Academic journal article School Psychology Review

Studying Change in Dominance and Bullying with Linear Mixed Models

Academic journal article School Psychology Review

Studying Change in Dominance and Bullying with Linear Mixed Models

Article excerpt

Abstract. It is argued that studies of early adolescent peer victimization and bullying should be longitudinal because of the dynamism of this developmental period. Traditional methods for analyzing longitudinal data axe inadequate because of the strict data requirements and inflexibility of models. A better alternative is linear mixed models (LMMs) for repeated measures. LMMs have less restrictive data requirements and much flexibility in the type of models that may be specified. Using empirical data from middle school students, it is shown how LMMs can be used to examine three major aspects of change in dominance and bullying. The first is unconditional change, which involves treating the sample as an entire group and modeling the mean trajectories of dominance and bullying over time. The second is conditional change, which involves examining gender differences in mean change of dominance and bullying over time. The third is dynamic change, which involves examining the longitudinal covariation between bullying and dominance controlling for trajectory effects. The algebra of the LMMs is presented from a multilevel perspective assuming a random effects model. The results are discussed in terms of dominance theory and highlight the advantages of the LMM approach to data analysis in the study of adolescent peer victimization and bullying.


The study of bullying and victimization among children has increased across the past decade (see Pellegrini, 2002, for a review). This increase is a response to theoretical issues, such as the debate over varying functions of aggression across the life span, and practical problems, such as the increased public attention to salient acts of school violence. From a theoretical perspective, adolescence is an especially interesting period to study because of its dynamism. Unfortunately, many studies of adolescence have used contemporaneous designs that do not explicitly address change. Our orientation stresses the role of longitudinal research designs to study the ways in which bullying develops across the period of early adolescence.

Adolescence is a developmental period marked by numerous changes. Physical changes occur with the onset of puberty in the form of rapid body growth and rapidly developing secondary sexual characteristics. Ecological changes occur as young people transition from primary to middle school. Given this dynamism, the repeated measurements of longitudinal designs are most appropriate for studying bullying and victimization in early adolescence. Longitudinal designs yield all the information of cross-sectional designs but are uniquely informative about change in bullying and victimization constructs across time.

The most common method of longitudinal analysis is repeated measures multivariate analysis of variance (RM-MANOVA). RM-MANOVA has some weaknesses that make it a suboptimal method for analyzing longitudinal data. A better alternative is linear mixed models (LMMs). This article focuses on the use of LMMs in addressing questions of change in dominance and bullying. Data collected on the same individuals at 4 data points of the first 2 years of middle school (sixth and seventh grades) are analyzed. We show how LMMs can be used to (a) model unconditional linear and nonlinear change in dominance and bullying over time, (b) examine gender group differences in dominance and bullying change trajectories (i.e., conditional change), and (c) examine the longitudinal covariation of bullying and dominance (controlling for trajectory).

Dominance Theory and Expected Results

From a group-level perspective, social dominance is a relational variable that orders individuals in a hierarchy according to their access to resources (Pellegrini, 2002; Pellegrini & Bartini, 2001; Pellegrini & Long, 2003; Strayer, 1980). Specifically, adolescent male peer groups are typified by dominance hierarchies. Dominance, or group leadership, is established when groups are newly forming (e. …

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