Hostname: page-component-6766d58669-mzsfj Total loading time: 0 Render date: 2026-05-24T04:02:57.142Z Has data issue: false hasContentIssue false
  • English
  • Français

Causal Inferences with Group Based Trajectory Models

Published online by Cambridge University Press:  01 January 2025

Amelia M. Haviland  and
Daniel S. Nagin
Amelia M. Haviland*
Affiliation:
Rand Corporation
Daniel S. Nagin
Affiliation:
Carnegie Mellon University
*
Requests for reprints should be sent to Amelia M. Haviland, Associate Statistican, Rand Corporation, Pittsburgh, PA 15213, USA. E-mail: Amelia_Haviland@rand.org
Get access Rights & Permissions [Opens in a new window]

Abstract

A central theme of research on human development and psychopathology is whether a therapeutic intervention or a turning-point event, such as a family break-up, alters the trajectory of the behavior under study. This paper lays out and applies a method for using observational longitudinal data to make more confident causal inferences about the impact of such events on developmental trajectories. The method draws upon two distinct lines of research: work on the use of finite mixture modeling to analyze developmental trajectories and work on propensity scores. The essence of the method is to use the posterior probabilities of trajectory group membership from a finite mixture modeling framework, to create balance on lagged outcomes and other covariates established prior to t for the purpose of inferring the impact of first-time treatment at t on the outcome of interest. The approach is demonstrated with an analysis of the impact of gang membership on violent delinquency based on data from a large longitudinal study conducted in Montreal.

Keywords

Causal inferencefinite mixture modelspropensity scores

Information

Type
Original Paper
Information
Psychometrika , Volume 70 , Issue 3 , September 2005 , pp. 557 - 578
Copyright
Copyright © 2005 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

The research has been supported by the National Science Foundation (NSF) (SES-99113700) and the National Institute of Mental Health (RO1 MH65611-01A2). It also made heavy use of data collected with the support from Québec’s CQRS and FCAR funding agencies, Canada’s NHRDP and SSHRC funding agencies, and the Molson Foundation. We thank Stephen Fienberg, Susan Murphy, Paul Rosenbaum, the editor, Paul De Boeck, and two anonymous reviewers for their insightful suggestions.

References

Cloward, R.A., Ohlin, L.E. (1960). Delinquency and Opportunity: A Theory of Delinquent Gangs. New York: Free Press.Google Scholar
Cohen, A.K. (1955). Delinquent Boys: The Culture of the Gang. Glencoe, IL: Free Press.Google Scholar
Drake, C. (1993). Effects of misspecification of the propensity score on estimators of treatment effect. Biometrics, 49, 1231–1236.CrossRefGoogle Scholar
Elder, G.H. Jr. (1985). Perspectives on the life course. In Elder, G.H. Jr. (Eds.), Life Course Dynamics. Ithaca, NY: Cornell University Press.Google Scholar
Elder, G.H. Jr. (1998). The life course as developmental theory. Child Development, 69, 1–12.CrossRefGoogle ScholarPubMed
Farrington, D.P. (1986). Age and crime. In Tonry, M., Morris, N. (Eds.), Crime and Justice: An Annual Review of Research, Vol. 7. Chicago: University of Chicago Press.Google Scholar
Haviland, A., Nagin, D.S., Rosenbaum, P.R. (2005) Combining group-based trajectory analysis, propensity scores, and matching for causal analysis of the effect of gang membership on violence. Manuscript under preparationGoogle Scholar
Imbens, G. (2004). Nonparametric estimation of average treatment effects under exogeneity: A review. Review of Economics and Statistics, 86, 4–29.CrossRefGoogle Scholar
Jones, B.L., Nagin, D., Roeder, K. (2001). An SAS procedure based on mixture models for estimating developmental trajectories. Sociological Research and Methods, 29, 374–393.CrossRefGoogle Scholar
Korn, E.L., Graubard, B. (1999). Analysis of Health Surveys. Series in Probability and Statistics. New York: Wiley.CrossRefGoogle Scholar
Lacourse, E., Nagin, D., Vitaro, F., Claes, M., Tremblay, R.E. (2003). Developmental trajectories of boys delinquent group membership and facilitation of violent behaviors during adolescence. Development and Psychopathology, 15, 183–197.CrossRefGoogle ScholarPubMed
Leon, A.C., Hedeker, D. (2005). A mixed-effects quintile-stratified propensity adjustment for effectiveness analyses of ordered categorical doses. Statistics in Medicine, 24, 647–658.CrossRefGoogle ScholarPubMed
Leon, A.C., Mueller, T.I., Solomon, D.A., Keller, M.B. (2001). A dynamic adaptation of the propensity score adjustment for effectiveness analyses of ordinal doses of treatment. Statistics in Medicine, 20, 1487–1498.CrossRefGoogle ScholarPubMed
Li, Y.P., Propert, K.J., Rosenbaum, P.R. (2001). Balanced risk set matching. Journal of the American Statistical Association, 96, 870–882.CrossRefGoogle Scholar
Muthén, B.O. (2001). Second-generation structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class/latent curve modeling. In Sayers, A., Collins, L. (Eds.), New Methods for the Analysis of Change. Washington, DC: American Psychological Association.Google Scholar
Muthén, B., Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55, 463–469.CrossRefGoogle ScholarPubMed
Nagin, D.S. (1999). Analyzing developmental trajectories: Semi-parametric, group-based approach. Psychological Methods, 4, 39–177.CrossRefGoogle Scholar
Nagin, D.S. (2005). Group-Based Modeling of Development. Cambridge, MA: Harvard University Press.CrossRefGoogle Scholar
Nagin, D., Farrington, D., Moffitt, T. (1995). Life-course trajectories of different types of offenders. Criminology, 33, 111–139.CrossRefGoogle Scholar
Nagin, D.S., Land, K.C. (1993). Age, criminal careers, and population heterogeneity: Specification and estimation of a nonparametric, mixed Poisson model. Criminology, 31, 327–362.CrossRefGoogle Scholar
Pogarsky, G., Lizotte, A.J., Thornberry, T.P. (2003). The delinquency of children born to young mothers: Results from the Rochester Youth Development Study. Criminology, 41, 101–138.CrossRefGoogle Scholar
Robins, J.M. (1987). A graphical approach to the identification and estimation of causal parameters in mortality studies with sustained exposure periods. Journal of Chronic Disease, 40 Suppl. 2139S–161S.CrossRefGoogle Scholar
Robins, J., Greenland, S., Hu, F. (1999). Estimation of the causal effect of time-varying exposure on the marginal mean of a repeated binary outcome. Journal of the American Statistical Association, 94, 687–770.CrossRefGoogle Scholar
Roeder, K., Lynch, K., Nagin, D. (1999). Modeling uncertainty in latent class membership: A case study in criminology. Journal of the American Statistical Association, 94, 766–776.CrossRefGoogle Scholar
Rosenbaum, P.R. (2002). Observational Studies (2nd ed.). New York: Springer-Verlag.CrossRefGoogle Scholar
Rosenbaum, P., Rubin, D. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70, 41–55.CrossRefGoogle Scholar
Rosenfeld, R., Bray, T.E., Egley, A. (1994). Facilitating violence: A comparison of gang-motivated, gang-affiliated, and non-gang youth homicides. Journal of Quantitative Criminology, 15, 495–516.CrossRefGoogle Scholar
Rubin, D.B. (1979). Using multivariate matched sampling and regression adjustment to control bias in observational studies. Journal of the American Statistical Association, 74(366), 318–328.Google Scholar
Short, J.F. Jr., Stodtbeck, F.L. (1965). Group Process and Gang Delinquency. Chicago: University of Chicago Press.Google Scholar
Thornberry, T., Krohn, M., Lizotte, A., Smith, C., Tobin, K. (2003). Gangs and Delinquency in Developmental Perspective. Cambridge, UK: Cambridge University Press.Google Scholar
Tremblay, R.E., Desmarais-Gervais, L., Gagnon, C., Charlebois, P. (1987). The preschool behavior questionnaire: Stability of its factor structure between culture, sexes, ages, and socioeconomic classes. International Journal of Behavioral Development, 10, 467–484.CrossRefGoogle Scholar
Wasserman, L. (1999). Comment on ‘Estimation of the causal effect of time-varying exposure on the marginal mean of a repeated binary outcome’. Journal of the American Statistical Association, 94, 704–706.Google Scholar