Participants were students at three urban public middle schools in the southeastern United States who participated in a six-year study (author reference) to evaluate school-level implementation of the Olweus Bullying Prevention Program (Olweus & Limber, 2010). The majority of students at these schools were African American adolescents from low-income families, most of whom (i.e., 74% to 85%) were eligible for the federal free lunch program. The evaluation study involved a multiple baseline design that used randomization to determine the order and timing of initiating intervention activities in each school. Based on this randomization schedule, the intervention was implemented at one of the schools beginning in the project’s second year, at a second school beginning in the project’s third year, and at a third school beginning in the project’s sixth year. About 630 students were randomly selected from the sixth, seventh, and eighth grade rosters at each school in the fall of 2010. During each of the five subsequent school years, a new random sample of sixth graders was recruited along with a random sample of seventh and eighth graders to replace those who left the school (15%) or withdrew from the study (4%) before completing the eighth grade. Active parental permission and student assent were obtained from approximately 80% of all eligible students. Data were collected every three months in the fall (late October through early November), winter (late January through early February), spring (late April through early May), and in the summer between school years (late July through early September). The evaluation study used a planned missing-data design (Graham, Taylor, & Cumsille, 2001) such that each participant was randomly assigned to complete two of four waves of data during each year they participated.

For the present study, we created a cross-sectional dataset by randomly sampling one wave from each participant using an algorithm that provided about the same number of participants from each grade and time of year. The final sample of 2,118 students included 703 to 709 students from each grade. These represented 98% of all those from whom parental consent and student assent were obtained. Their mean ages were 11.7 (SD = 0.66), 12.7 (SD = 0.69), and 13.8 (SD = 0.70), for sixth, seventh, and eighth graders, respectively. The sample was 52% female. Seventeen percent of the sample identified their ethnicity as Hispanic or Latino. Students were asked to identify their race by endorsing one or more categories. The majority (81%) self-identified as Black or African American. This included 73% of the total sample who endorsed it as the sole category and 8% who endorsed it as one of several categories. The remainder of the sample included 5% who identified themselves as White, 10% who did not endorse any racial category, and 3% who endorsed one of the remaining categories. Most (i.e., 91%) of those who did not endorse any of the racial categories were Hispanic or Latino. Single mother was the most frequently reported family structure (41%), 25% lived with both biological parents, 21% lived with a parent and stepparent, 6% lived with a relative without a parent, and 3% with a father without a mother or stepmother. More than half (58%) completed the measures during a year when the Olweus Bullying Prevention Program was being implemented at their school.

Research staff described the study to potential participants and gave them student assent and parental consent forms to review with their parents. Staff followed up with parents via phone and home visits as needed. Students received a $5 gift card for returning consent forms whether or not they participated. Research staff informed participants of their rights as research participants, including the option to decline or limit participation at any time. Participants received a $10 gift certificate for completing any portion of the survey. Research assistants administered the measures using a computer-aided personal interview to small groups of students in the schools during the school years and in individual student’s homes or community locations during the summers. Core education teachers completed ratings of each student’s behavior during the three waves of data collection that took place during the school year. The University’s Institutional Review Board reviewed and approved all procedures.

The Beliefs About Fighting Scale (BAFS; Farrell et al. 2012) instructs adolescents to rate their level of agreement with 23 items representing general beliefs about the use of aggression and the appropriateness of using fighting or aggression in various contexts (see Table 1). Items were written to represent four themes that emerged from a qualitative study in which adolescents described beliefs that influenced whether they would use physical aggression or a nonviolent response in situations that involved conflicts with peers (Farrell et al., 2008). Additional items were based on a review of other measures of adolescents’ beliefs about aggression. Respondents rated each item on a 4-point anchored scale: 1 - Strongly disagree, 2 - Disagree, 3 - Agree, 4 - Strongly agree. As previously noted, participants were given the option of skipping items. Participants completed 94.5% of the total possible responses.

We conducted confirmatory factor analyses to compare competing models of the structure of the BAFS. We conducted all analyses in Mplus 8 using weighted least squares mean- and variance-adjusted estimators (WLSMV) that treated scores on each item as ordered categorical variables. Although WLSMV makes use of all available data, it uses a pairwise present approach, which is more restrictive than maximum likelihood estimation. Unfortunately, maximum likelihood estimators are computationally intensive, particularly with models involving more than three or four factors and with large sample sizes (Muthén & Muthén, 2012). For this reason, WLSMV is often the best option for analysis of categorical variables (Brown, 2006). This analysis is comparable to a graded response item-response theory model. We compared competing models based on the difference test function in Mplus (Muthén & Asparouhov, 2006) where applicable, and measures of overall model fit. We used Hu and Bentler’s (1999) recommendation as general guidelines for evaluating model fit. We considered models to have a good fit based on cutoffs of close to .95 or higher for the comparative fit index (CFI) and Tucker-Lewis fit index (TLI), and close to .06 or lower for the root mean square error of approximation (RMSEA). We conducted multiple group analyses to test for measurement invariance across sex, grade, and intervention status. This involved comparing an unconstrained model that specified the same structure for each group (i.e., configural invariance) to a model that constrained corresponding factor loadings and thresholds for each factor to the same values across groups (i.e., scalar or strong factorial invariance). We followed recommendations by Cheung and Rensvold (2014) who argued that a change in the CFI (i.e., ΔCFI) of less than .01 is a more appropriate test of model invariance than the chi-squared difference test because the latter may detect very minor differences in fit in large samples such as in the present study.

A final set of analyses examined relations between the BAFS factors and student and teacher measures of physical aggression, victimization, and nonviolent behavior. Analyses were based on structural equation models that included latent variables representing BAFS factors and concurrent measures based on student or teacher report. We first examined correlations with the BAFS factors. We then used latent variable regression models to determine the extent to which each BAFS factor was uniquely related to the concurrent measures controlling for sex, grade, and intervention status. We evaluated statistical significance based on p < .05.

Our initial analysis evaluated three models of the structure of the BAFS: (a) the hypothesized four-factor model; (b) a two-factor model with separate factors representing beliefs against fighting and beliefs supporting fighting; and (c) a single-factor model. Although the four-factor model fit the data significantly better than the two competing models, its overall fit was marginal (see Model 1 in Table 2). We therefore conducted exploratory analyses to identify items that may not have fit well within the four-factor structure. We investigated this by testing an exploratory structural equation model (Asparouhov & Muthen, 2009; Marsh et al., 2009) that allowed each item to load on all of the factors and used a target rotation based on the hypothesized four-factor structure. Within this model all of the items had their strongest loading on their hypothesized factor (i.e., λs = .47 to .91). However, five of the items had cross-loadings of .30 or higher on a second factor (see Table S1). These items also had the lowest loadings on their hypothesized factor (i.e., λs = .47 to .64).

Based on these findings we re-ran the three competing models after excluding one item from each factor that showed the poorest discrimination in the exploratory analyses. The four-factor model again fit the data significantly better than the two competing models, and had a more acceptable overall fit (see Model 5 in Table 2). Standardized loadings for this model were all significant, ranging from .72 to .86, with an average value of .79 (see Table 1). Within this model, correlations among the four factors were generally as expected, with significant positive correlations among the three factors representing beliefs supporting aggression (rs = .43 to .73, see Table 3). As expected, the Beliefs Against Fighting factor was negatively correlated with the Beliefs Supporting Proactive Aggression factor (r = −.16). However, it was not significantly correlated with the Beliefs Supporting Reactive Aggression factor, and was positively correlated with the Fighting is Sometimes Necessary factor (r = .32). The Beliefs Supporting Reactive Aggression factor was highly correlated with the Fighting is Sometimes Necessary and Beliefs Supporting Proactive Aggression factors (rs = .71 and .60, respectively).

We assessed the local fit of the four-factor model by examining correlation residuals that represented the difference between the correlations obtained for the sample and correlations estimated by the model (Goodboy & Kline, 2017). Residuals ranged from .00 to .26 in absolute value (see Table S2). Of the 171 residuals, 24 had absolute values that exceeded .10, 6 exceeded .15, and 2 exceeded .20. Goodboy and Kline (2017) suggested that values exceeding .10 may indicate poor prediction for a pair of variables, but noted that there is no “magic number” of absolute correlation residuals exceeding .10 that would invalidate a model. Within the current study the pattern of residuals suggested that the model did the poorest job of accounting for relations between items in the Fighting is Sometimes Necessary factor and those in the other three factors. Residuals for these correlations included 17 of the 24 values exceeding .10.

We conducted further analyses of the four-factor model using multiple group models to determine the extent to which there was support for measurement invariance across sex, grade, and intervention status (i.e., whether they completed measures while at a school where the intervention was being implemented). Models specifying configural invariance across sex, grades, and intervention status all fit the data well, as did models based on separate analyses of each group (see models 8, 10, and 12 in Table 2). Imposing strong measurement invariance resulted in a statistically significant decrease in model fit based on the difference test for sex (p = .003), but not for grade or intervention status (see Table 2). However, in no case did imposing strong measurement invariance result in a reduction in model fit based on comparison of the RMSEA, CFI, and TLI as measured to two decimal places. In fact, in most cases the more parsimonious models imposing measurement invariance resulted in improvements in fit indices. The only decrease in the CFI occurred for sex, but the decrease (i.e., .001) fell well below the cutoff of .01 recommended by Cheung and Rensvold’s (2014).

Establishing strong measurement invariance made it possible to compare mean scores across groups. We estimated effect sizes for mean comparisons by calculating Cohen’s d based on the pooled standard deviations from each group. As hypothesized, girls endorsed stronger beliefs against the use of aggression than did boys (d = 0.34, p < .001; see Table 3). However, there were no significant sex differences on the other three BAFS factors (ds = −0.04 to 0.02). Consistent with our hypotheses, compared with sixth grade students, seventh and eighth grade students were less likely to endorse beliefs against fighting and more likely to endorse beliefs that fighting is sometimes necessary and beliefs supporting both reactive and proactive aggression (ds = .29 to .53). However, mean comparisons did not reveal any significant differences between seventh and eighth grade students at p < .05.

We conducted a series of analyses to examine relations between the BAFS factors and concurrent measures of aggression, victimization, and nonviolent behavior. Models included the four BAFS factors, and latent variables representing factors based on items from the adolescent and teacher report measures. By convention, all latent variables were constrained to have a mean of 0 and SD of 1.00. Separate models were tested for student reports on the PBFS-AR (N = 2,118), student ratings on the Effective Nonviolent Intentions scale (N = 1,353), and teacher ratings on the PBFS-TR (N = 1,576). The sample size was lower for the Effective Nonviolent Intentions Scale because it was not administered during the last two years of the project, and for the PBFS-TR because data were not collected from teachers during the summer waves. We also ran a model to evaluate correlations between the PBFS-AR, Effective Nonviolent Behavior Scale, and PBFS-TR. This revealed small, but significant cross-informant correlations between student and teacher measures of physical aggression scales (r = .23, p < .001), victimization (r = .09, p <.019), and effective nonviolent behavior (r = .18, p < .001).

The measurement models used to estimate correlations between the BAFS and student and teacher ratings on the PBFS fit the data well, with a somewhat poorer fit for the analysis of the intentions for nonviolent behavior scale (see models 1 to 3 in Table 4). Figure 1 provides point estimates and 95% confidence intervals for correlations between the four BAFS factors and other measures. Within this figure, a different marker and line represent each BAFS factor. The measures they are correlated with are depicted on the horizontal axis with student and teacher measures on the left and right sides of the figure, respectively. These correlations are also reported in Table S3. As expected, whereas the PBFS-AR Physical Aggression factor was negatively correlated with the Beliefs Against Fighting factor, it was positively correlated with all three factors supporting the use of aggression (rs = .32 to .41). Adolescents’ report of their frequency of experiencing victimization was positively correlated with all four BAFS factors (rs = .11 to .26). However, counter to our hypothesis, this correlation was not stronger for beliefs supporting reactive aggression than for beliefs supporting proactive aggression. Adolescents’ report of their intention to use nonviolent responses in problem situations was positively correlated with beliefs against fighting (r = .61), was not significantly correlated with beliefs that fighting is sometimes necessary (r = .04), and was negatively correlated with beliefs supporting the use of reactive and proactive aggression (rs = −.23 and −.33, respectively). As would be expected, there were weaker associations between the BAFS factors and teacher ratings of student behavior (see right half of Figure 1). The strongest associations were for the BAFS Beliefs Against Fighting factor, which was negatively correlated with teacher ratings of physical aggression and physical victimization (rs = −.26 and −.23, respectively), and positively correlated with the PBFS-TR Effective Nonviolent Behavior factor (r = .18). We found small significant correlations between the Beliefs Supporting Proactive Aggression factor and teacher ratings of physical aggression and physical victimization. The remaining correlations were less than .10 in absolute value with the exception of a negative correlation between beliefs supporting reactive aggression and teacher ratings of nonviolent behavior (r = −.11).

We next examined the relations between each of the BAFS factors and adolescent and teacher ratings of physical aggression, victimization, and nonviolent behavior within a regression model that included all four BAFS factors and controlled for sex, grade, and intervention status (see Table 4 for fit indices and Table 5 for regression coefficients). The four BAFS factors accounted for 22.4% of the variance in adolescents’ reports of their frequency of physical aggression after controlling for the covariates. Each of the factors except for Beliefs Supporting Reactive Aggression accounted for a unique portion of the variance in physical aggression with coefficients in the expected direction. The BAFS factors accounted for 11.7% of the variance in adolescent reports of their frequency of victimization. Within this model, the Beliefs That Fighting Is Sometimes Necessary and Beliefs Supporting Proactive Aggression factors were positively related to the frequency of victimization. In contrast, the Beliefs Supporting Reactive Aggression factor was negatively related to the frequency of victimization and The Beliefs Against Fighting factor was not related to victimization. The BAFS factors accounted for 38.4% of the variance in student reports of their intentions to use nonviolent strategies in conflict situations. The majority of this variance was accounted for by the Beliefs Against Fighting factor, with significant but smaller contributions from the Beliefs Supporting Reactive Aggression and Beliefs Supporting Proactive Aggression factors. The Fighting is Sometimes Necessary factor was not related to nonviolent intentions after controlling for the other BAFS factors.

The four BAFS factors accounted for 4.5% to 6.4% of the variance in the teacher ratings of physical aggression, physical victimization, and nonviolent behavior (see Table 4 for fit indices and Table 5 for regression coefficients). The Beliefs Against Fighting factor emerged as a significant predictor in each case and in the expected direction with negative associations with physical aggression and victimization, and positive relations with effective nonviolent behavior. It was the only one of the four BAFS factors uniquely related to teacher ratings of students’ frequency of physical aggression. The Fighting is Sometimes Necessary factor did not emerge as a significant predictor of any of the three teacher report variables. The Beliefs Supporting Reactive Aggression factor was negatively associated with the frequency of nonviolent behavior, and the Beliefs Supporting Proactive Aggression factor was negatively associated with teacher ratings of the frequency of physical victimization.

The current study had several limitations that merit consideration. We examined cross-sectional associations between beliefs and measures of aggression, victimization, and nonviolent behavior. This addressed our objectives, which were to evaluate the structure of the BAFS and its concurrent validity with measures of related constructs. However, the cross-sectional design does not clarify whether beliefs are a cause or consequence of adolescents’ behavior, or whether the direction of these effects vary across dimensions. For example, the notion that adolescents’ beliefs supporting reactive aggression will increase their frequency of aggression is consistent with social-cognitive theory. At the same time, it is quite plausible that beliefs that fighting is sometimes necessary may emerge as a consequence of victimization experiences. Bidirectional effects are also plausible as suggested by ecological models of development (Bronfenbrenner, 1979). Further research examining reciprocal longitudinal relations between beliefs and behavior is needed to clarify the direction of these effects and to explore the underlying mechanisms by which beliefs influence adolescents’ behavior. Moreover, our analysis of relations between beliefs and measures of adolescents’ frequency of aggression and victimization may not do full justice to the complexity of these relations. There is growing evidence supporting distinct differences in patterns of relations between aggression and victimization such that youth who are both aggressive and victimized may be qualitatively different and hold different beliefs compared with those who are only aggressive or only victimized (e.g., Bettencourt & Farrell, 2013). .

Although we evaluated the concurrent validity of the BAFS based on adolescent and teacher ratings, both are imperfect criteria. The strong relations between adolescents’ reports of their beliefs and their behavior (i.e., R² change of .12 to .38) may in part reflect shared method variance. We attempted to address this by examining relations with teacher ratings, but these also have limitations. In particular, they are based on a limited sample of behavior that reflects adolescents’ behavior not just at school, but specifically in the presence of teachers. Adolescents are far more likely to engage in nonviolent behavior in these situations. This is reflected in the low correlations we found between student and teacher measures (i.e., rs = .09 to .23). It is therefore not surprising that adolescents’ reports of their beliefs were not strongly related to teacher ratings of adolescents’ behavior (R² change of .04 to .06). Differences in findings may have also been influenced by the fact that whereas the teacher report measure specifically focused on physical victimization, the student measure assessed multiple forms of victimization.

Our sample consisted of students in middle schools that served a predominantly African American population of students, many of whom came from single-parent families in urban communities with high rates of poverty and crime. The BAFS was designed to provide a relevant measure of beliefs among this population and was based on qualitative studies that were conducted with similar populations of adolescents with input from others within the community (Farrell et al., 2008). Although this made our sample relevant to evaluating this measure, it remains to be seen whether this measure would be appropriate for use with other populations of adolescents.

This study underscored the importance of developing measures of adolescents’ beliefs that reflect more than simply supporting or not supporting the use of aggression. Adolescents’ beliefs reflect their increased cognitive ability and the complexity of contingencies in their environments and previous experiences. The results of this study suggest that the BAFS is a promising measure of the nuanced array of beliefs that urban adolescents hold about fighting (see supplement for final measure). However, more research is needed to: (a) clarify the contextual factors that activate adolescent’s beliefs about fighting, particularly among those youth who also believe that fighting is wrong; (b) examine longitudinal changes in adolescents beliefs about fighting over the course of middle school and into high school; and (c) disentangle the complex relations between beliefs about fighting and behaviors over time among urban adolescents. Social-cognitive interventions that target beliefs and attitudes will likely need to address the multidimensional nature of adolescents’ beliefs about aggression to achieve maximum effectiveness. That is, rather than simply having global discussions about the acceptability or effectiveness of aggression, it is important to assess adolescents’ beliefs about aggression under varying circumstances and attempt to address those beliefs. There is likely to be dissonance between the goals of the program and adolescents’ beliefs, which are likely rooted in their experiences and the norms of their current environment. Incorporating frank conversations about the nuances of adolescents’ beliefs about aggression will likely increase the ecological validity of interventions and the legitimacy of program facilitators in the perceptions of adolescents.