Growth mixture models in longitudinal research

Latent growth curve models as structural equation models are extensively discussed in various research fields (Curran and Muthén in Am. J. Community Psychol. 27:567–595, 1999; Duncan et al. in An introduction to latent variable growth curve modeling. Concepts, issues and applications, 2nd edn., Lawrence Earlbaum, Mahwah, 2006; Muthén and Muthén in Alcohol. Clin. Exp. Res. 24(6):882–891, 2000a; in J. Stud. Alcohol. 61:290–300, 2000b). Recent methodological and statistical extension are focused on the consideration of unobserved heterogeneity in empirical data. Muthén extended the classic structural equation approach by mixture components, i.e. categorical latent classes (Muthén in Marcouldies, G.A., Sckumacker, R.E. (eds.), New developments and techniques in structural equation modeling, pp. 1–33, Lawrance Erlbaum, Mahwah, 2001a; in Behaviometrika 29(1):81–117, 2002; in Kaplan, D. (ed.), The SAGE handbook of quantitative methodology for the social sciences, pp. 345–368, Sage, Thousand Oaks, 2004). The paper discusses applications of growth mixture models with data on delinquent behavior of adolescents from the German panel study Crime in the modern City (CrimoC) (Boers et al. in Eur. J. Criminol. 7:499–520, 2010; Reinecke in Delinquenzverläufe im Jugendalter: Empirische Überprüfung von Wachstums- und Mischverteilungsmodellen, Institut für sozialwissenschaftliche Forschung e.V., Münster, 2006a; in Methodology 2:100–112, 2006b; in van Montfort, K., Oud, J., Satorra, A. (eds.), Longitudinal models in the behavioral and related sciences, pp. 239–266, Lawrence Erlbaum, Mahwah, 2007). Observed as well as unobserved heterogeneity will be considered with growth mixture models. Special attention is given to the distribution of the outcome variables as counts. Poisson and negative binomial distributions with zero inflation are considered in the proposed growth mixture models variables. Different model specifications will be emphasized with respect to their particular parameterizations.