Causal Inferences in Finite Mixture-based Trajectory Models, with Application to the Impact of Gang Membership on Violent Delinquency

• Activity Number: 199
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
• Sponsor: Social Statistics Section
• Author(s): Amelia Haviland*+ and Daniel Nagin
• Companies: Carnegie Mellon University and Carnegie Mellon University
• Keywords: causal inference ; finite mixture models ; propensity scores ; kernel estimation ; gangs and violence

Abstract

A developmental trajectory describes the course of a behavior over age or time. A turning point describes some event which alters that trajectory. We build upon recent advances in identifying trajectory groups based on finite mixture modeling to devise improved methods for drawing causal inferences about the impact of turning point events. Based on the work of Rosenbaum and Rubin, we draw connections between trajectory groups and both balancing scores and kernel estimation. This allows us to identify the empirical conditions under which trajectory probabilities qualify as balancing scores. Where the trajectory probabilities do qualify as balancing scores, we show how they can be used as weights in a kernel matching procedure to obtain treatment effects. We demonstrate this approach with an analysis of the impact of gang membership on violent delinquency in a large Canadian longitudinal dataset.