The database used comes from the Estrategia evaluativa integral UEE 2016–2 (Integrated assessment strategy UEE 2016–2 of the State of Baja California; Rodríguez-Macías et al., 2017) study applied on 15,861 Mexican students from the three grades of low secondary education (ISCED level 2; UNESCO Institute for Statistics, 2012). Following a selection process, 851 cases were removed due to missing values, reading errors and response patterns. Subsequently, an additional 1,621 cases that presented outliers in the ERECVE General index (GI) were eliminated as well (scores lower than 25 and higher than 43). In total, the results from 13,389 cases were considered for this study. The distribution of students according to gender was 6,935 females (51.8%) and 6,454 males (48.8%); females had a mean age of 13.08 years (SD = 0.96) and males 13.09 years (SD = 0.98); the mean age for first graders was 12.05 (SD = 0.98), for second graders was 13.08 (SD = 0.95) and for third graders was 14.11 (SD = 0.96). The distribution, according to the three school grades of low secondary education, was 4,632 students from the first grade (34.60%), 4,317 from the second grade (32.24%), and 4,440 from the third grade (33.16%).

The ERECVE is a self-reporting instrument devised by Rodríguez-Macías et al. (2017) for the Integrated assessment strategy UEE 2016–2 of the State of Baja California, which encompasses categories established according to the approach of school bullying as a group violence process (Olweus, 1993; Salmivalli et al., 1996) and to the PRQ created by Salmivalli et al. (1996). The ERECVE consisted of 19 items with five ordinal response options (never, rarely, monthly, weekly, and daily) in which the student indicated how often they experienced various events related to roles of participation in bullying and school violence. For the statistical analyses on the data, the response options ranged from 1 for never to 5 for daily. These items were distributed into five subscales: victim’s role, defender or conciliator’s role, sole bully’s role, social bully’s role and bystander’s role. Sánchez-Ariza (2019) reported that the ERECVE shows acceptable reliability (α = 0.71, ρ = 0.79, ω = 0.77) and total item-score correlation indices (Rpbis = 0.28). Likewise, an acceptable fit was obtained for the original five-factor model (χ ² = 34,686.86, df = 171, p < 0.00, CFI = 0.91, TLI = 0.89, RMSEA = 0.048, IC = 95% [0.047, 0.050]), SRMR = 0.38). The subscales and the items of ERECVE are shown in Table 1.

Data analysis was organized in three stages: 1) obtaining descriptive statistics and analyses on normality, linearity, multicollinearity and reliability assumptions; 2) dimensionality analysis using Confirmatory Factor Analysis (CFA); and 3) factorial invariance analysis through Multigroup Confirmatory Factor Analysis (MGCFA). Statistical tests and analyses were performed using the RStudio software through various statistical packages, in particular: dplyr and plyr, to organize data and obtain descriptive statistics; corrplot to obtain the correlation matrix between items; lavaan to formalize the model structure and obtain fit values; and semTools to carry out sequential comparisons between nested models. In addition, IBM SPSS and AMOS were used to generate graphs and validate the obtained data.

During the first stage, the mean scores and standard deviation of general index and global scale of ERECVE were calculated. GI was obtained by the sum of the gross score of the participants in each item, meanwhile, Global scale (GS) was obtained by calculating of the average score of the scale items. Given the purpose of this study, the statistical values were calculated dividing the participants by gender. Furthermore, the normality, linearity, reliability and multivariate normality assumptions were verified. The Lilliefors-corrected Kolmogorov-Smirnov goodness-of-fit comparison test was conducted to verify the normality assumptions; a p > 0.03 result (Dallal and Wilkinson, 1986) suggests a normal data distribution. The multivariate normal distribution was determined using the Bartlett sphericity test and the Measure of Sampling Adequacy (MSA) by Kaiser-Meyer-Olkin (KMO); a criterion of p ≤ 0.50 was set for the Bartlett test (Hair et al., 2019) and MSA ≥0.70 for KMO (Hill, 2011; Hair et al., 2019). In turn, the Cronbach’s alpha (α), Rho ordinal standardized alpha (ρ), and McDonald’s Omega coefficient (ω) indices were calculated for the ERECVE item’s reliability analysis; the established cutoff criteria were α ≥ 0.70, ρ ≥ 0.70 (Hair et al., 2019) and ω ≥ 0.80 (Nájera-Catalán, 2019).

In the second stage, a CFA was conducted with the purpose of validating the reconfigured structure of the original ERECVE five-factor model as reported in earlier studies (Rodríguez-Macías et al., 2017; Sánchez-Ariza, 2019). The CFA was performed using the maximum likelihood estimation method; to that end, Hu and Bentler (1999) recommendations regarding model fit assessment were observed. The fit indices and criteria suggested by the authors are: Comparative Fit Index (CFI) ≥ 0.95, Tucker-Lewis Index (TLI) ≥ 0.95, Standardized Root Mean square Residual (SRMR) ≤ 0.08 and Root Mean Square Error of Approximation (RMSEA) ≤ 0.06.

For the third and last stage, an MGCFA was conducted to obtain the factorial invariance by gender; the reconfigured model obtained from the CFA of the previous stage served as a baseline. The recommendations by Bryne et al. (1989), Jöreskog and Sörbom (1979), Jöreskog (1971) and Vandenberg and Lance (2000) were followed to conduct the MES analysis using the sequential restriction procedure, which focuses on comparing models with increasingly restrictive specific parameters. It was determined whether the reconfigured model’s structure had the same fit for both female and male (configurational invariance), whether factorial loads on both groups were equal (metric invariance), whether the reported scores were related to latent scores (scale invariance), and whether they had the same measurement error level for each item between both groups (invariance of error variance). A common criterion for considering factorial invariance as adequate is that the difference of chi-square (Δχ ² ) is not significant (p > 0.05). However, because the Δχ ² calculation varies according to the sample size, several authors (e.g., Vandenberg and Lance, 2000; Cheung and Rensvold, 2002) recommend calculating fitness indices unaffected by the sample size, such as CFI and RMSEA. Therefore, the criteria to consider the invariance assumption as valid in this study were: a CFI difference between models smaller than −0.01 (ΔCFI p < −0.01) and RMSEA approaching or smaller than 0.06 (RMSEA <0.06).

The mean score of GI in the ERECVE was 33.48 (SD = 3.90) and the mean score for female and male students was 33.33 (SD = 3.85) and 33.65 (SD = 3.96), respectively. Means and standard deviations of scores of the GS of the ERECVE ranged between 1.04 and 4.05 and between 0.26 and 1.37, respectively. The mean scores of the GS and by-gender of the ERECVE are presented in Table 2. Likewise, Figure 1 shows distributions of the mean scores of the participants by-subscale.

In terms of the ERECVE scores, the results of the application allow for comparisons in the prevalence of bullying with other populations. It’s found that approximately one in six (17.5%) Baja Californian youth suffer bullying situations by their classmates and approximately one in eleven (8.7%) suffer bullying by peers from other classrooms or grades. Likewise, bullying in Baja California is lower than the global average (one of every three students; United Nations Educational, Scientific and Cultural Organization, 2019). ERECVE results are consistent with the prevalence rates of bullying in Mexican populations (Organization for Economic Co-operation and Development, 2017; Vega-Cauich, 2019), where it is estimated that one in five students suffer bullying by their school peers.

Furthermore, the examinees indicate that they exercise violence toward their classmates inside the institution at least once a week and outside the institution at least once a month. Lastly, it was found that the other situations of bullying and violence outlined by the ERECVE occur rarely or not at all. In view of the foregoing, we suggest that most of the surveyed students take the victim and sole bully roles during the school bullying and violence process. These results differ from the prevalence reported in international studies, where the roles associated with social bully, bystander or defender are the most frequent (Salmivalli et al., 1996; Sutton and Smith, 1999; Goossens et al., 2006). In Mexico, the study by Alcántar-Nieblas et al. (2018) indicates that students take roles similar (pro-social and uninvolved) to defender or bystander more frequently.

Regarding the results of the preliminary analyses of the technical quality of the ERECVE, the Lilliefors-corrected Kolmogorov-Smirnov goodness-of-fit comparison test yielded an adequate result, so the normality assumption in the ERECVE GI scores was accepted. The reliability analysis yielded GI scores of α = 0.72, ρ = 0.73, and ω = 0.80 (see Table 3), which were similar to the ones reported in other research efforts (Rodríguez-Macías et al., 2017; Sánchez-Ariza, 2019) and allowed to validate the ERECVE reliability assumption. Regarding the multivariate normality assumption, the KMO test results suggest a high correlation between the variables (MSA = 0.76); moreover, the results from the Bartlett sphericity test were convergent and significant (χ ² = 50,823.27; df = 171; p < 0.001), so the results from the ERECVE are deemed to comply with a multivariate normal distribution.

The original ERECVE five-factor model had a fit deemed insufficient according to the a-priori established criteria (χ ² = 4,152.42, df = 142, p < 0.00, CFI = 0.92, TLI = 0.90, RMSEA = 0.046, IC 95 [0.045–0.47], SRMR = 0.037); in particular, the CFI and TLI indices did not show values equal or higher than the required threshold. With the purpose of improving the model’s fit, and because of its high values for the standardized residual covariance, item S144.3 was removed (I experience violence from one of my school teachers) and covariance was distributed into four item pairs (S144.1-S144.9, S144.3-S144.4, S143.1-S143.5, and S143.6-S143.8). In so doing, the revised five-factor model presented fit values above the a-priori established criteria (χ ² = 1,999.70, df = 121, p < 0.00, CFI = 0.96, TLI = 0.95, RMSEA = 0.034, IC 95 [0.033–0.35], SRMR = 0.030). Most of the correlations among the five-factors showed moderate to high values, both positive and negative (Figure 2). The standardized factorial loads of the revised model showed adequate values and were statistically significant (p < 0.01): for the first factor (victim’s role) they ranged between 0.22 (S114.4) and 0.55 (S144.2); for the second factor (defensor’s role), between 0.46 (S143.8) and 0.54 (S143.4); for the third factor (sole bully’s role), between 0.50 (S144.8) and 0.65 (S144.7); for the fourth factor (social bully’s role), between 0.60 (S143.7) and 0.73 (S143.5); and for the fifth factor (bystander’s role), between 0.68 (S144.11) and 0.91 (S144.10).

An MGCFA was conducted with the purpose of examining whether both female and male low secondary education students conceptualized school violence equally. Having assessed that the five-factor model’s structure was the same for both groups (configurational model), the obtained results indicated acceptable fit values (χ ² = 2,297.6, df = 244, p < 0.05, CFI = 0.955, RMSEA = 0.035), so the assumption that the model’s internal structure was the same for both groups was deemed acceptable. Moreover, evidence of invariance was obtained for the weak (ΔCFI = −0.002, ΔRMSEA = 0.000), strong (ΔCFI = −0.009, ΔRMSEA = 0.003), and strict (ΔCFI = −0.006, ΔRMSEA = 0.001) models. These results validate the assumptions on equivalence of factorial loads, intercepts and error variance between both subgroups. Fit indices and comparisons among nested models are shown in Table 4.

School bullying is a topic of interest for both educational and government institutions. This phenomenon is characterized by its collective nature and the roles that each of the participants may take (Olweus, 1993; Salmivalli et al., 1996; Salmivalli, 2010). For this research, different analyses were carried out to obtain metric evidence of construct validity regarding of the internal structure and factorial invariance aspects of the ERECVE. The accomplishments and contributions linked to the procurement of said evidence are of different hierarchies. First, it was verified that the ERECVE results possess appropriate metric properties consistent with previous studies (Rodríguez-Macías et al., 2017; Sánchez-Ariza, 2019). Secondly, we obtained evidence of construct validity of the internal structure aspect. The model proposed by Rodríguez-Macías et al. (2017) and validated by Sánchez-Ariza (2019) was revised; the revised model kept the five original factors (see Figure 1) matching each of the roles seen in situations of school bullying and violence (Salmivalli et al., 1996; Salmivalli, 2010). The changes made to the original model were: 1) removal of item S144.3 from factor 1; and 2) distribution of error variance into four item pairs. Thereby, the revised model showed fit indices exceeding the criteria suggested by MES specialists (Hu and Bentler, 1999; Vandenberg and Lance, 2000; Cheung and Rensvold, 2002) and above those reported by Sánchez-Ariza. (2019). In view of the foregoing, the ERECVE internal structure is deemed to offer advantages by accurately identifying the roles taken by the students compared to other instruments that group several roles within one same factor.

Thirdly, the correlations among the revised model factors underscore several important considerations. On the one hand, results are similar to those obtained by Sánchez-Ariza. (2019) and measurements are therefore consistent. On the other hand, several researchers have reported results similar to the correlations of latent variables found in this study. Evidence of correlation was found between seemingly incompatible roles, however, the roles taken by students might change depending on the underlying social context, and thus it is possible that, for example, one individual takes the role of bully and victim at the same time according to the circumstances during the bullying situation (Salmivalli et al., 1996; Gumpel et al., 2014; Menesini and Salmivalli, 2017).

The victim’s role factor presents moderate positive correlations (r = 0.28 and 0.25) with the sole bully’s role and bystander’s role; low correlation (r = 0.05) with the social bully’s role; and moderate negative correlation (r = −0.27) with the defender’s role. In terms of the correlation between the victim and sole bully roles, authors such as Goossens et al. (2006) and Salmivalli (2010) conceptualize it as a subgroup of the victim’s role, naming it victims-bullies. Their distinctive characteristics are increased levels of anxiety and being prone to respond aggressively to provocation from their peers (Salmivalli, 2010). No clear correlation was found with regards to the victim-bystander pair. Written sources report that students taking the victim’s role and the bystander’s role are considered weak among their peers, however, bystanders exhibit more pro-social behaviors (Pouwels et al., 2016). Similarly, Gumpel et al. (2014) and Olweus (1993) indicate that bystanders see the victim as outsiders to the social group and justify the aggressions inflicted upon the victims at some degree.

In addition, we recommend a more thorough research focusing on the relationship between the bystander’s role and victim’s role. The low correlation in terms of the association between the victim’s role and the social bully’s role is thought to stem from the fact that victims tend to be rejected by the group members, besides from showing clear differences with regards to social skills (Olweus, 1993; Salmivalli et al., 1996; Salmivalli, 2010). Lastly, the negative correlation between the victim role and the conciliator’s role can be explained by the fact that students who perform help or cooperation acts are negatively associated with the victim’s role (van den Berg and Cillessen, 2013) and because of the sharp differences in social skills (Olweus, 1993; Salmivalli et al., 1996; Salmivalli, 2010).

The sole bully’s role presents moderate positive correlations (r = 0.21) with the social bully’s role and bystander’s role factors. Regarding the sole bully-social bully relationship, both are considered to exercise violent behaviors, with the most notable difference being that the sole bully is a leader, whereas social bullies act as their henchmen (Olweus, 1993; Salmivalli et al., 1996; Salmivalli, 2010). The moderate relationship between the bully’s role and the bystander’s role is thought to be a result of them being potentially aware of other violent acts by taking part in violent acts in the first place; however, they do not participate as social bullies.

The correlations of the defender’s role factor have negative coefficients with each of the other factors. This indicates that students showing friendship ties with their peers and participating in activities that benefit the community (volunteering, cultural activities, support to others, etc.) are less prone to commit or tolerate school bullying or violence acts. Several studies show to what results this relationship converges (e.g., Veenstra et al., 2005; Crespo-Ramos et al., 2017). Nevertheless, some studies have yielded dissenting results, for example, Demaray et al. (2016) found that students taking the defender’s role correlate negatively with the ability to maintain interpersonal relationships. Likewise, Cillessen and Mayeux. (2004) and Lucas-Molina et al. (2014) suggest that students associated with this role exercise violent behaviors, especially when confronting the sole and social bullies.

Results from the MGCFA support the evidence of factorial invariance across genders for the ERECVE. Having obtained acceptable fit indices during the sequential comparison of nested models, surveyed men and women can be considered to conceptualize school bullying and violence in the same manner. Any score difference between men and women is deemed to convey the individual variability of the construct and not a rationale for bias due to the examinee’s gender. This represents a step forward in measuring the roles of school bullying and violence. Although similar instruments have previously obtained evidence for factorial invariance (Lucas-Molina et al., 2014; Alcántar-Nieblas et al., 2018), the ERECVE is considered a feasible alternative for measuring school bullying and violence at a large scale in secondary school institutions within the Mexican education system.

Among the limitations of the present study, each of the scales presented internal consistency values below the criteria established a-priori (see Table 3). The victim, sole, social and defender scales have inadequate values in the ω index and the sole, social and bystander scales have inadequate values in α and ρ indexes. Low α values can be explicated due to tau-equivalence violation (Green and Yang, 2009) and the item scores weren’t continuous (Gadermann et al., 2012). Inadequate values of ω and ρ indexes suggest a thorough revision of the scale. Results of internal consistency analysis (α = 0.81 to 0.93) don’t coincide with those reported by Salmivalli et al. (1996), however, it’s important to remember that this study was applied in a population of 573 Finnish children, in addition to using the original instrument which has a greater number of items. Likewise, they do not report the results of the ρ and ω indexes, which have greater precision in the type of instruments used in this study.