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Updated: Oct 17, 2025

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
Published on: September 17, 2019
Playing the long game: A multivariate multilevel non-linear growth curve model of long-term effects in a randomized
Patricio Troncoso1, Neil Humphrey2
1Institute for Social Policy, Housing and Equalities Research (I-SPHERE), Heriot-Watt University, Edinburgh Campus, Scotland EH14 4AS, United Kingdom; Manchester Institute of Education, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom.
Abstract:
This cluster randomized controlled trial (RCT) examined the impact of the Good Behavior Game (GBG) on children's developmental trajectories of disruptive behavior, concentration problems, and prosocial behavior from middle childhood (ages 6-7 years) to early adolescence (ages 10-11 years). Seventy-seven schools in England were randomly assigned to intervention and control groups. Allocation was balanced by school size and the proportion of children eligible for free school meals. Children (N = 3084) ages 6-7 years at baseline were the target cohort. Outcome measures, assessed via the Teacher Observation of Child Adaptation Checklist, were taken prior to randomization (baseline - Time 1) and annually for the next 4 years (Time 2 to Time 5). During the 2-year main trial period (Time 1 to Time 3), teachers of this cohort in intervention schools implemented the GBG, whereas their counterparts in the control group continued their usual practice. A multivariate multilevel non-linear growth curve model indicated that the GBG reduced concentration problems over time. In addition, the model also revealed that the intervention improved prosocial behavior among at-risk children (e.g., those with elevated symptoms of conduct problems at Time 1, n = 485). No intervention effects were unequivocally found in relation to disruptive behavior. These findings are discussed in relation to the extant literature, strengths and limitations are noted, and practical and methodological implications are highlighted.
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