Abstract
This paper builds upon two prior papers by Haviland and Nagin (Psychometrika 70:1–22, 2005) and Haviland, Nagin, and Rosenbaum (Working paper, 2006) that attempt to bring the key attributes of an experiment to the analysis of non-experimental longitudinal data. Using a case study of the facilitation effect of gang membership on violence, it systematically examines the contribution of group-based trajectory modeling to the achievement of covariate balance in observational data. In this case study, inclusion of the posterior probabilities of group membership (PPGM), from a model on the pre-treatment measures of the outcome variable, created closer balance on these key covariates than did analyses that did not include them. Still closer balance was obtained on these key covariates by stratifying the analysis by trajectory group. This stratification was achieved by fitting separate propensity score models and matching gang joiners to gang abstainers within trajectory group. In addition, we demonstrated that further balance could be obtained on additional covariates by including PPGM from a model on pre-treatment longitudinal data of these covariates. While this case study is only one empirical example, we believe that it provides useful empirical evidence on the value of performing within trajectory group causal inference in observational longitudinal data and on the use of the PPGM in achieving balance in propensity score-based causal inference.
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Notes
For discussion of the rationale for estimating the trajectory model over this age period see Haviland and Nagin (2005).
The original version of the question, as asked in French, was “Au cours des 12 derniers mois, as-tu fais partie d’un groupe de jeunes (gang) qui fait des mauvais coups?”
Variable matching is one of several possible methods for using propensity scores to create balanced treatment and control groups. It is not clear that other possible methods such as stratification and weighting would lead to different conclusions about the effect of trajectory group modeling on achieving balance, but that has not yet been determined.
The means for the controls are calculated by first calculating the mean of the matched controls for each joiner and then taking the average of these means.
In this case, due to the relatively small sample sizes, this criterion is more stringent than traditional significance levels for a t-test.
This match used the same variable matching rates for trajectory group 1 but increased the rate for trajectory group 2 to between 1 and 7 with an average of 5. Many versions of the stage 3 match were attempted before we settled on the final variable match rate. The results were comparable when the larger and smaller number of matches were used in group 2. At stage 4, the larger number of matches resulted in a more favorable match.
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Acknowledgments
The research was 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 of Québec’s CQRS and FCAR funding agencies, Canada’s NHRDP and SSHRC funding agencies, and the Molson Foundation.
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Haviland, A.M., Nagin, D.S. Using group-based trajectory modeling in conjunction with propensity scores to improve balance. J Exp Criminol 3, 65–82 (2007). https://doi.org/10.1007/s11292-007-9023-3
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DOI: https://doi.org/10.1007/s11292-007-9023-3