“MUERTOS” DE ROTERDAM.

Initial Results

Table 1 represents the univariate statistics of the sample. Males (50.3%) and females (49.7%) had an evenly distributed participation in the study (M = 0.50, SD = 0.50). Moreover, the average age of respondents was 14.08 years (SD = 1.94), and the demographic distribution of race was 38.1% white, 23.4% African American, 24.8% Hispanic, 4.5% Asian, 1.0% Native American, 2.7% multiracial, and 5.5% other race. The average parents’ educational attainment was a partial college education (M = 2.99, SD = 1.11). In terms of spending time online, the majority of youths reported an average between 2-3 times a week and every day (M = 3.26, SD = 1.08). The respondents reported having some guardianship (M = 4.33, SD = 3.94) and some of them reported that their friends cyberbullied others (M = 0.54, SD = 1.45). Overall, 11% of the adolescents reported being cyberbullied, more than 6% reported themselves as cyberbullying offenders, and 3.5% of them reported being both a cyberbullying victim and offender in the last 30 days. Because most adolescents are not victims or offenders of crime or deviance, 89% of the respondents in this sample were not victimized and 94% of them did not bully others. In

addition, this affects the percent correctly classified as shown in the models below. For example, the percent correctly classified are in the 80% and 90% levels because most of the respondents were not involved in cyberbullying as victims or offenders in the last 30 days.

Multivariate Results

The logistic regression results on cyberbully victimization are shown in Table 2. The opportunity and victimization model shows that males were significantly less likely than females to be victimized (B = -0.484, p < .001). Age was another significant control variable (B = 0.071, p < .01). The model correctly classifies about 90%6 of the cases, but it does a weak job of

predicting victimization7 (R²Δ = 0.033). Overall, model 1 supports the first hypothesis because it

6

As discussed earlier, not many adolescents are involved in cyberbullying as victims or offenders, so this affects the percent correctly classified.

7

The Nagelkerke R², or goodness-of-fit, is a pseudo R² and it should be considered as a

proportional reduction in error (Walker & Maddan, 2009). Therefore, the Nagelkerke R² should not be interpreted as the percent explained in the dependent variable; instead, it should be interpreted as the percent change from model to model, predicting the same outcome variable, with the higher Nagelkerke R² indicating a better prediction of the outcome variable.

Variables M/% SD Min Max

Male 50.3% Female 49.7% Age 14.08 1.94 10 18 White 38.1% African American 23.4% Hispanic 24.8% Asian 4.5% Native American 1.0% Multiracial 2.7% Other race 5.5% Parents' education 2.99 1.11 1 5 Opportunity 3.26 1.08 0 4 Guardianship 4.33 3.94 0 16 Differential association 0.54 1.45 0 8 Victimization = Yes 11.1% 0.32 0 1 Offending = Yes 6.6% 0.25 0 1

Both Victimization and 3.5% Offending = Yes

Table 1

suggests that having opportunity to access the Internet positively and significantly increased the likelihood of a youth becoming a cyberbully victim (B = 0.241, p < .001).

For model 2, where guardianship is added to the model, males were also significantly less likely than females to be the cyberbully victims (B = -0.396, p < .001). Similar to model 1, age and opportunity were positively significant (B = 0.093, p < .001 and B = 0.250, p < .001, respectively). In addition, the second hypothesis was not supported because the guardianship model suggests that there is an association between cyberbullying offending and victimization when parents or teachers talked to adolescents about being safe on the computer and cell phone.

Variables B S.E. EXP(B) B S.E. EXP(B)

Male -0.484*** 0.102 0.613 -0.396*** 0.103 0.673 Age 0.071** 0.026 1.070 0.093*** 0.026 1.097 White is reference group

African American 0.390 0.254 1.477 0.577* 0.258 1.781 Hispanic 0.202 0.263 1.224 0.164 0.267 1.178 Asian -0.120 0.265 0.988 0.045 0.268 1.046 Native American 0.605† 0.318 1.831 0.701* 0.322 2.016 Multiracial 0.387 0.538 1.472 0.412 0.545 1.509 Other race 0.237 0.391 1.267 0.402 0.395 1.495 Parents' education -0.002 0.046 0.988 0.012 0.046 1.012 Opportunity 0.241*** 0.054 1.284 0.250*** 0.057 1.284 Guardianship 0.104*** 0.012 1.109 Constant -3.948*** 0.475 0.019 -4.936*** 0.497 0.007 Nagelkerke R² -2 Log Likelihood Table 2

Logistic Regression on Cyberbullying Victimization (n = 4,159)

Model 1 Model 2 Opportunity Guardianship 2835.274*** 2763.957*** 88.9% correct 88.9% correct 0.033 0.066 * p < 0.05, ** p < 0.01, *** p < 0.001. †p < 0.10

Model 2 also shows that African Americans and Native Americans were significantly more likely than whites to be victimized when they report having guardianship (B = 0.577, p < .05 and B = 0.701, p < .05, respectively). The guardianship model correctly classifies about 90% of the cases, and the pseudo R² suggests that this model does a better job of predicting victimization (R²Δ = 0.066).

Table 3 presents the logistic regression results for cyberbullying offending. Model 3 correctly classifies over 93% of the cases and it does poor job of predicting offending (R²Δ = 0.016). The results suggest that adolescents who spent more time online were significantly more likely to have an increased likelihood of bullying others (B = 0.244, p < .01); hence, this supports hypothesis 3.

In model 4, differential association is added to the cyberbullying offending model.

Results show that when youths spent more time online and have friends who cyberbullied others, they were significantly more likely to cyberbully others as well (B = 0.256, p < .01 and B = 0.624, p < .001, respectively); thus, hypothesis 4 was supported. The differential association model correctly classifies 94% of the cases. The pseudo R² indicates that this model does a better job of predicting offending (R²Δ = 0.298).

The relationship between victimization and offending is shown in model 5. The

victimization model suggests a relationship between cyberbullying offending and victimization because adolescents who have been victimized were significantly more likely to cyberbully others when they have opportunities to access the Internet and friends who are cyberbullies (B = 1.884, p < .001, B = 0.204, p < .05, and B = 0.522, p < .001, respectively). This finding supports the fifth hypothesis because youths who have been cyberbullied were 6½ times more likely to become cyberbully offenders. Model 5 correctly classifies more than 94% of the cases. The

Variables B S.E. EXP(B) B S.E. EXP(B) B S.E. EXP(B) B S.E. EXP(B)

Male 0.015 0.127 1.015 -0.138 0.148 0.871 0.075 0.155 1.078 0.075 0.155 1.078 Age 0.063† 0.033 1.065 0.041 0.038 1.042 0.024 0.040 1.024 0.024 0.040 1.024 White is reference group

African American -0.341 0.276 0.711 -0.355 0.321 0.701 -0.468 0.344 0.627 -0.466 0.344 0.627 Hispanic -0.021 0.281 0.979 -0.156 0.330 0.855 -0.138 0.352 0.871 -0.136 0.352 0.873 Asian -0.373 0.287 0.689 -0.380 0.334 0.684 -0.344 0.356 0.709 -0.343 0.356 0.710 Native American -0.022 0.371 0.978 -0.344 0.450 0.709 -0.633 0.489 0.531 -0.626 0.490 0.535 Multiracial -0.040 0.652 0.961 -0.324 0.745 0.723 -0.368 0.808 0.692 -0.359 0.807 0.699 Other race 0.026 0.432 1.027 -0.204 0.526 0.816 -0.127 0.544 0.881 -0.123 0.544 0.884 Parents' education 0.009 0.058 1.009 0.063 0.066 1.065 0.050 0.068 1.051 0.050 0.068 1.051 Opportunity 0.244** 0.070 1.276 0.256** 0.079 1.292 0.204* 0.082 1.227 0.192† 0.104 1.212 Differential association 0.624*** 0.031 1.866 0.522*** 0.032 1.686 0.506*** 0.094 1.659 Victimization 1.884*** 0.159 6.582 1.886*** 0.159 6.590 Differential Association x 0.005 0.027 1.005 Opportunity Constant -4.193*** 0.576 0.015 -4.732*** 0.678 0.009 -4.703*** 0.710 0.009 -4.669*** 0.733 0.009 Nagelkerke R² -2 Log Likelihood †p < 0.10

NOTE: A second interaction was computed between differential association and victimization; however, there is only a slight change of coefficients and log Table 3

Model 6 Differential Association Victimization Interaction Opportunity

Model 3 Model 4 Model 5

94.5% correct Logistic Regression on Cyberbullying Offending (n = 4,159)

93.4% correct

0.016 0.298

94.0% correct 94.5% correct 0.368

likelihood from the first interaction, thus, they are not reported here.

1381.217*** 1381.185*** 1989.688** 1510.257***

0.368

pseudo R² indicates that with the addition of the victimization variable in this model, there was an increase in predicting offending (R²Δ = 0.368).

Model 6 adds the interaction between the differential association and opportunity on cyberbully offending. The model correctly classifies over 94% of the cases while there was no change in the pseudo R² (R²Δ = 0.368). The results suggest that victims of cyberbullying who are friends with cyberbullies were significantly more likely to offend others via technology (B = 1.886, p < .001 and B = 0.506, p < .001, respectively). The findings also show a positive interaction between differential association and opportunity, however, the interaction was not statistically significant. Therefore, hypothesis six was not supported.

A receiver operating characteristic (ROC) curve analysis was also computed to examine the goodness-of-fit for model 6 because many respondents did not cyberbully others in the last 30 days, thus, the percent correctly classified may be misleading. Model 6 was chosen for this analysis because it includes all the variables in this study and the differential association- opportunity interaction. As noted above, a ROC curve analysis is a measure of goodness-of-fit for the logistic regression model, and it does this by measuring the sensitivity (true positive rate) and specificity (false positive rate) levels to determine all possible cutoff points (Gorr, 2009). The ROC curve is generated by plotting the sensitivity level against the specificity level. The area under the curve (AUC) shows how well the predicted probabilities classified or fit the cases in the model. The AUC values closer to 1.0 mean the predicted probabilities reliably classify cyberbully offenders and non-offenders where values closer to 0.5 indicate that the predicted probabilities did no better than chance at classifying both groups. For model 6, the results show the AUC value is 0.88, which indicates that the predicted probabilities did better than chance at classifying offenders and non-offenders (see Figure 1). This can also be seen in figure 1 where

the slope is closer to 1 on the sensitivity or true positive rate side of the figure.

One of the difficulties of logistic regression is the results are not easy for non-specialists to interpret (Burruss & Kempf-Leonard, 2002). To make the interpretation of the multivariate effects in logistic regression easier to understand, I have developed a case scenario based on the results from model 5. Figure 2 shows an average victim/non-victim respondent: fourteen-year- old, white, male, parents’ education status, opportunity, and percent likelihood to cyberbully at each level of differential association. The figure shows the escalation of the percent likelihood to cyberbully others at each level of differential association for victim/non-victim. Victims are

more likely to become offenders as the level of differential association increases. For example, at level five, the victims are 63% likely to cyberbully compared to non-victims who are 21% likely to offend. At the highest level of differential association, the victims are almost at 90%

likelihood to offend compared to the non-victims who are at 55%. It should be noted that the percent difference between the groups is not clearly linear as the differential association level increases. This indicates that as the differential association level increases, the gap of

cyberbullying between victims and non-victims is becoming smaller because victims are less likely to offend while non-victims are more likely to offend. Stated differently, an increase in the percent likelihood to offend among victims and non-victims is not consistent at each differential association level.

Figure 2. Case Scenario: Percent likelihood of engaging in cyberbullying by victim status 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 8 Percent Likelihood to Cyberbully

Differential Association Level