Using the Group‐Based Trajectory Model to Study Crime Over the Life Course

Abstract

Recognizing that social, behavioral, and biological processes evolve over time, criminologists have been interested in how the phenomenon of crime changes over time and thus have paid close attention to developmental trajectories of crime. Several research methodologies and statistical techniques have been developed to permit study of developmental trajectories. This paper provides a non‐technical overview of a method developed to examine behavioral changes over age or time—group‐based trajectory modeling (GBTM). Following background material, we provide an overview of the technique. This is followed by a discussion of the applicability of the method to a variety of criminological questions, a brief review of the existing applications of the method, including the software used, as well as the advantages and disadvantages of the trajectory approach for particular questions. The paper concludes with an outline of methodological and substantive “next‐steps” regarding GBTM and its application in criminology and criminal justice research.

Notes

1. Trajectory‐based methods lend themselves to the presentation of findings in the form of easily understood graphical and tabular data summaries (Nagin 2005, p. 3), and the output from the method serves many useful functions. First, after sorting individuals into the trajectories, researchers can treat the groups as categories and examine how risk/protective factors vary across the groups. This classify/analyze approach provides basic description about how the various trajectories differ along key variables. Second, the trajectories can be used as outcome variables in a multinomial logistic regression framework, where independent variables predict membership in the groups. A third function is the use of the group classifications as predictors in a regression‐based framework. This approach allows for an examination of how certain variables relate to outcomes after considering unobserved individual differences measured via trajectories.

2. If the underlying distribution is indeed discrete and not continuous, then an increase in sample size will not artificially lead to an increase in the number of groups identified.

3. These data‐related features also affect the conclusions drawn from non‐GBTM approaches.

4. It is important to bear in mind that the variation within the trajectory is random variation conditional on trajectory (group) membership, while the variation between the trajectories is structural. Still, B. Muthén (personal communication, 24 January 2007) argues that GBTM does indeed assume that individuals belong to a trajectory group. He indicates that to the extent that GBTM views this as merely an approximation, then researchers should use a growth mixture model where within‐class variation is allowed.

5. Controlling for exposure time through age 32 identified only five groups, but the predicted number of offenses was much higher with exposure time data. Still, by age 32, the offending patterns in the exposure time analysis appeared to diminish.