Mixture Regression Analysis: The Effects of Anti-Bullying Interventions on Bullying Behavior

• In Event: The Utility of Mixture Modeling to Understanding Heterogeneous Effects in Educational Studies

Abstract

Over the last two decades, bullying researchers and educational practitioners have made important progress in reducing the level of bullying in schools and classrooms. Although it is good news that anti-bullying intervention programs are effective, the benefits of these programs are modest overall and vary substantially (see Gaffney et al., 2021). Program results are limited because anti-bullying intervention programs may not influence all individuals equally. Further advancing anti-bullying programs in critical ways will require researchers to move beyond examining the overall effectiveness of intervention programs to focus on which subgroups of students benefit from these programs and which might not. The current study builds on the prior research by considering bullies; specifically, the first goal is to identify subtypes of bullies based on peer status (i.e., bullying, popularity, likeness, rejection, victimization) and the second goal is to examine which characteristics of bullies are associated with changes in bullying behavior after participation in an anti-bullying intervention program.
Participants were a subsample of the KiVa anti-bullying program with a large randomized controlled trial designed, which includes approximately 8,000 students from 77 Finnish elementary schools. The data used in this study were collected at two time points: before program implementation, at the end of the school year in May 2007 (T1; pretest) and one year after implementation, at the end of the subsequent school year in May 2008 (T2; posttest). All measures were students’ unlimited peer nominations by classroom level.
The current study proceeded in three analytical steps. First, overall bullies were identified based on a cut-off score. Because the rate of bullying in classrooms is rather low, we adopted a relatively lenient cut-off criterion of 0.5. In the second step, using latent profile analysis, the overall bully was disaggregated as popular bully (26 %), pure bully (58 %), and victimized bully (16 %) (see Figure 1). In the third step, to investigate the effect of the KiVa intervention effect on bullying behavior across the three bully groups, we conducted mixture regression (see Table 1). The bullying behavior of only pure bullies in the KiVa intervention program decreased significantly from T1 to T2 (= -0.20, SE = 0.10, p < 0.05).
Most prior analyses of the effectiveness of anti-bullying interventions have used linear regression models. However, this method is limited to estimating the average effects of predictors in a population. Our mixture regression model’s results showed clearer when compared to a conventional regression analysis. The conventional regression model, which considered the overall sample with the same dependent and independent variables, shows that the coefficients are similar to the results of pure bullies and that the interaction effect of the KiVa intervention was significantly related to bullying behavior at T2 (= -0.12, SE = 0.07, p < 0.05). Taken together, this pattern of results indicates that while conventional regression analysis suggests that the KiVa intervention reduces bullying in the overall bully group, mixture regression models reveal that the KiVa intervention reduces bullying behavior among pure bullies but not among popular bullies or victimized bullies.

Authors

• Hye-Young Yun, University of California - Los Angeles

• Karen L. Nylund-Gibson, University of California - Santa Barbara

• Christina Salmivalli