Victims

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University of Louisville, Kentucky. Bradford W. Reyns, PhD ... Keywords: adolescent victimization; criminal opportunity; peer networks; social network analysis.

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Violence and Victims

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Violence and Victims, Volume 27, Number 5, 2012

Patterns of Victimization Between and Within Peer Clusters in a High School Social Network Kristin Swartz, PhD University of Louisville, Kentucky

Bradford W. Reyns, PhD Weber State University, Ogden, Utah

Pamela Wilcox, PhD Jessica R. Dunham, MS University of Cincinnati, Ohio This study presents a descriptive analysis of patterns of violent victimization between and within the various cohesive clusters of peers comprising a sample of more than 500 9th–12th grade students from one high school. Social network analysis techniques provide a visualization of the overall friendship network structure and allow for the examination of variation in victimization across the various peer clusters within the larger network. Social relationships among clusters with varying levels of victimization are also illustrated so as to provide a sense of possible spatial clustering or diffusion of victimization across proximal peer clusters. Additionally, to provide a sense of the sorts of peer clusters that support (or do not support) victimization, characteristics of clusters at both the high and low ends of the victimization scale are discussed. Finally, several of the peer clusters at both the high and low ends of the victimization continuum are “unpacked,” allowing examination of within-network individual-level differences in victimization for these select clusters.

Keywords: adolescent victimization; criminal opportunity; peer networks; social network analysis

T

he scientific literature on victimization includes considerable empirical support for the idea that environmental contexts within which individuals are embedded exert important influences and/or provide criminal opportunity above and beyond individual-level risk factors. For example, many contextual studies of victimization focus on rather large, somewhat distal contexts, such as neighborhoods (e.g., Miethe & McDowall, 1993; Sampson, Raudenbush, & Earls, 1997; Sampson & Wooldredge, 1987). In the case of adolescent or young adult victimization, schools/campuses have been particularly notable contexts of interest (e.g., Burrow & Apel, 2008; Campbell, Wilcox, Ousey, & Clayton, 2002; Fisher, Sloan, Cullen, & Lu, 1998; Payne, Gottfredson, & Gottfredson, 2003; Schreck, Miller, & Gibson, 2003; Wilcox, Tillyer, & Fisher, 2009).

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Although containing some important social sources of variation in victimization, neighborhoods and schools typically contain considerable within-group heterogeneity that gets washed out in analyses of between-neighborhood or between-school effects. Indeed, it is likely that many of the important group-level effects occur within, rather than between, schools. Nonscientific observation within any given school reveals that group contexts such as peer networks or cliques seem to form based on common interests (e.g., extramural sports, social or academic clubs) or social similarities (e.g., similar physical attractiveness, racial characteristics, family wealth); indeed, the idea of school-based cliques is ingrained in our culture. More scientifically speaking, cohesive friendship groups—what we refer to as “peer clusters”—are, in fact, typically thought to be one of the most important contexts for understanding adolescent crime-related behavior (Warr, 2002). We approached this study with the belief that peer clusters might serve as a relatively small, homogeneous environment, providing varying degrees of opportunity for victimization (Schreck, Fisher, & Miller, 2004). However, our overall objective was not to provide an explanatory analysis of the effects of characteristics of peer clusters on victimization. Rather, our objective was much more descriptive in nature and considered a first step toward an eventual understanding of the ways in which peer clusters impact victimization risk. With this descriptive objective in mind, a specific aim of this study was to, first, explore whether victimization varied across the friendship clusters comprising an overall school-based peer network. We accomplished this by way of visualization techniques associated with social network analysis (SNA), along with supplemental multilevel model analysis of cross-cluster variation. Next, we aimed to provide descriptions of the cross-cluster variation we observed, with a particular focus on the spatial positioning and social character of high- versus low-victimization groups. Finally, we aimed to describe individual-level variation in victimization within high- and low-victimization clusters, also noting the spatial positioning of individual victims within these clusters. We accomplished these specific aims by performing SNA on data collected from approximately 550 high school adolescents, who named up to five of their closest friends in the course of a group-administered survey. For all descriptive analyses, we used measures of peer network characteristics created based on data from the nominated peers themselves. Throughout this study, we employed the following definitions in distinguishing two important types of peer group contexts: (a) peer clusters—the immediate group of peers with which the individual associates, based on who individuals named as their “closest friends” (with up to five nominations allowed per respondent) and (b) peer network—the broader system of ties and linkages created by multiple, interwoven sets of peer clusters within the entire sample. Clusters and networks will be measured via “SNA” methodology.

THEORETICAL BACKGROUND: PEERS AND VICTIMIZATION Very little work has focused on peer clusters—especially school-based peer clusters—as contextual units of analysis, important in understanding victimization. In contrast, there is a fairly large literature on the influence of conventional versus delinquent individuallevel peer associations on victimization. This latter-mentioned literature includes studies examining victimization that may have occurred in the community (e.g., Henson, Wilcox, Reyns, & Cullen, 2010; Jensen & Brownfield, 1986; Lauritsen, Laub, & Sampson, 1992; Lauritsen, Sampson, & Laub, 1991; Schreck & Fisher, 2004; Schreck et al.,

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2004; Schreck, Stewart, & Fisher, 2006; Schreck, Wright, & Miller, 2002) as well as studies examining victimization, which occurs in schools specifically (Ousey, Wilcox, & Brummel, 2008; Ousey, Wilcox, & Fisher, 2011; Schreck et al., 2003; Tillyer, Fisher, & Wilcox, 2011; Wilcox et al., 2009). Unlike the previous work, this study does not focus on the explanatory effects of an individual’s conventional versus delinquent peer associations. However, such previous work is still relevant in that it provides theoretical rationale on why we would expect to observe variation in victimization across school-based peer clusters. Explanations for the effects of individual peer associations on victimization vary somewhat across the studies cited previously, but a particularly prevalent theory is that peers determine adolescent lifestyles and routine activities, which, in turn, impact opportunities for victimization. According to lifestyle-routine activities theory, lifestyles and daily activities impact one’s opportunity to become a victim because they affect exposure to motivated offenders, vulnerability as a potential target, and level of guardianship (e.g., Cohen & Felson, 1979; Hindelang, Gottfredson, & Garofalo, 1978; Osgood, Wilson, O’Malley, Bachman, & Johnston, 1996). The implied importance of peer associations in lifestyle-routine activity theory—as providers of differential levels of criminal/victim opportunity—has also been used to account for the robust sociodemographic correlates of adolescent victimization (e.g., male, lower income, nonwhite) evident in the literature (e.g., Truman & Rand, 2010). Variation in victimization based on individual demographic characteristics has been explained using the principle of homogamy in conjunction with the notion of criminal opportunity. According to the principle of homogamy, individuals are likely to associate with others who are similar to themselves. This principle can be manifested in an individual’s association with peers who share demographic characteristics (e.g., race, wealth). Thus, if an individual belongs to an offending-prone demographic group (e.g., male), then his associations are likely to expose him to more risk of victimization than his female counterparts. To summarize this example, male adolescents are likely to associate with other males (because of homogamy), and associating with other males increases one’s chances of victimization because of the shared time together in the course of lifestyles or routine activities—activities that are more likely to involve delinquency than are shared activities among females. Hindelang and his colleagues (1978) summarize this perspective as follows: . . . the patterns of personal characteristics that combine to yield high likelihoods of suffering a personal victimization are characteristics that inferentially may be associated with differences in personal lifestyles. These lifestyles, in turn, may be related to being in places and situations with high opportunities for criminal victimization. (p. 121)

Thus, overall, the implication of much previous work on adolescent victimization is that individual peer associations are important, with the notion of “opportunity” being a key to understanding that importance. Although this previous work is quite informative, we believe that an important new direction for research on adolescent victimization is to explore peer associations, not only as individual-level characteristics, but also as social contexts embedded within a larger network of peers. Doing so will allow us to begin to understand how the contextual nature of peer clusters, and their positioning within a broader network of peers, influences victimization above and beyond individual-level peer associations. In our view, an aggregate-level routine activity theory provides the rationale for why peer groups, as social contexts, likely experience differential rates of

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victimization. As contexts, they likely provide to their members differing aggregate levels of exposure to motivated offenders, vulnerability, and guardianship.

Studies of School-Based Friendship Clusters As reviewed earlier, whether one associates with delinquent or delinquency-prone peers is important. However, an individual’s place/role within his or her peer group and the structure and character of the peer group itself may also have an impact on victimization. These sorts of effects have been examined quite extensively in the criminology literature examining the influence of peers and peer groups, especially those that are school based, on general delinquency (e.g., Haynie, 2001; Haynie & Osgood, 2005; Haynie & Payne, 2006; Kraeger, Rulison, & Moody, 2011; McGloin, 2009; McGloin & Shermer, 2009; Nijhof, Scholte, Overbeek, & Engels, 2010).1 For instance, in a groundbreaking study using data from the National Longitudinal Study of Adolescent Health (Add Health data), Haynie (2001) examined the effects of cluster density, centrality, and popularity on delinquency. She reported that influences of peer delinquency on respondents’ delinquency tended to matter most when the respondents were centrally located in their peer cluster, when these clusters were dense, and when the individual respondents were popular (i.e., connected or tied to many others through friendship).2 Despite the focus on delinquent offending as opposed to victimization, studies mentioned above are informative in considering the nature of adolescent peer networks as well as the possible connections between network characteristics and victimization. In fact, Schreck, Stewart, and Osgood (2008) have argued that because many theories of crime have also been fruitfully applied to explaining victimization outcomes, researchers may well want to consider the further implications of this victim–offender overlap. Along these lines, work by Haynie (2001) is useful in considering the possible influences of peer cluster structures on victimization outcomes. Thus, building on the work of Haynie (2001), and considering that similar networkrelated processes may be at work within victimization-prone peer groups, Schreck et al. (2004) examined the peer group as a context for explaining violent victimization. Based on their analyses of the Add Health data, these authors reported that the rate of delinquency characterizing one’s peer cluster increases victimization risk, even after controlling for other peer cluster characteristics.3 However, the density of an individual’s peer cluster, his or her centrality within the cluster, and his or her popularity within the cluster interacted with peer delinquency to impact victimization risk. For instance, dense and delinquent clusters were those most likely to provide a context conducive to victimization. Theoretically, these findings make sense from the standpoint of lifestyle-routine activities theory. Dense groups with high levels of delinquency provide high levels of exposure (to motivated offenders) among members, a target-rich context, and a context with relatively little capable guardianship (Schreck et al., 2004; see also Wilcox, Land, & Hunt, 2003). Schreck et al. (2004) also found that individual location (centrality) and popularity within their peer cluster appeared to make one a more likely target for violence in delinquent groups. Again, these findings are consistent with the opportunity perspective. Central and popular members of delinquent clusters are well connected to their friends, and offenders are among those friends. Offenders in such groups thus know a good deal of information about central and popular members, including information about valuable targets (i.e., for theft) they may possess, physical or mental vulnerabilities they may have, and how well guarded they tend to be. In other words, offenders more readily know about

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the opportunity for victimization provided by central and popular members within their peer group. In contrast, relatively little may be known about the opportunity provided by peripheral members. Interestingly, Schreck et al. (2004) found that central and popular individuals were at less risk than peripheral members in more conventional (nondelinquent) peer clusters. Such results are also consistent with a lifestyle-routine activities perspective. For instance, Schreck et al. (2004) suggested that connections in conventional groups did not serve to increase exposure to offenders or provide information to offenders about target suitability because offenders were not part of the group. Instead, connections in conventional groups might have served to enhance guardianship, with central members having the most protection from friends (Schreck et al., 2004). In sum, a great number of studies have suggested that individual association with delinquent peers is correlated with victimization. Yet, most victimization research to date has simply tried to address these important peer effects by including a measure of “delinquent friends,” as self-reported by research subjects themselves (e.g., Schreck et al., 2006; Wilcox et al., 2009). What is neglected in most prior victimization research is examination of the structure and nature of the peer group as a contextual unit of analysis. In fact, most prior studies of victimization have not employed sampling strategies or instrument designs that adequately capture peer association in a way that allows their effects on behavior to be reliably estimated in sufficient detail or as a contextual effect. Schreck et al.’s (2004) analysis of the Add Health data represents an important exception and points to a new direction in victimization research.

THE PRESENT STUDY In this study, we built on and complement past work, particularly the work of Schreck et al. (2004) that examines the link between peers, peer clusters, and adolescent victimization, although we focused specifically on victimization that occurs in school. In line with Schreck et al. (2004), we identified peer clusters and individual positions within those clusters. Furthermore, we measured the behavior of peers to whom individual respondents were tied using data from the peers themselves. More specifically, as in the Add Health study, we used data asking survey respondents to name up to five of their closest friends in the course of a group-administered survey. These nominated peers were also included in the survey, allowing for a more accurate appraisal of peer clusters. Unlike previous adolescent victimization studies, however, we explored these peer clusters within a school-based sample’s broader social network, and, again, we focused on school-based victimization specifically. We examined, in a visually descriptive sense, the spatial location of highversus low-victimization clusters within the overall school-based social network. In doing so, we noted the social proximity between high- and low-victimization clusters. In other words, we explored whether high-victim clusters were somewhat contiguous, or closely tied, to one another or, in contrast, spread apart. We also observed whether high-victimization clusters were central or peripheral within the overall network of the school.4 High- and low-victim clusters were described according to various attributes including cluster size, demographic composition, average low self-control, and average delinquency. Finally, as a descriptive complement to the few existing studies of peer networks and victimization to date, we unpacked several high- and low-victim peer clusters to discern the

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within-cluster patterning of victimization among the individuals comprising these groups. As such, we aimed to illustrate how victimization was distributed within cohesive clusters— whether it was shared among members or concentrated among a few individuals.

METHODS Data The data used to analyze peer networks and estimate the effects of peer-network characteristics on victimization were obtained from a 2006 study of students from a midsized high school in Kentucky (National Instititute on Drug Abuse [NIDA] grant DA-11317, Richard Clayton, private investigator [PI]). The high school used for sampling was the only public high school within the county. Self-report surveys were administered in the homeroom period during the second week of classes (mid-August) to all students from whom active parental consent was obtained. Surveys asked students to provide the names of their five closest friends, regardless of whether the friends attended the school. With only one public school in the county, however, most nominated friends were students at the same school. In addition to asking about friendships, the group-administered survey asked questions about past victimization experiences, self-reported delinquency, family and school attachments, self-control, and personality. The sample included 541 participants, approximately 78% of the school’s student population. Demographically, the sample looked very similar to the overall population for the high school in terms of gender (52% female), whereas the sample somewhat overrepresented nonwhite students (15% of the sample vs. 10% of the population). Nearly all nonwhite students in this school context were African American. Also, the sample was slightly skewed toward younger ages because the response rate was higher among the larger ninth grade cohort than it was schoolwide (84% vs. 78%). The average parental socioeconomic status of respondents was 4.17 (1 5 low to 7 5 high). Although not necessarily representative of all U.S. high school students, the sample has characteristics making it a uniquely valuable dataset for the sort of research questions addressed herein. When mapping peer clusters within a larger social network of students, and when using the data from the nominated peers to characterize peer clusters (as opposed to the single-informant approach), it is necessary to have participation by as close to 100% of the students in a targeted population as possible. Ideal for such purposes are geographic localities with only one public school that would be attended by all same-age adolescents (with possible exceptions being youths attending private schools, being schooled at home, or having already graduated from or otherwise left the school). The school district in which these data were collected, therefore, was well suited for the study. Although sample generalizability is a limitation, the data do allow for a unique exploration of the character of peer clusters (vis-à-vis victimization) within almost the entire network of students at the school (and within the community at large).

Measures of Variables Violent victimization was our key variable of interest. We examined both the average level of victimization characterizing peer clusters and the victimization experienced by individuals within the clusters. Violent victimization, at the individual level, was measured as the total number of times respondents reported having experienced the

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following during the summer preceding the survey: (a) having had money or property taken by force, (b) having had a gun pulled on her or him, and (c) having had a weapon other than a gun pulled on her or him. It should be noted that the “past summer” time referent for this victimization measure corresponds to about a 12-week period, and there was only a 2-week gap between this referent period and survey administration, at which time respondents also reported their top five friendships. Descriptive statistics provided in Table 1 reveal that the average total times students reported experiencing serious violent victimization was 0.73. However, individual scores ranged from 0 to 30. At the cluster level, average victimization was 0.74, with clusters experiencing between 0 and 4.38 victimizations per person.5

TABLE 1. Variables, Scales, and Descriptive Statistics Variables

Scale

M

SD

Range

N

Individual-level variables Violent victimization

(Sum of violent victimization)

0.73

3.61

0–30

537

Gender

(0 5 Male, 1 5 Female)

0.52

0.50

0–1

541

Age

(Respondent’s age in years)

16.68

1.21

14–18

536

Race

(0 5 White, 1 5 Nonwhite)

0.15

0.36

0–1

541

Parental SES

(1 5 Low to 7 5 High)

4.17

1.49

1–7

489

Mother attachment

(1 5 Low to 5 5 High)

3.82

0.76

1–5

540

Impulsivity

(1 5 Low to 4 5 High)

1.82

0.73

1–4

529

Delinquency

(1 5 Low to 7 5 High)

1.31

0.71

1–7

538

Violent victimization

(Average violent victimization)

0.74

1.11

0–4.38

57

Gender

(Proportion female)

0.52

0.41

0–1

57

Age

(Average age in years)

15.67

0.93

14–18

57

Race

(Proportion nonwhite)

0.15

0.17

0–0.83

57

Parental SES

(Average parental SES)

4.16

0.74

2.50–5.83

57

Mother attachment

(Average mother attachment)

3.80

0.35

2.90–4.39

57

Impulsivity

(Average impulsivity)

1.86

0.33

1.21–2.82

57

Delinquency

(Average delinquency)

1.31

0.23

1.02–2.24

57

Cluster size

(Number of students in cluster)

9.54

6.11

4–27

57

Cluster-level variables

Note. SES 5 socioeconomic status.

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We considered various demographic, social, and behavioral characteristics when describing how victimization varied across peer clusters within the overall network and between individuals within the peer clusters. More specifically, we characterized both clusters and individuals based on gender, race, age, criminal behavior, and impulsivity. Respondent gender was measured as a dichotomous variable (0 5 male, 1 5 female). Within-cluster aggregated gender, therefore, produced a measure of proportion female. Respondent race was measured as a dichotomous variable (0 5 white, 1 5 nonwhite), and within-cluster aggregated race thus measured the proportion nonwhite. Age was measured in years for each respondent; cluster-level age structure was measured as the average age of all cluster members. Individual delinquency was measured as an index based on the respondents’ reported participation in 13 different delinquent acts during the previous summer. Each of the 13 items was measured as an ordinal scale, tapping frequency, with scores ranging from 1 5 0 days to 7 5 60 or more days. We averaged scores for each respondent to create an overall delinquency index, with 1 representing low delinquency and 7 representing high delinquency (Cronbach’s alpha 5 .89). Individual delinquency scores were then aggregated within peer clusters, yielding an average delinquency score for each cluster. At the individual level, impulsivity was constructed by averaging responses to 11 survey items asking respondents how strongly they agreed with statements such as “I have trouble controlling my temper,” “I have difficulty remaining seated at school,” “I have difficulty keeping attention on tasks,” and “I am nervous or ‘on edge’.” Values on each of the 11 items ranged from 1 (never true) to 4 (always true). Averaging values across the 11 items resulted in an index score for each student, with 1 representing low impulsivity and 4 representing high impulsivity (Cronbach’s alpha 5 .93). A measure of average impulsivity resulted by aggregating individual scores within each cluster.

ANALYTIC STRATEGY SNA, hierarchical Poisson-based regression models, and descriptive statistical analysis were all used in this study. First, SNA techniques were used to construct the overall complete peer network and the various cohesive peer clusters comprising that network. Variation in victimization across networks was depicted visually through SNA, but it was also assessed using hierarchical Poisson-based regression models. Finally, characteristics of the overall network and the individual peer clusters were described using univariate analyses with SPSS. Because SNA is relatively new in terms of its application to victimization, it is described in greater detail in the following text.

Social Network Analysis Networks exist in many contexts and are formed based on different types of relations among actors in a network. In this study, the network under investigation consists of students within a high school, and the type of relation between students that was focused on was friendship. Analytic assessment of the ties or relations within a network is often referred to as the SNA. SNA consists of both visualization and empirical analyses. Visualization allows for the pictorial display of the network with nodes and lines of various colors and shapes. Pictorial displays are important because they allow for both the researcher and the reader to visualize an abstract network. Empirical analyses can also

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be conducted to determine network statistics, such as network cohesion, actor centrality, and the existence of possible network subgroups. Our analysis employed both empirical and visualization techniques to create the overall peer network and the various cohesive peer clusters comprising that network. More specifically, we used UCINET 6 (Borgatti, Everett, & Freeman, 2002) and NetDraw (Borgatti, 2002) to construct the network, analyze the subgroup structure, and construct clear pictorial views of elements of each of the networks.

RESULTS To begin, the overall network characterizing the sample was created, representing the friendships among all students in the study. This network is shown in Figure 1. The relations among the 541 students (each represented as a node in Figure 1) were based on each respondent’s reported top five friendships (as asked in the survey). The network depicted was created by transforming all of the survey-based friendship data into a network matrix via UCINET and then inputting the matrix into NetDraw for analysis. To distinguish cohesive subgroups of friendships within the larger network—what we call peer clusters—we analyzed this network with the hierarchical clustering of geodesic distances technique (Lumsden, 2006). Hierarchical clustering of geodesic distances provides multiple sets of groupings (i.e., multiple “solutions”) through the use of softwarebased algorithms6 where nodes (individuals, in this case) are included in or excluded from a cluster based on their geodesic distance7 from other members of the cluster. To select the optimum representation of the peer clusters among the various possible solutions, we considered both the size of the resulting clusters and their cohesiveness. Details regarding this technical process are contained in the “Methodological Appendix.” Suffice to say here, this analysis resulted in a network of 56 peer clusters. Again, these clusters represented cohesive sets of friendships among the 541 individuals in the high school. These clusters ranged in size from 4 to 27 members, with an average of 9.54 members per cluster. Subsequently, the network of peer clusters (as opposed to the network of individuals shown in Figure 1) was created via UCINET 6. For this network of peer clusters, ties between any two clusters consisted of the total number of friendships existing between the individuals comprising each cluster. NetDraw was used to create attribute-based visualizations of the peer group clusters. Figure 2, for instance, depicts the peer clusters as nodes (indicated as squares). The figure shows the varying level of victimization across these clusters (based on the size of the square) as well as the number of connections between individuals across clusters (illustrated by the thickness of the line). So, the largest squares in Figure 2 are clusters with the highest rates of victimization. The darkest lines in Figure 2 reflect the largest number of friendship ties between individuals across the two groups being connected. Figure 2 indicates interesting spatial patterning regarding high- versus low-victimization clusters. Those peer clusters that suffered from the highest violent victimization rates were more centrally located within the peer cluster network. These groups were more “connected” to other clusters compared to those clusters that experienced the least victimization. This supports previous research examining the importance of the centrality of individuals within clusters (e.g., Schreck et al., 2004). The results shown here suggest that a similar phenomenon occurs when considering the centrality of peer clusters within

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Figure 1.

Complete individual friendship-based network.

Victimization Between and Within Peer Clusters

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Figure 2.

Peer cluster network by average violent victimization.

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a network of clusters. Interestingly, however, although the high-victimization clusters were well connected within the context of the broader network, they are not particularly well connected to one another. This is depicted in Figure 2 in that high-victimization groups are not connected with thick lines. There does not appear to be evidence of diffusion of victimization from high-victimization clusters to “nearby” clusters. In other words, victimization does not appear to “spread” from high-victim clusters to their most closely linked clusters. Regarding the peer clusters with the lowest victimization rates, Figure 2 indicates that they are located on the outskirts of the overall social network. Again, this finding is consistent with some of the findings from previous studies of individual centrality within clusters, with less central individuals often at reduced risk for victimization. Beyond the visual depiction offered by Figure 2, we assessed further whether significant variation in our measure of violent victimization existed across peer clusters. Statistical variation in victimization across the peer clusters was examined with hierarchical, Poisson-based regression models, using the HLM 6 software (Raudenbush & Bryk, 2002). We estimated a variance component based on an unconditional (intercept-only) multilevel negative binomial regression model of violent victimization.8 Significant variation across peer clusters for violent victimization was demonstrated (variance component 5 1.209, SD 5 1.100, p 5 .000), thus supporting the visual difference shown in Figure 2.

High-Victimization Clusters The next step was to look more closely at a few clusters at the high and low ends of the serious victimization spectrum for descriptive purposes. Figure 3 provides illustrations of the three peer networks that experienced the greatest serious violent victimization. The nodes depicted in Figure 3 represent the individuals within the clusters. Table 2 summarizes descriptive statistics associated with these three high-victimization clusters in comparison to all clusters. Group 25, as shown in Figure 3 and summarized in Table 2, experienced the most violent victimization with a rate of 8.69 (compared to the overall cluster-level mean of

Group 25

Group 34

Group 42

8.69

8.17

8.00

Figure 3. Clusters with highest victimization.

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TABLE 2. High-Victimization Cluster Characteristics Cluster 25

Cluster 34

Cluster 42

Cluster-Level M

Violent victimization

8.69

8.17

8.00

0.74

Proportion female

0.88

0.00

0.20

0.52

14.75

16.70

17.20

15.68

Proportion nonwhite

0.44

0.17

0.00

0.15

Average impulsivity

2.00

1.98

2.15

1.86

Average delinquency

1.14

2.10

1.71

1.31

Average age

Cluster size

16

6

10

9.54

0.74). This cluster was substantially larger than the average cluster size of 9.54 members, with 16 members. Group 25 also had a greater percentage of nonwhite students (44%) and female (88%) students than the average cluster in the network. The mean age for this cluster was below the cluster-level average age. Furthermore, the mean level of criminal behavior displayed by this cluster was slightly below average. Finally, the cluster exhibited an above-average level of impulsivity. The disaggregation of the cluster illustrated in Figure 3 revealed that three female individuals within the cluster were largely driving the high victimization rate. Two of these individuals were nonwhite, 15 years of age, and reported less criminal behavior than the average for the sample. The third individual experiencing a high level of victimization for this cluster was a White female, 17 years of age. All three individuals had above-average impulsivity. Interestingly, these three individuals were located on the periphery of the peer cluster. This pattern differs from the spatial pattern observed at the cluster level. In general, clusters experiencing the highest rates of victimization were more centrally located within the overall cluster-based network. The individuals within this cluster with the highest victimization, however, were located on the outskirts of the cluster. With a serious violent victimization rate of 8.17, the peer cluster experiencing the second highest rate of serious violent victimization is Group 34. As shown in Figure 3, this peer cluster comprised only six individuals, which is smaller than the average cluster size of 9.54. The cluster was predominantly White (83%) and 100% male. The mean age (16.7) was above the cluster-level average age. The mean rate of delinquency and the average impulsivity for this peer cluster were both above average (see Table 2). Similar to Group 25, only a few members of the cluster were driving the high-victimization rate of the cluster. In this case, only two members really appeared to experience high levels of victimization. Both were White males with above-average reported delinquency. Unlike the previously discussed cluster, these two individuals experiencing the bulk of this cluster’s victimization were well connected to the other individuals within the cluster. The peer cluster experiencing the third highest violent victimization rate was Group 42, with a victimization rate of 8.00. This peer cluster comprised 10 students (see Figure 3), which is slightly above the average cluster size. The network was entirely White and predominantly male (80%). The average age (17.2) of the peer cluster was above the average of all clusters. The delinquency and impulsivity exhibited by this cluster both exceeded cluster-level averages as well. Inspection of individuals within this network

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Figure 4.

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Group 45

Group 22

Group 31

0.11

0.25

0.25

Clusters with lowest victimization.

revealed that it was two White males driving the high-victimization rate for this peer network. Both of these individuals reported higher than average delinquency and greater than average impulsivity. The individual reporting the highest violent victimization was located on the periphery of the cluster, but the individual reporting the second highest violent victimization was located at the center of the cluster. However, these two individuals were connected to one another.

Low-Victimization Clusters There were several clusters that experienced no victimization, thus there was no variation in victimization in such groups to describe. However, the peer clusters experiencing the lowest nonzero serious violent victimization rates are depicted in Figure 4. This set of clusters, with the lowest average victimization rates includes Group 45 (M 5 0.11), Group 22 (M 5 0.25), and Group 31 (M 5 0.25). These three groups were comprised of nine, four, and four individuals, respectively and were very similar to one another. The clusters were predominantly White, with only one nonwhite member across all three groups. All three clusters were entirely female and older, on average, than other clusters in the network. The average delinquency reported for each of these clusters is lower than the cluster average. One of the three clusters reported greater average impulsivity than other clusters in the network; however, the other two clusters experiencing the least violent victimization reported below-average impulsivity. Obviously, victimization was not pervasive across members of low-victimization clusters. When serious victimization existed at all within these groups, it tended to occur to only one member of the cluster.

CONCLUSIONS AND DISCUSSION The objectives of this study were to describe victimization between and within peer clusters comprising an overall high school friendship network. We accomplished this by doing

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the following: (a) visually displaying peer clusters within the overall network structure of the school; (b) assessing (through SNA and HLM) the variation in violent victimization across peer clusters in the overall network; (c) examining the sociospatial relationships that existed between high- and low-victimization peer clusters; and (d) providing quantitative descriptions of the peer clusters, along with the individuals within these peer clusters that experienced the highest and lowest victimization rates. Analysis surrounding these objectives revealed some interesting patterns. Foremost, violent victimization varied significantly across peer clusters within the high school network examined—that is, cluster membership mattered for violent victimization. Furthermore, visualization of the network of peer clusters (by level of victimization) indicated that clusters with the highest levels of victimization were located in the central part of the overall network of clusters, although they were not closely tied to one another. Clusters with the lowest levels of violent victimization were on the outskirts of this network. Description of clusters at the high and low ends of the serious victimization continuum revealed interesting comparisons, as was summarized in Table 2. In general, the descriptive findings provide support for lifestyle exposure theory and the principle of homogamy in that the high-victimization peer clusters included in the study were rather homogenous and appeared to provide an important contextual opportunity for victimization. Those clusters experiencing the highest victimization typically shared characteristics of high-risk demographic groups, thus placing them at a higher risk for victimization. These groups also appeared to have lifestyles and positions within the broader social network that provided ample exposure to potentially motivated offenders. For example, aside from the anomaly of Group 25, the clusters at the high end of the continuum were predominantly male, disproportionately nonwhite, older, and centrally located within the overall peer network structure. Two of the three clusters on the high end of the victimization continuum exhibited higher than average delinquency. The clusters that experienced the lowest non-zero victimization were even more homogenous than those at the high end of the continuum. The clusters however, were comprised of low-risk demographic groups. For instance, they were exclusively female and White (except for one individual). Furthermore, the groups with low victimization rates were located on the periphery of the overall social network, supporting the idea that they were least exposed to potential offenders. Finally, these clusters reported below-average delinquency, which also serves as a protective factor against victimization for the individuals within the group. When the highest victimization peer clusters were unpacked and individual-level variation in victimization within the groups was explored, it was found that one or two individuals within each cluster tended to drive the cluster-level victimization rate. These individuals were largely male, older, more impulsive, and involved in delinquency. The locations of these individuals within the clusters varied, with some individuals being well connected within the cluster, whereas others were located on the periphery of the cluster.

Limitations and Future Directions Although this study allowed a unique view of victimization within peer network and cluster contexts, there are important accompanying limitations that should be considered. First, this study is not explanatory in nature but, rather, descriptive. The data presented do not allow for an explanation of how the attributes examined influence victimization. However, they do provide an important glimpse into the potential explanatory roles of individual

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and cluster characteristics within a larger network. Second, the sample used herein is somewhat limited, being drawn from a single school within a predominantly rural state. As such, the sample was not necessarily representative of all U.S. high school students and, therefore, generalizability may be limited. However, this sample did allow for a very high level of participation among members of the social network targeted—that is, almost the entire school population was included in the sample. This is vital to the successful study of networks. Furthermore, the description of victimization within and between peer clusters revealed by these data supported theory (i.e., routine activities theory; principle of homogamy) and previous individual-level analyses using national data. Hence, we do not suspect that the data are anomalous in any way. In closing, limitations regarding analytic techniques (not explanatory) and generalizability are recognized. However, we assert that this study makes a unique contribution to the literature on adolescent victimization by taking an initial step toward understanding patterns of victimization both between and within peer clusters comprising an overall high school friendship network. Future studies can build on the description provided here and more fully develop explanatory models of adolescent victimization that estimate individual and peer cluster characteristics simultaneously, in multivariate, multilevel analyses. Such analyses would allow for rigorous assessment of contextual effects associated with peer clusters, providing clearer understanding about whether peer clusters are important contexts in explaining the risk of adolescent violent victimization and if so, which characteristics of clusters matter most as either risk or protective factors.

NOTES 1. Haynie and others using the National Longitudinal Survey of Adolescent Health (Add Health data) primarily analyzed school-based friendship networks because of the research design. Surveys in which respondents were asked to identify close friends were administered in school, and a school roster was attached to surveys for students to use in identifying their friends. Although some respondents still listed friends outside of school, such friends had to be dropped from analyses because no corresponding characteristics of these nonschool friends were known to researchers. 2. Haynie (2001) used the term peer network rather than peer cluster to describe her findings. However, her use of peer network is similar to the term peer cluster used in this study. Haynie did not examine the linkages among clusters within a broader social network (what we term peer network), thus she did not have the two types of peer contexts that we have here. 3. Similar to Haynie (2001), Schreck et al. (2004) examined only one type of peer group—what we term peer cluster (although like Haynie, they used the term peer network to depict this sort of group). 4. In contrast, Schreck and his colleagues (2004) characterized individuals within clusters. Individuals were characterized according to the density of their cluster and their popularity and centrality within the cluster. 5. We also explored minor violent victimization measured as the number of times the respondent reported experiencing the following during the summer immediately preceding the survey: (a) having been pushed/grabbed/shoved, or (b) having been punched/hit/slapped/kicked. Each item was coded as the number of times ranging from 0 5 zero times to 10 5 10 or more times. Scores from the two items were summed to create a measure of total minor violent victimization. Although these victimization experiences could potentially include serious assaults, the prevalence of such experiences (32% of students reporting) suggests that most involved minor aggression. However, this measure did not vary significantly across peer clusters, so we chose not to report findings pertaining to minor violent victimization here. 6. See Johnson (1967) for an in-depth description of hierarchical subgroup clustering.

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7. The geodesic distance between two nodes consists of the length of the path (i.e., the number of ties or lines) between the two nodes (Borgatti, DeJordy, & Halgin, 2008). 8. HLM models are capable of appropriately recognizing that students within the same network may be more similar to one another compared to students of a different network. In other words, HLM recognizes the nonindependence among students nested within peer network contexts. Neglecting to account for this nonindependence can result in biased standard errors, increasing the likelihood of reaching erroneous conclusions regarding cross-cluster variation in victimization (Raudenbush & Bryk, 2002). Because of the skewed nature of the count-based measure of victimization, a negative binomial specification was most appropriate. 9. The density of a cluster is calculated by dividing the number of existing ties by the number of possible ties. The E-I Index provides a comparison of the ties that exist externally versus internally to the cluster. Technically, the resulting value is the calculation of the total number of external cluster member ties minus the total number of internal cluster ties, then divided by the total number of network ties.

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Wilcox, P., Land, K. C., & Hunt, S. A. (2003). Criminal circumstance: A dynamic multicontextual criminal opportunity theory. New York, NY: Aldine de Gruyter. Wilcox, P., Tillyer, M. S., & Fisher, B. S. (2009). Gendered opportunity?: School-based adolescent victimization. Journal of Research in Crime and Delinquency, 46, 245–269. Acknowledgments. This research was sponsored, in part, by grant DA-11317 from the NIDA, Richard Clayton, PI. Neither Dr. Clayton nor NIDA are responsible for the findings presented herein. Correspondence regarding this article should be directed to Kristin Swartz, PhD, University of Louisville, Department of Justice Administration, 210 Brigman Hall Louisville, KY 40292. E-mail: [email protected]

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METHODOLOGICAL APPENDIX Our overall goal was to identify clusters within the larger network of individuals (in a sense, breaking the network of individuals down into a smaller number of nodes by placing individuals within cohesive clusters). The hierarchical clustering of geodesic distances technique determines group clusters using a bottom-up approach instead of a top-down approach. In other words, the technique starts with all individuals in separate clusters and combines clusters via a software algorithm (see, Johnson, 1967). “Natural breaking points” exist where smaller cohesive clusters could conceivably get merged into larger clusters (through the bottom-up approach), yet cohesiveness of the resulting merged clusters does not necessarily improve. So, natural breaking points are helpful in delineating optimally cohesive groups. At the same time, it was not particularly useful for our purposes to examine extremely small peer clusters. In fact, very small cluster sizes made estimation of statistical variation in victimization across the clusters unreliable. Thus, in determining the most appropriate depiction of the peer clusters representative of the entire network of students, we had to balance the need for adequately sized clusters with the need for cohesive (and thus theoretically meaningful) clusters. We assessed the natural breaking points among the groupings yielded from the hierarchical clustering of geodesic distances, whereby smaller clusters were merged into larger clusters. This assessment consisted of, first, the visual examination of the groupings on either side of a natural breaking point with the purpose of ensuring that the merger of smaller clusters to larger clusters occurred at optimal points. Second, we assessed the cluster cohesion in clusters surrounding natural breaking points through calculation of the average group density and E-I Index.9 Cluster cohesion is important in determining the optimum set of clusters because it provides an assessment of the strength of the ties among the actors in a cluster. The existence of this strength of ties correlates to the level of social forces that exist and that can potentially be exerted on members of the group (Wasserman & Faust, 1995). Comparison of the set of clusters we decided upon in comparison to other possible sets we could have used to depict the network yielded the following conclusions. First, the examination of various groupings with a higher number of clusters (i.e., those with more clusters than the set ultimately selected) consisted mostly of additional one-person clusters (i.e., isolates). Second, the merger of any additional clusters among the set selected failed to notably improve values of group cohesion while appreciably increasing the size of the clusters. Following the selection described earlier, some small clusters still remained. Thus, the final stage of group determination consisted of merging individuals from those clusters with only one to three members into an existing larger cluster based on successive hierarchical clustering mergers. In other words, if the individual existed in a cluster of n 5 1 to n 5 3, for the selected set of groupings, it was merged into one of the other clusters. The individual was merged into the cluster that the hierarchical clustering algorithm would have added it to in successive group mergers. To assess consistency of this process, we checked to ensure that the group was the one in which the individual had the most ties.

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