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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
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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

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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.

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