Using group-based trajectory modeling in conjunction with propensity scores to improve balance

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.

Daniel S. NaginEmail:

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Amelia Haviland   (Ph.D., Statistics and Public Policy, Carnegie Mellon University), is an Associate Statistician at RAND Corporation. Her research focuses on causal analysis with observational data and analysis of longitudinal and complex survey data. Dr. Haviland has published articles on delinquency outcomes related to gang membership and employment, economic outcomes related to racial and gender discrimination, and health outcomes related to gender and heart disease. She currently works on applications in criminology, health and health economics. Daniel S. Nagin   is Teresa and H. John Heinz III Professor of Public Policy and Statistics at Carnegie Mellon University. His research interests include the developmental course of violent and other criminal behavior, the preventive effects of criminal and non-criminal sanctions, and statistical methods for the analysis of longitudinal data. He is the author of Group-Based Models of Development (Harvard University Press, 2005).