Group-Based Trajectory Modeling: An Overview
This chapter provides an overview of a group-based statistical methodology for analyzing developmental trajectories – the evolution of an outcome over age or time. A detailed account of the method’s statistical underpinnings and a full range of applications are provided in Nagin (2005).
In this discussion, the term developmental trajectory is used to describe the progression of any phenomenon, whether behavioral, biological, or physical. Charting and understanding developmental trajectories is among the most fundamental and empirically important research topics in the social and behavioral sciences and medicine. A few prominent examples include: criminological analyses of the progression and causes of criminality over life stages or of time trends of reported crime across geographic locations, psychological studies of the course and antecedents of psychopathologies, sociological investigations into the interaction between human behavior and social context over time, and medical research on the impact of treatments on the progress of diseases.
Longitudinal data – data with a time-based dimension – provide the empirical foundation for the analysis of developmental trajectories. Most standard statistical approaches for analyzing developmental trajectories are designed to account for individual variability about a mean population trend. However, many of the most interesting and challenging problems in longitudinal analysis have a qualitative dimension that allows for the possibility that there are meaningful sub-groups within a population that follow distinctive developmental trajectories that are not identifiable ex ante based on some measured set of individual characteristics (e.g., gender or socioeconomic status). In psychology, for example, there is a long tradition of taxonomic theorizing about distinctive developmental progressions of these sub-categories. For research problems with a taxonomic dimension, the aim is to chart out the distinctive trajectories, to understand what factors account for their distinctiveness and to test whether individuals following the different trajectories also respond differently to a treatment such as a medical intervention or major life event such as the birth of a child. This chapter describes an approach, based upon a formal statistical model, for conducting group-based analysis with time- and age-based data.
KeywordsPhysical Aggression Developmental Trajectory Multivariate Normal Distribution Trajectory Group Population Member
This research has been supported by the National Science Foundation (NSF) (SES-99113700; SES-0647576) and the National Institute of Mental Health (RO1 MH65611–01A2).
- Bergman LR (1998) A pattern-oriented approach to studying individual development: snapshots and processes. In: Cairns RB, Bergman LR, Kagan J (eds) Methods and models for studying the individual. Sage Publications, Thousand Oaks, CAGoogle Scholar
- Bryk AS, Raudenbush SW (1992) Hierarchical linear models for social and behavioral research: application and data analysis methods. Sage Publications, Newbury Park, CAGoogle Scholar
- Christ M, Krishnan R, Nagin DS, Guenther O (2002) An empirical analysis of web site stickiness. Proceedings of the 10th European conference on information systems (ECIS-02), Gdansk, PolandGoogle Scholar
- Cramér H (1946) Mathematical methods of statistics. Princeton University Press, Princeton, NJGoogle Scholar
- Elder GH (1985) Perspectives on the life course. In: Elder GH Jr (ed) Life course dynamics. Cornell University Press, IthacaGoogle Scholar
- Everitt BS, Hand DJ (1981) Finite mixture distributions. Chapman and Hall, LondonGoogle Scholar
- Goldstein H (1995) Multilevel statistical models, 2nd edn. Edward Arnold, LondonGoogle Scholar
- Greene WH (1990) Econometric analysis. Macmillan, New YorkGoogle Scholar
- Griffith E Chavez J (2004) Communities, street guns and homicide trajectories in Chicago, 1980–1995: merging methods for examining homicide trends across space and time. Criminology 42:941–978Google Scholar
- Krishnan R (2008) Trajectories of ring tone downloads. Paper under preparation. Carnegie Mellon University, Pittsburgh, PAGoogle Scholar
- Magnusson D (1998) The logic and implications of a person-oriented approach. In: Cairns RB, Bergman LR, Kagan J (eds) Methods and models for studying the individual. Sage Publications, Thousand Oaks, CAGoogle Scholar
- Moffitt TE (1997) Adolescence-limited and life-course-persistent offending: a complementary pair of developmental theories. In: Thornberry TP (ed) Advances in criminological theory. Transaction Publishers, New Brunswick, NJ, pp 11–54Google Scholar
- Muthén BO (2001) Second-generation structural equation modeling with a combination of categorical and continuous latent variables: new opportunities for latent class/latent curve modeling. In: Sayers A, Collins L (eds) New methods for the analysis of change. American Psychological Association, Washington, DCGoogle Scholar
- Nagin DS (2005) Group-based modeling of development. Harvard University Press, Cambridge, MAGoogle Scholar
- Piquero A (2008). Taking stock of developmental trajectories of criminal activity over the life course. In: Liberman AM (ed) The long view of crime a synthesis of longitudinal research. Springer, New York, NYGoogle Scholar
- Thiel H (1971) Principals of econometrics. Wiley, New York, NYGoogle Scholar
- Titterington DM, Smith AFM, Makov UE (1985) Statistical analysis of finite mixture distributions. Wiley, New YorkGoogle Scholar
- Tremblay RE, Nagin DS (2005) Aggression in humans. In: Tremblay RE, Hartup WW, Archer J (eds) Developmental origins of aggression. Guilford, New York, NYGoogle Scholar
- van Bokhoven I Van Goozen SHM, van Engeland H, Schaal B, Arseneault L Séguin JR, Nagin DS Vitaro F, abd Tremblay RE. (2005) Salivary cortisol and aggression in a population-based longitudinal study of adolescent males. J Neural Transm 112:1083–1096Google Scholar
- Warr M (2002) Companions in crime: the social aspects of criminal conduct. Cambridge University Press, New YorkGoogle Scholar
- Weisburd D, Morris N, Groff E (2008) Hot spots of juvenile crime: a longitudinal study of crime incidents at street segments in Seattle, Washington. Working paper. James Madison University, Fairfax, VAGoogle Scholar