Group-Based Trajectory Model
Also known as: GBTM, Group-Based Modeling of Development, Nagin Trajectory Model, Semiparametric Group-Based Modeling, Latent Class Growth Analysis
Group-based trajectory modeling (GBTM) is a finite-mixture method that identifies clusters of individuals who follow similar developmental paths of a behavior — most famously offending — over age or time. Introduced to criminology by Daniel Nagin and Kenneth Land in 1993, it replaces the assumption of a single average trajectory with a small number of distinct latent groups, each described by its own polynomial curve and its share of the population.
Key highlights
- Summarizes complex longitudinal heterogeneity into a small number of substantively interpretable developmental paths.
- Accommodates count, binary, and censored outcomes through appropriate link functions within one framework.
- Does not require specifying random-effects distributions, making it a flexible, semiparametric approximation to the unknown trajectory distribution.
- Provides posterior membership probabilities and group sizes that map directly onto criminological typologies such as adolescence-limited and life-course-persistent offenders.
- Supports extensions that link trajectory membership to covariates and to later outcomes, enabling rich life-course analyses.
Intuition
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How it works
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When to use it
Use GBTM when you have repeated longitudinal measures of a behavior or outcome on a sample of individuals and want to summarize the heterogeneity in developmental paths into a few interpretable groups — for example, distinguishing life-course-persistent from adolescence-limited offenders. It is well suited to count, binary, or censored outcomes measured across age. It is less appropriate when you believe development is genuinely continuous and a single growth curve with random effects (a growth mixture model or latent growth curve) better reflects the process, or when groups are reified as if they were discrete natural kinds rather than statistical approximations. Sample sizes of several hundred or more are typically needed to estimate distinct groups reliably.
Strengths & limitations
- Summarizes complex longitudinal heterogeneity into a small number of substantively interpretable developmental paths.
- Accommodates count, binary, and censored outcomes through appropriate link functions within one framework.
- Does not require specifying random-effects distributions, making it a flexible, semiparametric approximation to the unknown trajectory distribution.
- Provides posterior membership probabilities and group sizes that map directly onto criminological typologies such as adolescence-limited and life-course-persistent offenders.
- Supports extensions that link trajectory membership to covariates and to later outcomes, enabling rich life-course analyses.
- The number of groups is not known a priori and is chosen by fit indices (BIC) and judgment, so results can be sensitive to that decision.
- Latent groups are statistical approximations, not necessarily real subpopulations, yet they are frequently reified in applied work.
- The local-independence assumption can be violated when strong within-person serial dependence remains after conditioning on group.
- Estimation can converge to local maxima, so multiple start values are required, and very small groups may be unstable.
- It models the marginal trajectory distribution and does not, by itself, identify causes of group membership without further modeling.
Common pitfalls
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Applications
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Frequently asked
How do I choose the number of trajectory groups?
The standard practice is to fit models with increasing numbers of groups and compare the Bayesian Information Criterion (BIC), favoring the model where BIC stops improving meaningfully, then confirm the solution with separation diagnostics: average posterior probabilities of at least about 0.7 per group, odds of correct classification above 5, and group sizes large enough to interpret. Substantive interpretability and parsimony should override marginal statistical gains.
How does GBTM differ from a growth mixture model?
Both are finite-mixture longitudinal models, but GBTM (latent class growth analysis) fixes the within-group variance of the growth parameters to zero, so every member of a group shares the same trajectory shape with only sampling variation. Growth mixture models allow random effects within each group, permitting individual variation around each group's mean curve. GBTM is more parsimonious and easier to estimate; growth mixture models are more flexible but harder to identify.
Are the trajectory groups real categories of offenders?
Nagin himself cautions that the groups are a statistical approximation to an underlying continuous distribution of developmental paths, not necessarily distinct natural kinds. They are valuable for description, communication, and linking development to covariates and outcomes, but reifying them as discrete offender types — assuming a person belongs definitively to one immutable class — overstates what the model supports.
Sources
- 1.Nagin, D. S., & Land, K. C. (1993). Age, criminal careers, and population heterogeneity: Specification and estimation of a nonparametric, mixed Poisson model. Criminology, 31(3), 327–362.
- 2.Nagin, D. S. (2005). Group-Based Modeling of Development. Harvard University Press.ISBN 9780674016866
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Cite this page
ScholarGate. (2026, June 22). Group-Based Trajectory Model. ScholarGate. https://scholargate.app/criminology/group-based-trajectory-model