Violent Physical Bullying Victimization At School: Has There Been A .

Q. Fu et al. imbalance exists because multiple forms of power (e.g., coercive power and legitimate power) are associated with interpersonal relations (French and Raven 1959). Third, the presence of power imbalance in indirect or more subtle forms of bullying has been questioned because less powerful individuals may spread rumors against others (Rigby 2002). In other words, the power-imbalance aspect is probably more relevant to violent physical bullying as victims are repeatedly attacked or harassed by students of greater power or strength. 3 Research on Temporal Patterns of Violent Physical Bullying Victimization Before evaluating existing literature on temporal patterns of violent physical bullying victimization, we discuss the relevance of three related yet distinct temporal variations—age, period, and cohort effects—to the study of bullying victimization. Age effects refer to physiological, psychological, and social changes embedded in the aging process. It has been shown that the transition from childhood to adolescence is characterized by rapid body changes and reestablishment of social relations, which have profound influences on physical bullying victimization (Olweus 1994; Pellegrini and Long 2002). In particular, it has been argued that early adolescence, known as a Bbrutalizing stage of the life course, is critical for the research on physical bullying victimization because physical aggression increases in tandem with growth of body sizes (Cairns and Cairns 1986). Period effects relate to variations in violent physical bullying victimization taking place at a time period that affect all cohorts simultaneously, and embodies the concurrent influences of socio-economic factors, historical events and environmental problems on students from all grades (Glenn 1976; Yang et al. 2008). For example, a temporal change in bullying victimization can occur with the introduction of new technology (such as the Internet and the development and diffusion of social networking sites) or legislation against school bullying, which simultaneously affects behaviors of all students at different ages/grades. Cohort effects pertain to variations in bullying victimization across groups of students who share a common year of birth or other life event such as being enrolled in the same school grade, which are affected by life-course experiences associated with membership in a particular birth cohort. Although there is a dearth of literature on cohort effects of bullying victimization, early exposure to overprotective mothers and higher levels of depressive symptoms may lead to being physically bullied in middle and high schools (Fekkes et al. 2006; Pepler et al. 2008; Smith and Myron-Wilson 1998; Sourander et al. 2000). The epidemic of school bullying can be shifted by differential exposure to risk factors of being bullied across different cohorts. 3.1 Age Trajectories of Bullying Victimization With regard to age/grade trajectories of physical bullying victimization among adolescents, declines in victimization from early adolescent to high-school years have been widely documented in both cross-sectional and longitudinal studies worldwide (Espelage and Swearer 2003; Nansel et al. 2001; Olweus 1994; Pellegrini and Bartini 2000). For example, a longitudinal study conducted in Toronto, Canada in which

Violent Physical School Bullying in the US, 1991 to 2012 participants aged 10 to 14 were followed more than 7 years, revealed that self-reported bullying victimization declined with increasing age regardless of forms of bullying victimization (Pepler et al. 2008). Results from a cross-sectional survey of more than 130,000 Norwegian students also showed that the percentage of students reported being exposed to direct physical bullying (relatively open attacks on the victim) decreased from grade 7 to grade 9 (roughly corresponding to ages 14–16) (Olweus 1994). There are several mechanisms accounting for the decreases of physical bullying victimization from early adolescence to young adulthood, especially in the form of violent bullying. First, early adolescence is a critical period when physical strength and body sizes grow rapidly with age. Although younger students tend to be victimized by others in school due to an imbalance of physical power between themselves and older students, as they age there are fewer older students and thus a lower risk of being victimized (Cairns and Cairns 1986; Smith et al. 1999). Second, direct physical bullying may indicate that younger students lack essential social and verbal skills with which to respond to such bullying. Once they acquire these complex skills in higher grades, direct bullying gives way to more subtle and sophisticated styles of aggression (Scheithauer et al. 2006; Smith et al. 1999; Woods and Wolke 2004). An age decline in violent forms of bullying is expected accordingly, although the prevalence of indirect bullying may stay constant or even increase. Third, as students grow up and move from a familiar school environment to a new one with the breakup of existing peer-to-peer social network connections, physical bullying and violence may be adopted as an aggressive strategy in order to attain dominance and re-establish peer relations in transitions to a new school environment, such as from primary schools to middle schools or from middle schools to high schools (Pellegrini and Long 2002; Staff and Kreager 2008). After dominance relationships are established through a series of aggressive or defensive social interactions (such as bullying) and reconciliation, more cooperative strategies are used by older students to maintain new peer relations in a new school environment (Hawley et al. 2002; Pellegrini and Long 2002). Fourth, physical bullying can have a selection effect on the composition of higher graders because frequent victims tend to be dropouts and thus fail to go on to higher grades. For example, ten percent of high-school dropouts identified fear of being harassed or attacked as the most important reason for leaving school (Greenbaum et al. 1989).1 Finally, there may also be a deterrence-control process at work in the slowdown of the frequencies of severe bullying as students age from the 8th grade (typically 13– 14 year old) to the 10th grade (typically 15–16 year old). According to ethnographic interviews of some juveniles assigned to juvenile court supervision for status offenses detention, there is recognition among at least some juveniles that, upon reaching their 16th birthday (generally corresponding to the 10th grade), persons who engage in the severe forms of bullying are at risk of being prosecuted in adult courts rather than in juvenile courts, and that the sanctions imposed in the adult courts for such behaviors are likely to be substantially more severe than these imposed in the juvenile courts (Land et al. 1992: Williams’ field notes). If a Bnothing to lose attitude about the future is associated with adolescent involvement in risky behaviors such as the use of weapons 1 Presumably, this selection effect also applies to bullies. Nevertheless, an age decline in bullying victimization is expected no matter whether such selection effect applies to both victims and bullies.

Q. Fu et al. (Harris et al. 2002), violent bullying will decrease once its potentially more severe costs are recognized by older adolescents. 3.2 Period and Cohort Patterns in Bullying Victimization Regarding period and cohort changes in bullying victimization, two issues have been raised by previous research. First, the prevalence of bullying victimization can be dramatically different from that of bullying offending (Pellegrini and Bartini 2000; Pellegrini and Long 2002; Smith et al. 1999; Sourander et al. 2000). For example, an 8-year longitudinal study in Finland showed that the prevalence of bullying victimization was consistently higher than that of bullying offending from 1989 to 1997, although the former decreased more rapidly than the latter (Sourander et al. 2000). A longitudinal study conducted in the U.S. reported that the decreases in self-reported victimization in early adolescence were at odds with increases in self-reported bullying (Pellegrini and Bartini 2000; Pellegrini and Long 2002). To reconcile these findings, it was hypothesized that only a specific group of students embedded in a larger pool of students in school is actually at risk of being bullied (Pellegrini and Long 2002; Smith et al. 1999). Likewise, it is possible that some of these targets of school bullying may report being bullied more intensely than others (Cairns and Cairns 1986; Nansel et al. 2001). Therefore, it is important for researchers to distinguish exposure to school bullying from the intensity and frequency of physical bullying. Studying violent physical bullying trends among 12th grade students using the same Monitoring the Future Study (MTF) dataset, Fu et al. (2013) found probabilities for being bullied were higher for students who were male, from singleparent or no-parent families, city dwellers, regarded religion as less important, and showed worse school performance, while persistently higher intensities were found for students who were male, African-American, city dwellers, and from single-parent or no-parent families. Second, the distinction between period and cohort changes in bullying victimization has not been properly addressed in prior research. While news reports of bullying victimization and its consequences increased dramatically in the 2000s (Fraire et al. 2008; Srabstein 2008), only a few studies examined temporal trends of physical bullying victimization at school. For example, a study conducted in Norway concluded that school bullying in the 1980s was more serious and frequent than that 10 to 15 years earlier (Olweus 1991). Johnston et al. (1993) found that the percentage of 12th graders threatened without a weapon increased by one-third from 1980 to 1992. Based on the National Crime Victimization Survey, Finkelhor (2013) saw a 74 % decline in the prevalence rates of violent victimization at school for youth aged 12–17 from 1992 to 2010. However, few studies conducted in more recent years have examined trends of violent physical bullying victimization over a relatively long time span. Moreover, little research has ever attempted to identify and separately estimate the age, period, and cohort effects underlying the trends of physical bullying victimization. If there indeed was an increase in physical bullying victimization in the U.S. in the 2000s, as suggested by media reports, scholars and policy makers should be cautious in interpreting such an increase as a period effect (e.g., as a failure of the nation’s recent anti-bullying efforts) if the contributions of age and cohort effects have not been distilled from the data.

Violent Physical School Bullying in the US, 1991 to 2012 4 Data This research is based on a nationally representative annual survey of youth in the United States, the Monitoring the Future: A Continuing Study of the Lifestyle and Values of Youth (MTF) study (http://monitoringthefuture.org/). Every year thousands of students from approximately 130 high schools nationwide participate in this survey and respond to a series of questions on values, behaviors, and characteristics of American adolescents. Although an annual survey of 12th graders has been a part of this study since 1975, annual surveys of 8th and 10th graders were not added to the MTF until 1991. In order to study both temporal trends over time as well as to make comparisons across the ages (grades), the current study analyzes violent physical bullying victimization reports of the 8th, 10th and 12th graders in the MTF study from 1991 to 2012. Instructed by MTF research staff, about 250,000 high school students in the 8th, 10th and 12th grades participate in this annual survey by completing selfadministered and machine-readable questionnaires at school. Because students who were targets of physical bullying might feel uncomfortable in describing their traumatic experience to interviewers, the information on bullying victimization is collected by the MTF in a self-report fashion, which is regarded as one of the most reliable methods for collecting data on school bullying (Ahmad and Smith 1990). 4.1 Measures of Violent Bullying Victimization It has been shown that measures of bullying victimization tend to be reliable if such measures offer a consistent definition of targeted bullying behaviors, ask respondents to report frequencies, and have a delimited time interval as the reference period (Bosworth et al. 1999; Olweus 1991). Since 1991, frequencies of four extreme forms of physical bullying victimization—physically threatening, violent, injurious—during the last 12 months have been consistently addressed by the following MTF questions regarding the school environment. BThe next questions are about some things which may have happened TO YOU while you were at school (inside or outside or in a school-bus). During the LAST 12 months, how often 1. 2. 3. 4. Has an unarmed person threatened you with injury, but not actually injured you? Has someone threatened you with a weapon, but not actually injured you? Has someone injured you on purpose without using a weapon? Has someone injured you with a weapon (like a knife, gun, or club)? These four targeted bullying behaviors in the MTF questionnaire are hereinafter referred as threatened without injury, threatened with a weapon, injury without a weapon and injury with a weapon, respectively. For each of the targeted behaviors, respondents were asked to choose from five frequency categories: 1) not at all, 2) once, 3) twice, 4) 3–4 times, and 5) 5 times. Annual frequency distributions of different forms of bullying victimization were retrieved from MTF codebooks for each annual survey of 8th, 10th and 12th graders.

Q. Fu et al. Although the MTF also investigates a series of school violence, misdemeanor, and criminal acts, only these four questions are relevant to physical bullying victimization, which is the exclusive focus of this research. When students were targeted by these aggressive and violent behaviors in a repetitive way, these questions corresponded to victimization from violent bullying at school. In particular, the harmful consequences associated with threats deserve attention. When victims are threatened by others, the option being given to the victims is frequently to either engage in undesired behaviors or surrender their belongings. Otherwise, threats can escalate to injuries. Even if victims manage to escape from threats, repetitive threats per se are associated with a series of negative mental-health outcomes, such as self-reported anxiety, depression, loss of selfesteem and suicidal ideation (Rigby and Slee 1999; Salmon et al. 1998). 5 A Two-Step Method for Analyzing the Temporal Characteristics of Combined and Truncated Count Data Because the reported bullying victimization frequency counts in the MTF data are grouped (3–4 times) and truncated (the uppermost response category is 5 times), their statistical analysis is nontrivial. To identify appropriate statistical distributions for analyzing the combined and truncated frequency count data, recall first that statistical models for dealing with rare events (count data) are built on the Poisson distribution (see, e.g., Fox 2008: 392–394; Long and Freese 2006: 394–396). A property of the Poisson distribution is that its expected value (mean) and variance are equal, but this statistical constraint is often violated by over-dispersed (i.e., variance is greater than the mean) empirical distributions of rare events. The over-dispersion in empirical distributions often results from excess zeroes, that is, from more observations with zero counts of an outcome event than would be expected if the data were distributed as a Poisson random variable. Exploratory data analyses showed that this is the case for the MTF count data for the four forms of violent physical bullying victimization. In other words, more 8th, 10th, and 12th graders are not at any risk of school-based bullying than would be expected if the bullying victimizations were distributed as Poisson variables. Unfortunately, no existing statistical models or software can be readily applied to conduct age-period-cohort analyses of combined and truncated count data with overdispersion. To overcome these difficulties in both statistical analyses and data structure, we developed a two-step method for analyzing the temporal (age, period and cohort) characteristics of combined and truncated count data. Step 1 A Zero-Inflated Poisson Model Estimated by Minimizing Least Absolute Deviations To model the grouped and over-dispersed count MTF data, in the first step of our empirical analyses we modified the assumption that bullying processes are operative for all high-school students, and instead estimated zero-inflated Poisson (ZIP) distributions (Fox 2008; Lambert 1992; Long and Freese 2006). Consequently, for each specific form of violent bullying victimization for each of the three school grades for each year of the MTF data, a pair of b 1 , was estimated by minimizing the sum of absolute parameters P;

Violent Physical School Bullying in the US, 1991 to 2012 deviations between observed frequencies and frequencies predicted by zeroinflated Poisson distribution: X b 1 ¼ argmin P; ð1Þ f x P; λ pobserved x ðP;λÞ x pobserved x where x 0, 1, 2, 3–4, 5 and represents the observed frequencies. The probability mass function f(i P,λ) of the zero-inflated Poisson distribution is defined as follows: 8 f x P; λ ¼ ð1 PÞ þ P*PoissonðλÞ ¼ ð1 PÞ þ P*expð λÞ when x ¼ 0 expð λÞ*λx : f x P; λ ¼ P * Poisson ðλÞ ¼ P * when x 0 x! ð2Þ where P is the proportion of students exposed to school bullying and λ is the mean number of occurrences (average number of bullying-victimization incidents) in a year/grade for any individual exposed to the risk of these forms of violent physical bullying. Conceptually, the ZIP model also specifies a twostage strategy for analyzing two different aspects of victimization from violent bullying. In the first stage, the exposure to violent bullying is estimated by a binomial distribution with the parameter P indicating the likelihood that a student is exposed to violent bullying. In the second stage, the intensity (mean rate) of bullying victimization for students exposed to the risk of being bullied is determined by a Poisson distribution with expectation λ. In the present study, P is the proportion of the population surveyed who are in the latent class of 8th, 10th, or 12th graders in a given school year at risk of being a victim of one of the four forms of physically threatening, violent, injurious bullying. If the exposure to bullying parameter P is estimated to be 1.0, then all students surveyed are at risk of victimization and the zero-inflated Poisson distribution reduces to a Poisson distribution. 2 The exposure to the process under study as denoted by parameter P of zero-inflated Poisson models is not identical to observed prevalence rates of the outcome event under study. In the present case, the observed prevalence rates are the proportions of students who report that they were bullied in an MTF survey. These rates are not identical to P because, for any Poisson distribution with intensity parameter λ, there is a non-zero number of observations for which the event count is expected to be zero. In other words, even among a group of students who are at risk of bullying victimization, a non-zero number is expected to report zero events in any specific time period. In brief, observed prevalence rates experiencing an event in sample surveys are the weighted average of: (1) the expected proportion of sample respondents who experience the event among those exposed to the event process for a specific Poisson rate parameter λ and (2) the proportion 1-P of the sample members who are in the latent class of individuals for whom the Poisson process is not operative and thus the outcome event count necessarily is zero. It is the 1-P part of this summation that enables the ZIP model to account for the excess zeroes or 2 The advantage of ZIP models over Poisson models can be suggested by comparing observed frequencies with predicted frequencies using different estimation strategies (see Appendix).

Q. Fu et al. number of observations with zero counts in empirical datasets such as the extreme bullying victimization counts in the MTF. Currently no exis

bullying, cyber bullying and so on, this paper specifically focuses on violent physical school bullying. Based on the recent definition of bullying above, physical school bullying, like other forms of bullying is associated with a series of harmful behaviors occurring repeatedly over time and characterizes an imbalance of power between