Measuring long term individual trajectories of offending using multiple methods

Criminal career researchers and developmental criminologists have identified describing individual trajectories of offending over time as a key research question. In response, recently various statistical methods have been developed and used to describe individual offending patterns over the life-course. Two approaches that are prominent in the current literature are standard growth curve modeling (GCM) and group-based trajectory models (GTM). The goal of this paper is to explore ways in which these different models with different sets of assumptions, do in fact lead to different outcomes on individual trajectories. Using a particularly rich dataset, the criminal career and life-course study, we estimate a unique trajectory for each individual in the sample using the GCM and GTM. We also estimate separate trajectories for each individual directly using the long time series. We then compare these three separate trajectories for each individual. We find that the average trajectories obtained from the different approaches match each other. However, for any given individual, these approaches tell very different stories. For example, each method identifies a rather different set of individuals as desistors. This comparison highlights the strengths and weaknesses of each approach, and more broadly, it reveals the uncertainty involved with measuring long term patterns of change in latent propensity to commit crimes.