Stage-Sequential Growth Mixture Modeling of Criminological Panel Data

The detection of distinctive developmental trajectories is of great importance in criminological research. The methodology of growth curve and finite mixture modeling provides the opportunity to examine different developments of offending. With latent growth curve models (LGM) (Meredith and Tisak, Psychometrika 55:107–122, 1990) the structural equation methodology offers a strategy to examine intra- and interindividual developmental processes of delinquent behavior. There might, however, not be a single but a mixture of populations underlying the growth curves which refers to unobserved heterogeneity in the longitudinal data. Growth mixture models (GMM) introduced by Muthen and Shedden (Biometrics 55:463–469, 1999) can consider unobserved heterogeneity when estimating growth curves. GMM distinguish between continuous variables which represent the growth curve model and categorical variables which refer to subgroups that have a common development in the growth process. The models are usually based on single-phase data which associate any event with a specific period. Panel data, however, often contain several relevant phases. In this context, stage-sequential growth mixture models with multiphase longitudinal data become increasingly important. Kim and Kim (Structural Equation Modeling: A Multidisciplinary Journal 19:293–319, 2012) investigated and discussed three distinctive types of stage-sequential growth mixture models: traditional piecewise GMM, discontinuous piecewise GMM, and sequential process GMM. These models will be applied here to examine different stages of delinquent trajectories within the time range of adolescence and young adulthood using data from the German panel study Crime in the Modern City (CrimoC, Boers et al., Monatsschrift fur Kriminologie und Strafrechtsreform 3:183–202, 2014). Methodological and substantive differences between single-phase and multi-phase models are discussed as well as recommendations for future applications.

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