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	Group-Based Trajectory Model	Tillväxtblandningsmodellen (Growth Mixture Model, GMM)
Ämnesområde	Criminology	Statistik
Familj	Regression model	Latent structure
Ursprungsår	1993	1999
Upphovsperson	Daniel S. Nagin & Kenneth C. Land	Bengt O. Muthén & Kerby Shedden
Typ	Finite-mixture model of longitudinal developmental trajectories	Latent class / longitudinal growth model
Ursprungskälla	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.	Muthén, B. O. & Shedden, K. (1999). Finite Mixture Modeling with Mixture Outcomes Using the EM Algorithm. Biometrics, 55(2), 463–469.
Alias	GBTM, Group-Based Modeling of Development, Nagin Trajectory Model, Semiparametric Group-Based Modeling	Büyüme Karışım Modeli (Growth Mixture Model — GMM), GMM, latent class growth analysis extension, mixture latent growth curve model
Närliggande	4	5
Sammanfattning	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.	The Growth Mixture Model, introduced by Muthén and Shedden in 1999, is a longitudinal latent variable method that identifies distinct subpopulations — latent trajectory classes — each following its own growth curve over time. It extends the standard Latent Growth Curve (LGC) model by allowing the sample to be composed of an unknown mixture of classes with different intercepts, slopes, and variance structures.