Encyclopedia of Criminology and Criminal Justice

2014 Edition
| Editors: Gerben Bruinsma, David Weisburd

Growth Curve Models with Categorical Outcomes

  • Katherine E. Masyn
  • Hanno Petras
  • Weiwei Liu
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-5690-2_404

Overview

Motivated by the limited available literature on the treatment of longitudinal binary and ordinal outcomes in a growth modeling framework, the goal of this entry is to provide an accessible and practical introduction of this topic for a criminological audience. The parameterization of categorical latent growth models is explained by integrating aspects of the more familiar conventional latent growth models and generalized linear models. Emphasis is placed on the process of model building, evaluation, and interpretation. The entry contains an elaboration of how to include predictors of developmental change in the model for covariate-related hypothesis tests along with remarks regarding of the importance of auxiliary information for assessing model validity and utility. Finally, several model extensions including nonlinear change, generalized growth mixture modeling, and longitudinal latent class analysis are discussed.

Introduction

Criminologists typically encounter data on...

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Notes

Acknowledgment

Dr. Weiwei Liu received support through a training grant from the National Institute of Mental Health while working on this entry (T32 MH18834). Correspondence concerning this article should be addressed to Hanno Petras, Ph.D., at JBS International, Inc., 5515 Security Lane, Suite 800, North Bethesda, MD 20852-5007, USA. Phone: (240) 645-4921. Email: hpetras@jbsinternational.com.

Recommended Reading and References

  1. Agresti A (2002) Categorical data analysis, 2nd edn. Wiley, New YorkGoogle Scholar
  2. Blozis SA, Conger KJ, Harring JR (2007) Nonlinear latent curve models for longitudinal data. Int J Behav Dev 31:340–346Google Scholar
  3. Bollen KA, Curran PJ (2006) Latent curve models: a structural equation perspective. Wiley, HobokenGoogle Scholar
  4. Britt CL, Weisburd D (2010) Logistic regression models for categorical outcome variables. In: Piquero AR, Weisburd D (eds) Handbook of quantitative criminology. Springer, New York, pp 649–682Google Scholar
  5. Collins LM, Lanza ST (2010) Latent class and latent transition analysis with applications in the social, behavioral, and health sciences. Wiley, HobokenGoogle Scholar
  6. Curran PJ, Obeidat K, Losardo D (2010) Twelve frequently asked questions about growth curve modeling. J Cogn Dev 2:121–136Google Scholar
  7. Enders CK (2010) Applied missing data analysis. Guildford Press, New YorkGoogle Scholar
  8. Feldman BJ, Masyn KE, Conger RD (2009) New approaches to studying problem behaviors: a comparison of methods for modeling longitudinal, categorical adolescent drinking data. Dev Psychol 3:652–676Google Scholar
  9. Kline RB (2010) Principles and practice of structural equation modeling, 3rd edn. Guilford Press, New YorkGoogle Scholar
  10. Kreuter F, Muthén B (2008) Analyzing criminal trajectory profiles: bridging multilevel and group-based approaches using growth mixture modeling. J Quant Criminol 24:1–31Google Scholar
  11. Liu LC, Hedeker D, Segawa E, Flay BR (2010) Evaluation of longitudinal intervention effects: an example of latent growth mixture models for ordinal drug-use outcomes. J Drug Issues 40:27–43Google Scholar
  12. Liu W, Lynne-Landsman S, Petras H, Masyn K, Ialongo N The evaluation of two first grade preventive interventions on childhood aggression and adolescent marijuana use: a latent transition longitudinal mixture model. Prev Sci (in press)Google Scholar
  13. Long JS (1997) Regression models for categorical and limited dependent variables. Sage, Thousand OaksGoogle Scholar
  14. MacDonald JM, Lattimore PK (2010) Count models in criminology. In: Piquero AR, Weisburd D (eds) Handbook of quantitative criminology. Springer, New York, pp 683–698Google Scholar
  15. Mehta PD, Neale MC, Flay BR (2004) Squeezing interval change from ordinal panel data: latent growth curves with ordinal outcomes. Psychol Methods 9(3):301–333Google Scholar
  16. Muthén BO (1996) Growth modeling with binary responses. In: Eye AV, Clogg C (eds) Categorical variables in developmental research: methods of analysis. Academic, San Diego, pp 37–54Google Scholar
  17. Muthén B (2001) Second-generation structural equation modeling with a combination of categorical and continuous latent variables: new opportunities for latent class/latent growth modeling. In: Collins LM, Sayer A (eds) New methods for the analysis of change. APA, Washington, DC, pp 291–322Google Scholar
  18. Muthén B (2004) Latent variable analysis: growth mixture modeling and related techniques for longitudinal data. In: Kaplan D (ed) Handbook of quantitative methodology for the social sciences. Sage, Newbury Park, pp 345–368Google Scholar
  19. Muthén B, Muthén LK (1998–2011). Mplus (Version 6.12) [Computer software]. Muthén & Muthén, Los AngelesGoogle Scholar
  20. Muthén LK, Muthén B (1998–2011) Mplus user’s guide, 6th edn. Muthén & Muthén, Los AngelesGoogle Scholar
  21. Nagin DS, Land KC (1993) Age, criminal careers, and population heterogeneity: specification and estimation of a nonparametric, mixed Poisson model. Criminology 31:327–362Google Scholar
  22. Nelder J, Wedderburn R (1972) Generalized linear models. J R Stat Soc 135(3):370–384Google Scholar
  23. Petras H, Masyn K (2010) General growth mixture analysis with antecedents and consequences of change. In: Piquero A, Weisburd D (eds) Handbook of quantitative criminology. Springer, New York, pp 69–100Google Scholar
  24. Piquero AR (2008) Taking stock of developmental trajectories of criminal activity over the life course. In: Liberman AM (ed) The long view of crime – a synthesis of longitudinal research. Springer, New York, pp 23–78Google Scholar
  25. Piquero AR, Farrington DP, Blumstein A (2007) Key issues in criminal career research: new analyses of the Cambridge study in delinquent development. Cambridge University Press, CambridgeGoogle Scholar
  26. Skrondal A, Rabe-Hesketh S (2004) Generalized latent variable modeling. Multilevel, longitudinal, and structural equation models. Chapman Hall, LondonGoogle Scholar
  27. Vermunt JK, Tran B, Magidson J (2008) Latent class models in longitudinal research. In: Menard S (ed) Handbook of longitudinal research: design, measurement, and analysis. Elsevier, Burlington, pp 373–385Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Harvard Graduate School of EducationCambridgeUSA
  2. 2.Research and DevelopmentJBS InternationalNorth BethesdaUSA
  3. 3.NORC at the University of ChicagoBethesdaUSA