A multilevel p2 model with covariates for the analysis of binary bully-victim network data in multiple classrooms

Many studies have been aimed at defining the exact nature of bullying, identifying bullies and their victims in school classes, investigating the personal and developmental characteristics of bullies and victims, and evaluating intervention programs to prevent bullying (see, e.g. Espelage & Swearer, 2003). Children have different roles in bullying (Schwartz, 2000), and some pairs of children lead to more bullying than others (Coie et al., 1999). Relatively little is known about the dyadic properties of bullies and victims (Rodkin & Berger, in press). Recently, a dual perspective theory of bullying was proposed, focusing on the dyadic nature of the bully-victim relationship (R. Veenstra et al., 2007). This theory is tested on pre-adolescent data from TRAILS (Tracking Adolescents’ Individual Lives Survey). TRAILS is designed to chart and explain the development of mental health and social development from preadolescence into adulthood (De Winter et al., 2005; Oldehinkel, Hartman, De Winter, Veenstra, & Ormel, 2004). Students were asked to report about several of their ties with classmates. This round robin design yields in principle two observations for each relationship between two children A and B, one from the perspective of child A (the nominator or ‘sender’), reporting whether or not s/he bullies child B (the target or ‘receiver’), and vice versa. These two reports may not always coincide and are less likely to be in agreement for a bullying tie than for a friendship tie. The set of dyadic data collected in a closed group forms a social network. Many methods and models have been proposed for social network analysis (see Wasserman & Faust, 1994). For a review on the intricacies of dyadic designs and dyadic data analysis, see Kenny, Kashy, and Cook (2006). We use a multilevel p2 model (Zijlstra, Van Duijn, & Snijders, 2006) to analyze bully network data from 54 classes collected in the TRAILS study. This model takes into account the dependent nature of the data and employs the characteristics of sender and receiver individually and as a dyad. Moreover, class characteristics can be used to explain differences per classroom; for instance, between prevalence rates of bullying in school classes. We follow the dual perspective theory as laid out by Veenstra et al. (2007) but slightly modify the covariates used in the analysis. In the next section we start with the definition and interpretation of the simple p2 model, followed by the multilevel p2 model, and its relation to other models for social network data. In Section 3, we present the data and theory to be tested. After a section introducing the interpretation of p2 model results, we present the results obtained for the dual perspective theory. The final section summarizes and discusses the findings.