators of an outcome of interest (e.g., the health status of chronic kidney disease patients as measured by their eGFR, hemoglobin, blood CO levels). Multi-trajectory modeling is an application of finite mixture modeling. We lay out the underlying likelihood function of the multi-trajectory model and demonstrate its use with two examples.

The evidence from this and studies of the motor system suggests more general involvement of neural circuitry beyond the neural systems for social behavior, communication, and reasoning, all of which share a high demand on neural integration of information.