<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.0 20120330//EN" "JATS-archivearticle1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" article-type="research-article"><?properties manuscript?><front><journal-meta><journal-id journal-id-type="nlm-journal-id">101550224</journal-id><journal-id journal-id-type="pubmed-jr-id">38936</journal-id><journal-id journal-id-type="nlm-ta">Psychol Violence</journal-id><journal-id journal-id-type="iso-abbrev">Psychol Violence</journal-id><journal-title-group><journal-title>Psychology of violence</journal-title></journal-title-group><issn pub-type="ppub">2152-0828</issn><issn pub-type="epub">2152-081X</issn></journal-meta><article-meta><article-id pub-id-type="pmid">30151328</article-id><article-id pub-id-type="pmc">6108089</article-id><article-id pub-id-type="doi">10.1037/vio0000210</article-id><article-id pub-id-type="manuscript">HHSPA982012</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>Examining Within-Person and Between-Person Associations of Family Violence and Peer Deviance on Bullying Perpetration among Middle School Students</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Grant</surname><given-names>Nickholas</given-names></name><degrees>MA</degrees><aff id="A1">University of Illinois, Dept. of Psychology, 603 East Daniel Street, Clinical and Community Division, Champaign, IL 61820-6925, Phone: 217-333-0631</aff><!--<email>ngrant4@illinois.edu</email>--></contrib><contrib contrib-type="author"><name><surname>Merrin</surname><given-names>Gabriel J.</given-names></name><degrees>PhD</degrees><aff id="A2">University of Victoria, Dept. of Psychology, 3800 Finnerty Road (Ring Rd), Victoria, British Columbia V8P 5C2, Phone: (250)-472-4823</aff><!--<email>gmerrin@uvic.ca</email>--></contrib><contrib contrib-type="author"><name><surname>King</surname><given-names>Matthew T.</given-names></name><degrees>MS</degrees><aff id="A3">University of Illinois, Dept. of Educational Psychology, 216 Psychology, 1310 S. Sixth Street, Counseling Psychology Division, Champaign, IL 61820-6925, Phone: ?</aff><!--<email>king56@illinois.edu</email>--></contrib><contrib contrib-type="author"><name><surname>Espelage</surname><given-names>Dorothy L.</given-names></name><degrees>PhD</degrees><aff id="A4">University of Florida, Dept. of Psychology, 945 Center Drive, Gainesville, FL 32611-2250, Phone: 352-273-2139</aff><!--<email>espelage@ufl.edu</email>--></contrib></contrib-group><pub-date pub-type="nihms-submitted"><day>25</day><month>7</month><year>2018</year></pub-date><pub-date pub-type="epub"><day>2</day><month>8</month><year>2018</year></pub-date><pub-date pub-type="ppub"><month>1</month><year>2019</year></pub-date><pub-date pub-type="pmc-release"><day>01</day><month>1</month><year>2020</year></pub-date><volume>9</volume><issue>1</issue><fpage>18</fpage><lpage>27</lpage><!--elocation-id from pubmed: 10.1037/vio0000210--><self-uri xlink:href="http://psycnet.apa.org/fulltext/2018-36392-001.html"/><abstract><sec id="S1"><title>Objective</title><p id="P1">Family violence and peer deviance have shown to be related to bullying perpetration. Although there are several cross-sectional investigations of these two factors in relation to bullying behavior, no known studies have examined their interactive associations. The current study examines the longitudinal associations of both factors on bullying perpetration using a multi-level approach.</p></sec><sec id="S2"><title>Method</title><p id="P2">Participants included 1,194 5<sup>th</sup>, 6<sup>th</sup>, and 7<sup>th</sup> grade students from four middle schools in a Midwest county. We examined the main and interactive relations between how individual reports of family violence and peer deviance fluctuated over time (i.e., within-person effects) and how average reported differences between individuals (i.e., between-person effects) were associated with levels of bullying perpetration.</p></sec><sec id="S3"><title>Results</title><p id="P3">Positive main effects were found for both family violence and peer deviance on levels of bullying perpetration. Within-person effects indicated that, on average, fluctuations from one&#x02019;s &#x02018;typical&#x02019; levels in family violence and peer deviance were associated with contemporaneous increases in bullying perpetration. A statistically significant time-variant interaction revealed that within-person family violence significantly exacerbated the relationship between within-person peer deviance and bullying perpetration. Furthermore, a statistically significant cross-level interaction revealed that the association between within-person peer deviance and bullying perpetration was stronger for individuals with higher average levels of between-person family violence (+1SD) compared to lower levels (&#x02212;1SD).</p></sec><sec id="S4"><title>Implications</title><p id="P4">These findings provide a more nuanced lens from which to view the co-occurring relations between family and peer ecologies. Prevention and intervention efforts should target peer relations to reduce the effect of family violence on bullying behavior.</p></sec></abstract><kwd-group><kwd>Bullying</kwd><kwd>Peer Deviance</kwd><kwd>Delinquent Peers</kwd><kwd>Family Violence</kwd><kwd>Domestic Violence</kwd></kwd-group></article-meta></front><body><p id="P5">Bullying is a pervasive issue today: approximately 21% of students between the ages of 12&#x02013;18 reported being bullied in 2015 (<xref rid="R33" ref-type="bibr">Musu-Gillette et al., 2018</xref>). Bullying perpetration is a multifaceted phenomenon that is characterized as the intentional, unsolicited, and repeated use of physical (e.g., hitting, kicking, pushing, shoving), verbal (e.g., name-calling, teasing), and/or social (e.g., spreading rumors, social exclusion) aggression toward one&#x02019;s peers to inflict physical, psychological, social, or educational harm (<xref rid="R21" ref-type="bibr">Gladden, Vivolo-Kantor, Hamburger, &#x00026; Lumpkin, 2014</xref>; <xref rid="R36" ref-type="bibr">Olweus, 1997</xref>). The relationship between perpetrator and victim is often characterized by an imbalance of strength and power, used to coerce a person of lesser strength or status (<xref rid="R35" ref-type="bibr">Olweus, 1993</xref>). If not prevented early, children are at risk for developing psychopathology in adulthood (<xref rid="R10" ref-type="bibr">Copeland, Wolke, Angold, &#x00026; Costello, 2013</xref>).</p><p id="P6">Over the last four decades, scholars have found that bullying is particularly prevalent in educational settings such as pre-school, primary, and secondary institutions (<xref rid="R23" ref-type="bibr">Hymel &#x00026; Swearer, 2015</xref>). Depending on the student&#x02019;s race/ethnicity, gender, and age, prevalence rates can vary. For instance, studies found race and ethnicity differences in levels of bullying perpetration, with African-American/Black and Latino youth reporting higher involvement in comparison to their white counterparts (<xref rid="R3" ref-type="bibr">Albdour &#x00026; Krouse, 2014</xref>). Likewise, males have reported bullying others more frequently than females (<xref rid="R37" ref-type="bibr">Pellegrini &#x00026; Bartini, 2000</xref>). Moreover, studies have found significant grade differences, with much higher levels of bullying observed in middle and secondary institutions than in elementary institutions; yet, levels of bullying others tend to decrease once at the secondary level (<xref rid="R17" ref-type="bibr">Espelage, Hong, Rao, &#x00026; Thornberg, 2015</xref>; <xref rid="R38" ref-type="bibr">Pellegrini &#x00026; Long, 2002</xref>; <xref rid="R37" ref-type="bibr">Pellegrini &#x00026; Bartini, 2000</xref>).</p><p id="P7">One possible explanation for the development of bullying perpetration comes from social learning theory, which suggests that &#x0201c;most human behavior is learned observationally through modeling: from observing others, one forms an idea of how new behaviors are performed, and on later occasions this coded information serves as a guide for action&#x0201d; (<xref rid="R7" ref-type="bibr">Bandura &#x00026; Walters, 1977</xref>, pg. 22). Specifically, in relation to physically aggressive and violent behavior, children who are exposed to violent behaviors within their immediate family and/or peer contexts may learn and accept such behavior as an appropriate method for dealing with conflict or reaching a desired goal (<xref rid="R2" ref-type="bibr">Akers, 2011</xref>; <xref rid="R6" ref-type="bibr">Bandura, 1973</xref>). Indeed, longitudinal studies have shown that exposure to family violence is related to high levels of bullying behavior (<xref rid="R5" ref-type="bibr">Bauer et al., 2006</xref>; <xref rid="R28" ref-type="bibr">Knous-Westfall, Ehrensaft, MacDonell, &#x00026; Cohen, 2012</xref>; <xref rid="R30" ref-type="bibr">Low &#x00026; Espelage, 2014</xref>); however, peer deviance has only demonstrated this association in cross sectional studies (<xref rid="R15" ref-type="bibr">Espelage, Bosworth, &#x00026; Simon, 2000</xref>; <xref rid="R19" ref-type="bibr">Ferguson, Miguel, &#x00026; Hartley, 2009</xref>). As such, there has been no examination of the longitudinal, joint associations of exposure to family violence and peer deviancy on levels of bullying perpetration to date. The current study aims to provide a better understanding of these joint associations across a middle school sample.</p><sec disp-level="2" id="S6"><title>Family Violence, Peer Deviance, and Bullying</title><p id="P8">According to the <xref rid="R45" ref-type="bibr">United States Department of Justice (2015)</xref>, family violence (also known as domestic violence) is defined as any pattern of violent, threatening, coercive or controlling behavior, including physical injury, direct or indirect threats, sexual assault, emotional and psychological abuse, damage to property, economic control, or social exclusion against current or past family members, a current or former intimate partner, or between individuals within a shared living space.</p><p id="P9">A recent review by <xref rid="R46" ref-type="bibr">Voisin and Hong (2012)</xref> highlighted several cross-sectional studies, yet, few longitudinal studies have found associations between forms of family violence and bullying behavior. For example, <xref rid="R28" ref-type="bibr">Knous-Westfall and colleagues (2012)</xref> conducted a 25-year longitudinal study investigating the impact of parental intimate partner violence (IPV) on relational and physical bullying and victimization across three generations. The authors measured both minor forms of physical IPV (e.g., hitting and grabbing) and psychological violence (e.g., physical threat) and more severe measures of IPV (i.e., violence that resulted in serious injuries). When controlling for externalizing and internalizing problems, they found that minor forms of IPV did not significantly predict physical bullying or relational peer bullying; however, they did find that exposure to severe IPV was significantly predictive of physical bullying in males. Another prospective longitudinal, multi-generational study conducted by <xref rid="R5" ref-type="bibr">Bauer and colleagues (2006)</xref>, examined the relationships among IPV, physical and relational forms of bullying, internalizing behavior problems, and social attention problems in children. They found that physical bullying was related to IPV based on parent report.</p><p id="P10">Outside the family context, peer relationships also play an important role throughout adolescent development, especially during the transition to middle school. According to <xref rid="R38" ref-type="bibr">Pellegrini and Long (2002)</xref>, it is a critical period in early adolescent development where youth begin to explore their social identity and status and may engage in negative peer relationships, which can influence problem behaviors (<xref rid="R41" ref-type="bibr">Salmivalli, 2010</xref>). For instance, scholars have found that peer deviance&#x02014;meaning to have peers who engage in criminal (e.g., theft, drug use, weapon carrying) and aggressive and violent behavior (e.g., hitting, fighting, damaging property)&#x02014;is a common risk factor for the development of externalizing behavior problems (Cotter, Wu, &#x00026; Smokowski, 2015; <xref rid="R20" ref-type="bibr">Gifford-Smith, Dodge, Dishion, &#x00026; McCord, 2005</xref>). With regard to bullying, studies have found a relation between peer deviance and bullying perpetration (e.g., <xref rid="R15" ref-type="bibr">Espelage et al., 2000</xref>; <xref rid="R19" ref-type="bibr">Ferguson et al., 2009</xref>). For example, <xref rid="R19" ref-type="bibr">Ferguson and colleagues (2009)</xref> found that depressed mood and associating with deviant peers were the strongest predictors of child self-reported bullying and rule-breaking behaviors.</p><p id="P11">As students begin to matriculate into secondary education, researchers have recognized the dynamic association between family and peer ecologies on the development of bullying behavior (<xref rid="R30" ref-type="bibr">Low &#x00026; Espelage, 2014</xref>; <xref rid="R39" ref-type="bibr">Pepler et al., 2008</xref>). For instance, <xref rid="R39" ref-type="bibr">Pepler and colleagues (2008)</xref> examined different developmental trajectories&#x02014;from early to late adolescence&#x02014;of youth bullying and general aggression behavior in 800 children, while also assessing for individual (i.e., bullying, moral disengagement), family (i.e., parental trust, parental monitoring, and conflict with parents), and peer (i.e., physically aggressive peers, conflict with peers, and susceptibility to peer pressure) factors. Four bullying trajectories were found: high-bullying group, early-moderate bullying group, moderate bullying group, and non-bullying group. When comparing the groups and the associated risk and protective factors, they found that students in the high bullying group showed little regard for the welfare or feelings for others, often came in conflict with parents and peers, and associated with peers who bully, especially at the beginning of mid-adolescence. In addition, a longitudinal study conducted by <xref rid="R30" ref-type="bibr">Low and Espelage (2014)</xref> found significant interactions when examining community violence exposure and bullying and victimization, in relation to individual (e.g., impulsivity and delinquent behavior), peer (e.g., deviant peers), and familial (e.g., parental monitoring) influences. They found that parental monitoring buffered the effects of community violence exposure on bullying by reducing delinquent behavior and involvement with deviant peers. Overall, these studies demonstrate that peer and family influences not only predict but having moderating effects on bullying behavior.</p><p id="P12">Despite previous findings suggesting that children&#x02019;s social context are important avenues by which to explore the development of bullying behavior, studies to date examining the joints effects of family violence and peer deviance have been limited to cross-sectional studies (<xref rid="R15" ref-type="bibr">Espelage et al., 2000</xref>; <xref rid="R19" ref-type="bibr">Ferguson et al., 2009</xref>). One limitation of cross-sectional studies is that statistical differences in the variables of interest are typically inferred across people (i.e., between-person effects), while disregarding how variables may vary within individuals&#x02019; over time (i.e., within-person effects; (Curran &#x00026; Bauer, 2012). For instance, when applying psychological theories of behavior (e.g., social learning theory), empirical research investigating these patterns often use between-person data (e.g., cross-sectional assessments) or model between-person effects, even though implicitly or explicitly implying within-person processes (i.e., an error of inference; Curran &#x00026; Bauer, 2012). However, an underlying presumption of social learning theory is that an individual&#x02019;s behavior will change (i.e., within-person processes) because of what they learn and observe within their social context (<xref rid="R6" ref-type="bibr">Bandura, 1973</xref>). Studies applying this theory often ignore that these factors may fluctuate over time, and that these fluctuations themselves may be important determinants of change in an individual&#x02019;s behavior (Curran &#x00026; Bauer, 2012). For example, <xref rid="R32" ref-type="bibr">Merrin, Davis, Berry, D&#x02019;Amico, and Dumas (2016)</xref> examined both the between- and within-person associations of crime, substance use, and social risk, using structural equation modeling (i.e., auto-regressive latent trajectory model with structured residuals). Despite past research showing that crime and substance use have a reciprocal relation, particularly when examining differences across individuals, the authors found that this relation was not evident when taking into consideration how individuals&#x02019; reports of crime and substance use fluctuated over time. As such, examining both within- and between-person effects would allow for a more substantive, developmentally meaningful, and statistically robust examination as well as have significant implications for theory (Curran &#x00026; Bauer, 2012). Thus, the current study utilizes this framework as a tool to investigate the role of adult and peer influences on bullying behavior, while also employing a multilevel approach in hopes of expanding on the literature that applies social learning theory to bullying behavior.</p></sec><sec id="S7"><title>The Current Study</title><p id="P13">Although findings from <xref rid="R30" ref-type="bibr">Low and Espelage (2014)</xref> and <xref rid="R39" ref-type="bibr">Pepler and colleagues (2008)</xref> demonstrate that there is a dynamic process between relational antecedents in both the peer and familial contexts that affect the development of bullying behavior over time, no longitudinal study, to date, has examined the interactive association of family violence and peer deviance. By employing a multilevel approach to examine both within- and between-person variables together, and how they may interact with each other (cross-level interaction), the current study examines the extent to which students&#x02019; fluctuations in exposure to family violence and peer deviance across time respectively and interactively affect their levels of bullying perpetration. In addition, there is the potential for moderating effects on bullying behavior to be found between family violence and peer deviance, especially because peer influences play a critical role during adolescence (<xref rid="R38" ref-type="bibr">Pellegrini &#x00026; Long, 2002</xref>). For example, for students reporting higher levels of bullying in relation to heightened exposure to family violence over time, this association may also be moderated by reported fluctuations in exposure to peer deviance (and vice-versa with family violence as a moderator). Our findings will provide a more dynamic investigation of how reported levels of bullying may vary at different levels of family and peer deviance exposure, thus, expanding on the literature that applies social learning theory to bullying behavior.</p><sec id="S8"><title>Research Questions</title><p id="P14">The current study used a large sample of middle school students to examine the longitudinal associations (4 waves) between family violence and peer deviance on bullying perpetration using a multilevel design. We sought to answer several research questions, including (a) on average, are there increases in bullying perpetration across middle school?; (b) on average, are higher levels of family violence and peer deviance predictive of higher levels of bullying perpetration respectively (i.e., between-person effects)?; (c) are time-specific fluctuations from one&#x02019;s typical level (i.e., within-person effects) of family violence and peer deviance associated with contemporaneous increases in bullying perpetration during middle school?; and (d) are there time-specific fluctuations&#x02014;both at the within-and between-person levels as well as at the cross level&#x02014;in family violence and peer deviance associated with contemporaneous increases in bullying perpetration?</p></sec></sec><sec sec-type="methods" id="S9"><title>Methods</title><sec id="S10" sec-type="methods|subjects"><title>Participants and Procedures</title><p id="P15">Participating students in this study were asked to complete a survey seeking information about their experiences with family violence, peer deviance, and bullying perpetration. Participants included 1,194 5<sup>th</sup>, 6<sup>th</sup>, and 7<sup>th</sup> grade cohorts from four middle schools in a Midwest county. The sample was 49.6% female; age 11 to 15 years at baseline (<italic>M</italic> = 13.46); and 58.7% (<italic>n</italic> = 701) identified as African American, 30.9% (<italic>n</italic> = 369) identified as White, and 10.4% (<italic>n</italic> = 124) identified as Other. Over two years, data were collected in the Spring and Fall semester for a total of four time points. Sample sizes for the 5<sup>th</sup> (wave 1 = 337, wave 2 = 303, wave 3 = 294, wave 4 = 273), 6<sup>th</sup> (wave 1 = 411, wave 2 = 379, wave 3 = 358, wave 4 = 341), and 7<sup>th</sup> (wave 1 = 444, wave 2 = 403, wave 3 = 373, wave 4 = 0) grade cohorts differed slightly over time except for the 7<sup>th</sup> grade cohort at wave 4. The 7<sup>th</sup> grade cohort were not followed into high school and thus only contribute three waves of data.</p><sec id="S11"><title>Parental consent</title><p id="P16">The current study was formally announced in school newsletters, school district newsletters, and e-mails from the principals prior to the Spring of 2008. Upon receiving approval from the institutional review board (IRB) and district school board, a waiver of active consent was distributed to each parent/guardian of the students enrolled in the school. The passive consent included a letter containing information about the purpose of the study, and parents/guardians were also invited to attend information meetings held in each community. Parents/guardians who did not wish to have their child participate in the study were asked to sign the information letter and return it to the researchers.</p><p id="P17">After parents/guardians turned in these forms, it was determined that 95% of students initially participated in the study. Students were asked to consent to participate in the study through an assent procedure described on the coversheet of the survey distributed to all remaining students. Surveys were later de-identified with code numbers so researchers could track their responses over multiple time points and ensure confidentiality.</p></sec><sec id="S12"><title>Survey administration</title><p id="P18">Students were initially informed about the nature of the study by one of the six trained research assistants, the principal investigator, or another faculty member who administered the survey. Surveys were conducted each semester (Spring and Fall) in classrooms ranging from 10 to 25 students. The survey took approximately 40&#x02013;45 minutes to complete. Members of the research team ensured confidentiality by ensuring students were sitting far enough away from one another. The survey was administered and read aloud while students responded individually.</p><p id="P19">Because the content of the survey could be upsetting to students, researchers assured them that their participation in the study was entirely voluntary and that they could skip any question or stop participating in the survey at any time. At least one appropriately trained doctoral-level psychology student was on site to provide immediate support to any student and direct him or her to the appropriate resources. Students were also provided the contact information of the research team to seek more information about the study. Also, students were reminded about in-school resources available to them (e.g., guidance counselors) should they feel the need to talk to someone as a result of completing the survey.</p></sec></sec><sec id="S13"><title>Measures</title><sec id="S14"><title>Demographics</title><p id="P20">Participants completed a demographic questionnaire that asked about their sex, age, grade, and race/ethnicity. Participants were given six options for their race/ethnicity: African American (not Hispanic), White (not Hispanic), Asian, Native American, Hispanic, and other (with an option to provide the most appropriate racial/ethnic descriptor).</p></sec><sec id="S15"><title>Bullying perpetration</title><p id="P21">The Illinois Bully Scale (<xref rid="R16" ref-type="bibr">Espelage &#x00026; Holt, 2001</xref>) is a nine-item scale assessing the frequency of bullying at school. Students were asked to recall how frequently they teased others, upset others for the fun of it, excluded others from their group of friends, helped harass others, and threatened to hit or hurt another student. Response options range from &#x0201c;never&#x0201d; to &#x0201c;7 or more times&#x0201d; in the past 30 days. Exploratory and confirmatory factor analysis has demonstrated the construct validity of this scale (<xref rid="R16" ref-type="bibr">Espelage &#x00026; Holt, 2001</xref>). In the development sample, factor loadings for these items ranged from .52 to .75, and this factor accounted for 31% of the variance in the factor analysis (<xref rid="R16" ref-type="bibr">Espelage &#x00026; Holt, 2001</xref>). This scale and the Youth Self-Report Aggression Scale correlated moderately (<italic>r</italic> = .65; <xref rid="R1" ref-type="bibr">Achenbach, 1991</xref>), supporting the notion that it was somewhat distinct from general aggression. Cronbach&#x02019;s alphas ranged from .86 &#x02013; .90 across assessment waves.</p></sec><sec id="S16"><title>Peer deviance</title><p id="P22">The Friend&#x02019;s Delinquent Behavior-Denver Youth Survey is a 7-item scale (<xref rid="R24" ref-type="bibr">Institute of Behavioral Science, 1987</xref>) that asks participants to report how many of their friends within the last year &#x0201c;Hit or threatened to hit someone,&#x0201d; &#x0201c;Purposely damaged or destroyed property that did not belong to them,&#x0201d; and &#x0201c;Used alcohol&#x0201d;, to name a few items. Response options were &#x0201c;None,&#x0201d; &#x0201c;Very Few,&#x0201d; &#x0201c;Some of them,&#x0201d; &#x0201c;Most of them,&#x0201d; and &#x0201c;All of them.&#x0201d; Cronbach&#x02019;s alphas ranged from .85 &#x02013; .88 across assessment waves.</p></sec><sec id="S17"><title>Family violence</title><p id="P23">The Family Con ict and Hostility Scale (<xref rid="R43" ref-type="bibr">Thornberry, Krohn, Lizotte, Smith, &#x00026; Tobin, 2003</xref>) was used to measure the level of perceived con ict and hostility in a student&#x02019;s family environment. This scale contains three items from a larger survey designed for the Rochester Youth Development Study: &#x0201c;How often is there yelling, quarreling, or arguing in your household?&#x0201d;, &#x0201c;How often do family members lose their temper or blow up for no good reason?&#x0201d;, and &#x0201c;How often are there physical ghts in the household, like people hitting, shoving, or throwing things?&#x0201d; Response options ranged from &#x0201c;never&#x0201d; to &#x0201c;always&#x0201d; on a four-point scale. Cronbach&#x02019;s alphas ranged from .79 &#x02013; .81 across assessment waves.</p></sec></sec><sec id="S18"><title>Analytic Plan</title><p id="P24">To address our research questions, we fit a taxonomy of growth models to our data (<xref rid="R42" ref-type="bibr">Singer &#x00026; Willett, 2003</xref>). We began by establishing a plausible functional form for individual&#x02019;s levels of bullying perpetration over time. We tested a series of unconditional and conditional models that included a null model, random intercept, fixed linear growth, and a random linear growth model. Fixed linear growth was not found to be significant (<italic>b</italic> = &#x02212;.006, SE = .008, <italic>p</italic> = .568) and random linear growth did not improve model fit (M1 to M2; &#x00394;LR = 0.30, &#x00394;<italic>df</italic> = 1, <italic>p</italic> = .596), suggesting that there was no significant average change in bullying over the four waves. As such, these growth parameters were removed from subsequent analysis. We also fit random intercept models for our main predictors (family violence and peer deviance) to assess whether there were meaningful variation at both the within- and between-person levels. All models were nested and tested based on significant reductions in &#x02212;2*log-likelihood using deviance tests.</p><p id="P25">In proceeding models, we addressed our research questions by examining systematic groups of conditional models. In Model 2, we controlled for age, race, and sex. For Model 3, we tested the within- and between-person main effects of family violence. We then added the within- and between-person main effects of peer deviance on individual levels of bullying perpetration in Model 4. Model 5, the final model in <xref rid="FD1" ref-type="disp-formula">Equation 1</xref>, we tested all possible interactions (within-person, between-person, and cross-level) between peer deviance and family violence on bullying perpetration. We excluded non-significant interactions for parsimony, leaving only two hypothesized interactions that examined peer deviance as a moderator of the relation between family violence and bullying in our final model. On levels of bullying perpetration, we estimated the within-person interactive effect of peer deviance and family violence. In addition, we allowed within-person peer deviance to vary as a function of between-person family violence. The stochastic part of the model allowed the intercept and within-person peer deviance to vary randomly across people.</p><p id="P26">Centering strategies are very important in multilevel models because they help separate the variance into different groups (e.g., within-person and between-person). Between-person, time-invariant predictors (level 2) were grand-mean-centered and again refer to average differences between people over time. Within-person, time-varying predictors (level 1) were person-mean-centered and again refer to time specific fluctuations from an individual&#x02019;s &#x02018;typical&#x02019; level (i.e., individual&#x02019;s average). By using these centering techniques, we could partition variance in our variables at two respective levels of analysis making them orthogonal to one another (<xref rid="R44" ref-type="bibr">Tofighi &#x00026; Enders, 2007</xref>). As such, individuals are treated as their own control, thereby adjusting for all observed and unobserved between-person (level 2) confounds.</p><p id="P27">To address non-normality, we used the Robust Maximum Likelihood (MLR) estimator available in Mplus 7.4 (<xref rid="R34" ref-type="bibr">Muth&#x000e9;n &#x00026; Muth&#x000e9;n, 1998&#x02013;2014</xref>). More specifically, we evaluated the extent to which our data were skewed and adjusted for the small amount of skewness we found across all variables by using MLR. To check these estimates, we also bootstrapped our standard errors (10,000), reran all models, and found the same results. Attrition in the current sample ranged from approximately 15&#x02013;20% over time. However, it should be noted that individuals that were in 7<sup>th</sup> grade at baseline transitioned to high school at wave 3 and thus do not contribute any information at wave 4. To address missing data, we fit all our models using full information maximum likelihood (FIML). Unlike listwise deletion, FIML allows participants to contribute all available information they have available without the need to remove participants due to missing data, unless participants have missing values on all the predictor variables. As such, data from all 1,194 participants were included. We took specific steps to examine the missing data patterns. First, we tested the extent to which our data was missing completely at random (MCAR) using Little&#x02019;s (1998) random MCAR test (<xref rid="R14" ref-type="bibr">Enders, 2010</xref>). The test for bullying perpetration was significant (<italic>X</italic><sup>2</sup> = 67.17, <italic>df</italic> = 28, <italic>p</italic> &#x0003c; .001), and indicated that the data were not MCAR. While there is no formal method for testing the missing at random (MAR) assumption without knowing the values of the missing dependent variable (i.e., bullying perpetration), we then examined the extent to which missing data were associated with sex and race. There were no differences in missing data patterns between males and females on bullying perpetration at wave 1 (<italic>X</italic><sup>2</sup> = 1.53, <italic>df</italic> = 1, <italic>p</italic> = .217), wave 2 (<italic>X</italic><sup>2</sup> = 0.42, <italic>df</italic> = 1, <italic>p</italic> = .515), or wave 4 (<italic>X</italic><sup>2</sup> = 0.12, <italic>df</italic> = 1, <italic>p</italic> = .912). However, females had a larger proportion of missing data on bullying perpetration at wave 3 (<italic>X</italic><sup>2</sup> = 5.47, <italic>df</italic> = 1, <italic>p</italic> = .019). For race, White participants had a larger proportion of missing data on bullying perpetration at wave 1 (<italic>X</italic><sup>2</sup> = 69.32, <italic>df</italic> = 2, <italic>p</italic> &#x0003c; .001), wave 2 (<italic>X</italic><sup>2</sup> = 54.54, <italic>df</italic> = 2, <italic>p</italic> &#x0003c; .001), wave 3 (<italic>X</italic><sup>2</sup> = 25.28, <italic>df</italic> = 2, <italic>p</italic> &#x0003c; .001), and wave 4 (<italic>X</italic><sup>2</sup> = 33.07, <italic>df</italic> = 2, <italic>p</italic> &#x0003c; .001) compared to Black and Other races. There were no differences between Black and Other race categories on bullying perpetration. By including race and sex in our models, we adjust for any bias due to missing data on these variables.</p><p id="P28"><xref rid="FD1" ref-type="disp-formula">Equation 1</xref>:</p><list list-type="simple" id="L1"><list-item><p id="P29"><bold>Level 1:</bold>
<disp-formula id="FD1"><label>(1)</label><mml:math id="M1" display="block" overflow="scroll"><mml:mrow><mml:msub><mml:mi mathvariant="italic">Bullying</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x003b2;</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003b2;</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="italic">FamilyVio</mml:mi><mml:msub><mml:mi mathvariant="italic">lence</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mover accent="true"><mml:mi mathvariant="italic">FamilyViolence</mml:mi><mml:mo>&#x000af;</mml:mo></mml:mover><mml:mi>i</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003b2;</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mspace width="0.16667em"/><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="italic">PeerDevia</mml:mi><mml:msub><mml:mi mathvariant="italic">nce</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mover accent="true"><mml:mi mathvariant="italic">PeerDeviance</mml:mi><mml:mo>&#x000af;</mml:mo></mml:mover><mml:mi>i</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003b2;</mml:mi><mml:mrow><mml:mn>3</mml:mn><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mspace width="0.16667em"/><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="italic">FamilyVio</mml:mi><mml:msub><mml:mi mathvariant="italic">lence</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x02217;</mml:mo><mml:mi mathvariant="italic">PeerDevia</mml:mi><mml:msub><mml:mi mathvariant="italic">nce</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003b5;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula></p></list-item><list-item><p id="P30"><bold>Level 2:</bold>
<disp-formula id="FD2"><label>(2)</label><mml:math id="M2" display="block" overflow="scroll"><mml:mrow><mml:msub><mml:mi>&#x003b2;</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x003b3;</mml:mi><mml:mn>00</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003b3;</mml:mi><mml:mn>01</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="italic">Sex</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003b3;</mml:mi><mml:mn>02</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="italic">Age</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003b3;</mml:mi><mml:mn>03</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="italic">Black</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003b3;</mml:mi><mml:mn>04</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="italic">Other</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003b3;</mml:mi><mml:mn>05</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mover accent="true"><mml:mi mathvariant="italic">FamilyViolence</mml:mi><mml:mo>&#x000af;</mml:mo></mml:mover><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003b3;</mml:mi><mml:mn>06</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mover accent="true"><mml:mi mathvariant="italic">PeerDeviance</mml:mi><mml:mo>&#x000af;</mml:mo></mml:mover><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula>
<disp-formula id="FD3"><label>(3)</label><mml:math id="M3" display="block" overflow="scroll"><mml:mrow><mml:msub><mml:mi>&#x003b2;</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x003b3;</mml:mi><mml:mn>10</mml:mn></mml:msub></mml:mrow></mml:math></disp-formula>
<disp-formula id="FD4"><label>(4)</label><mml:math id="M4" display="block" overflow="scroll"><mml:mrow><mml:msub><mml:mi>&#x003b2;</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x003b3;</mml:mi><mml:mn>20</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003b3;</mml:mi><mml:mn>21</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mover accent="true"><mml:mi mathvariant="italic">FamilyViolence</mml:mi><mml:mo>&#x000af;</mml:mo></mml:mover><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula>
<disp-formula id="FD5"><label>(5)</label><mml:math id="M5" display="block" overflow="scroll"><mml:mrow><mml:msub><mml:mi>&#x003b2;</mml:mi><mml:mrow><mml:mn>3</mml:mn><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x003b3;</mml:mi><mml:mn>30</mml:mn></mml:msub></mml:mrow></mml:math></disp-formula></p></list-item></list></sec></sec><sec sec-type="results" id="S19"><title>Results</title><sec id="S20"><title>Preliminary models</title><p id="P31"><xref rid="T1" ref-type="table">Table 1</xref> presents a taxonomy of our five nested models. The preliminary models showed support for several of our hypotheses. We fit a null model to our data and calculated an intra-class correlation of .513 that indicated that approximately 51% of the variability in individuals&#x02019; levels of bullying perpetration was due to between-person differences while 49% of variability was due to within-person differences across time.</p><p id="P32">Examining the demographic variables, Model 2 indicated that girls reported significantly lower levels of bullying perpetration across time (<italic>b</italic> = &#x02212;.06, SE = .026, <italic>p</italic> = .027) compared to their boy counterparts. Compared to boys, there was a &#x02212;.12 standard deviation decrease in bullying perpetration for girls. Further, Black students reported significantly higher average levels of bullying perpetration (<italic>b</italic> = .10, SE = .026, <italic>p</italic> &#x0003c; .001), such that Black students generally reported individual levels of bullying perpetration that were .22 of a standard deviation higher compared to their White counterparts. No differences were observed among individuals in the &#x02018;Other&#x02019; group when compared to White students. Additionally, age had a positive association with bullying perpetration in preliminary models but was non-significant in subsequent models.</p></sec><sec id="S21"><title>Between-person effects and bullying perpetration</title><p id="P33">Also, in <xref rid="T1" ref-type="table">Table 1</xref>, Models 3 and 4 display the main effects of the between-person associations of family violence and peer deviance. Significant between-person main effects were found, with individuals who reported higher levels of family violence (<italic>b</italic> = .12, SE = .013, <italic>p</italic> &#x0003c; .001) and peer deviance (<italic>b</italic> = .32, SE = .02, <italic>p</italic> &#x0003c; .001) also reported higher averages levels of bullying perpetration. That is, a one standard deviation increase in family violence was associated with a .26 standard deviation increase in bullying perpetration, and a one standard deviation increase in peer deviance was associated with a .50 standard deviation increase in bullying perpetration. Further, individuals who reported higher average levels of family violence and peer deviance showed higher levels of bullying perpetration in comparison to individuals with lower levels of family violence.</p></sec><sec id="S22"><title>Within-person effects and bullying perpetration</title><p id="P34">In <xref rid="T1" ref-type="table">Table 1</xref>, Models 3 and 4 present the main effects of the (time-specific) within-person associations. The main effects model indicated that when individuals reported higher levels of family violence, they also reported higher levels of bullying perpetration at the same occasion (<italic>b</italic> = .05, SE = .016, <italic>p</italic> = .002). However, this effect was very small. Specifically, a one standard deviation increase in within-person family violence was associated with a .06 standard deviation increase in bullying perpetration. Further, when individuals reported higher peer deviance, they also reported higher levels of bullying perpetration at the same time point (<italic>b</italic> = .20, SE = .023, <italic>p</italic> &#x0003c; .001). A one standard deviation increase in within-person peer deviance was associated with a .17 standard deviation increase in bullying perpetration.</p></sec><sec id="S23"><title>Within-and between-person interactive effects</title><p id="P35">We found two significant interactions: a within-person and cross-level interaction (see Model 5 in <xref rid="T1" ref-type="table">Table 1</xref>). At the within-person level, the positive relation among within-person family violence and bullying perpetration is especially pronounced at time points when individuals report high peer deviance (<italic>b</italic> = .12, SE = .04, <italic>p</italic> = .005). <xref rid="F1" ref-type="fig">Figure 1</xref> displays the plotted slopes of peer deviance at varying levels of family violence. This pattern is carried on as individuals report higher levels of family violence at any given occasion shown by the increasing slopes. It is noteworthy that at low levels of peer deviance (&#x02212;1 standard deviation) there is no discernable difference among varying levels of family violence, indicated by the non-significant positive simple slope for low (&#x02212;1SD) peer deviance. The positive simple slopes for the other two levels were significant (see <xref rid="F1" ref-type="fig">Figure 1</xref>).</p><p id="P36">A significant cross-level interaction (<italic>b</italic> = .06, SE = .03, <italic>p</italic> = .05) showed that within-person peer deviance varied as a function of between-person family violence on increased levels of bullying perpetration. For instance, individuals with higher average levels of family violence had significantly higher levels of bullying perpetration, even at low levels of within-person peer deviance. Moreover, when individuals reported high levels of peer deviance, levels of bullying perpetration were exacerbated particularly for the high between-person family violence group (+1 standard deviation). Positive simple slopes were significant for each level (see <xref rid="F2" ref-type="fig">Figure 2</xref>).</p></sec></sec><sec sec-type="discussion" id="S24"><title>Discussion</title><p id="P37">Given the dearth of literature on the associated effects of family violence and peer deviance exposure on levels of bullying perpetration, the current study sought to examine the longitudinal associations of both factors on bullying perpetration using a large sample of middle school students. Consistent with previous studies and social learning theory (<xref rid="R15" ref-type="bibr">Espelage et al., 2000</xref>; <xref rid="R19" ref-type="bibr">Ferguson et al., 2009</xref>), our findings showed that violence exposure within individuals&#x02019; intermediate family and peer contexts was associated with higher levels of bullying behavior. Though we cannot conclude that the bullying perpetrators learned and accepted observed violent and aggressive acts as appropriate methods for dealing with conflict or reaching a desired goal, these findings still affirm the notion that there is a relationship between exposure to violence and one&#x02019;s own perpetration of it.</p><p id="P38">It is important to underscore that bullying perpetration levels did not increase over the two years of this longitudinal study. This finding was unexpected in that we believed levels of bullying would increase significantly as students transitioned into and moved through middle school (5<sup>th</sup> and 6<sup>th</sup> grade), especially because levels of bullying tend to be more pronounced during that time (<xref rid="R17" ref-type="bibr">Espelage et al., 2015</xref>; <xref rid="R38" ref-type="bibr">Pellegrini &#x00026; Long, 2002</xref>; <xref rid="R37" ref-type="bibr">Pellegrini &#x00026; Bartini, 2000</xref>). For instance, <xref rid="R38" ref-type="bibr">Pellegrini and Long (2002)</xref> found that students&#x02019; levels of bullying perpetration increased significantly from 5th to 6th grade, and then began to decrease at the beginning of the 7th grade. However, we in general only found slight changes in bullying levels across waves, which were not significantly different from 0. Also, we did not assess students in elementary school, so we were, unfortunately, unable to assess the elementary-middle school transition.</p><p id="P39">Furthermore, we found dynamic relationships between exposure to family and peer deviance in how they affect bullying perpetration. Specifically, students with relatively elevated levels of both family violence and peer deviance at a given time reported particularly high levels of bullying perpetration at that time (see <xref rid="F1" ref-type="fig">Figure 1</xref>). In addition, increasing levels of peer deviance at a given time corresponded with higher levels of bullying perpetration at that time, especially for students with generally high levels of family violence across time (see <xref rid="F1" ref-type="fig">Figure 1</xref>).</p><p id="P40">A similar dynamic relation also existed across levels (cross-level interaction). We found a moderating effect where increasing levels of peer deviance at a given time exacerbated the relation between family violence exposure and levels of bullying perpetration. One plausible explanation for the moderating role of peer deviance on bullying behavior is that research on problem behaviors among adolescents indicate that youth who live in households characterized with high levels of family conflict and low positive family relations are less likely to receive adequate parental monitoring and more likely to associate with deviant peers over time (<xref rid="R4" ref-type="bibr">Ary, Duncan, Duncan, &#x00026; Hops, 1999</xref>). However, more research is needed to test this relation with bullying behavior.</p><p id="P41">The current study has multiple strengths worth noting. First, previous studies examining associations among peer deviance, family violence, and bully perpetration have largely been cross-sectional. Furthermore, longitudinal studies examining these associations have been limited in their methodological approach, whereas this study appears to be the first examining the longitudinal association among peer deviance, family violence, and bully perpetration using a time-variant, multilevel approach. Second, the current study examined both within- and between-person level effects, allowing researchers to examine average differences between people, and how individuals change respective to their own mean levels of bullying perpetration over time. More specifically, partitioning the variance at multiple levels of analysis allowed us to control for person-level dependencies (i.e., how individual&#x02019;s scores are correlated over time) and all observed and unobserved between-person confounds (i.e., how individuals differ from one another), which made for a more robust model, thereby adding to the substantive utility of our findings. By factoring in both within- and between&#x02013;level differences, this added interpretational value in terms of how we interpreted the relation between family violence and peer deviance on bullying perpetration, with non-significant average growth in levels of bullying perpetration and within-person effects showing significant fluctuations in reported levels.</p><sec id="S25"><title>Limitations</title><p id="P42">There are several limitations to this study that should be noted. First, the current study used data collected from self-reported measures of bullying. While self-report is the most commonly used method in bullying research (<xref rid="R11" ref-type="bibr">Cornell &#x00026; Brockenbrough, 2004</xref>), multi-informant methods of examining incidence of bullying such as peer- and teacher-reports should also be considered for future studies to reduce any threats to validity. Second, the current study examined middle school students from one Midwest county. Thus, the generalizability of these findings is geographically limited. Third, we were only able to examine bullying behaviors across a two-year span (four waves), looking at students who have already transitioned into or passed the 7<sup>th</sup> grade by the second wave. This may have limited our ability to detect significant average growth because our analysis did not include critical time periods where bullying behavior becomes pervasive, particularly around the 5<sup>th</sup> grade. Fourth, the MCAR tests was significant and indicated that the data were not missing completely at random. However, we examined MAR assumptions and included sex and race variables in our model to account for any potential bias due to missingness on these variables. Sixth, the 7<sup>th</sup> grade cohort was not followed into high school and thus do not contribute any information at wave 4. Lastly, although social learning theory provides a plausible explanation for the development of bullying behavior, it is limited in that it does not take into consideration the broader context. Bullying is indeed influenced by various other ecological contexts (e.g., school climate, neighborhood environment, cultural norms; <xref rid="R22" ref-type="bibr">Hong, &#x00026; Espelage, 2012</xref>) that this study did not include. Moreover, the question of why is it that youth who live in households characterized by high levels of family conflict associate more with deviant peers over time is interesting. However, the current study&#x02019;s theoretical framework and methodological approach do not provide data to answer this question. We can only hypothesize based on previous literature rooted in relational theory (in that an examination of the nature and quality of relationships on thoughts, behaviors, and attitudes is conducted) rather than a social-cognitive framework that focuses on the relation between cognitions (i.e., observation) and one&#x02019;s social environment on behavior (i.e., the imitation of observed interactions in one&#x02019;s social environment). Causal models linking pathways between characteristics of the peer and family relational context on bullying behavior is needed.</p></sec><sec id="S26"><title>Research Implications</title><p id="P43">In sum, these findings support previous research that points to the strong predictors of family violence and exposure to deviant peers on increased levels of bullying perpetration (<xref rid="R15" ref-type="bibr">Espelage et al., 2000</xref>; <xref rid="R19" ref-type="bibr">Ferguson et al., 2009</xref>). In line with social learning theory, bullying behavior did change in relation to reported levels of violence exposure within individuals&#x02019; immediate family and peer contexts. Expanding on social learning theory&#x02019;s explanation for bullying behavior, we also found a dynamic process between relational antecedents in the peer and family context when factoring in within-person differences. Specifically, we indeed found that fluctuations in violence exposure within individuals&#x02019; family and peer contexts were important determinants of change in an individual&#x02019;s bullying behavior. These findings provide a more nuanced lens from which to view the co-occurring relations between family and peer ecologies. Future research should incorporate statistical modeling that considers both between-person and within-person approaches in order to capture the complex interactions between family and peers on bullying perpetration. Also, adding protective factors in these models is critical to identify how youth exposed to family violence resist joining deviant peer groups.</p></sec><sec id="S27"><title>Clinical and Policy Implications</title><p id="P44">With regard to prevention and intervention efforts, delinquency and peer relations should be targeted to reduce the effect of family violence on bullying behavior. Interestingly, a recent randomized clinical trial of a middle school social-emotional learning program (Second Step; Committee for Children, 2008) reduced self-reported delinquency across the three-year evaluation, which in turn was associated with reductions in bullying perpetration (Espelage, Van Ryzin, Low, &#x00026; Polanin, 2015). While few anti-bullying programs target both the peer and family-level, programs that have focused on skill building at the peer-level have had success in reducing bullying perpetration. In the context of the current findings, identifying the skills and programs that build prosocial connections between peers seems is especially important. Two factors in specific &#x02013; social support and connectedness &#x02013; have been suggested to be protective factors against bully perpetration (<xref rid="R31" ref-type="bibr">McNeely &#x00026; Falci, 2004</xref>; <xref rid="R40" ref-type="bibr">Resnick, Ireland, &#x00026; Borowsky, 2004</xref>). According to SAMHSA&#x02019;s National Registry of Evidence-Based Programs and Practices, the Cross-Age Mentoring Program (CAMP) for Children with Adolescent Mentors (<xref rid="R25" ref-type="bibr">Karcher, 2000</xref>) is one program that includes these factors and offers a potential intervention for middle school students. CAMP&#x02019;s purpose is to promote social-emotional and cognitive development in students by fostering connectedness among their peers, school, family, and community and prevent problematic behaviors. Younger (4<sup>th</sup> to 8<sup>th</sup> grade) mentees are paired with older (9<sup>th</sup> to 11<sup>th</sup> grade) mentors who engage in structured meetings throughout the school year and for ten days over the summer. Though it has not been evaluated as an anti-bullying program, CAMP offers a potential intervention deserving of future research given its association with improved connectedness with parents (<xref rid="R26" ref-type="bibr">Karcher, Davis, &#x00026; Powell, 2002</xref>) and friends, culturally diverse peers, and their schools (<xref rid="R27" ref-type="bibr">Karcher, 2009</xref>). Future research may consider evaluating programs focused on connectedness and social support to improve peer relations.</p></sec></sec></body><back><ref-list><ref id="R1"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Achenbach</surname><given-names>TM</given-names></name></person-group><year>1991</year><source>Manual for the Youth Self-Report and 1991 Profile</source><publisher-loc>Burlington, VT</publisher-loc><publisher-name>University of Vermont Department of Psychiatry</publisher-name></element-citation></ref><ref id="R2"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Akers</surname><given-names>RL</given-names></name></person-group><year>2011</year><source>Social learning and social structure: A general theory of crime and deviance</source><publisher-name>Transaction Publishers</publisher-name></element-citation></ref><ref id="R3"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Albdour</surname><given-names>M</given-names></name><name><surname>Krouse</surname><given-names>HJ</given-names></name></person-group><year>2014</year><article-title>Bullying and victimization among african american adolescents: A literature review</article-title><source>Journal of Child and Adolescent Psychiatric Nursing</source><volume>27</volume><issue>2</issue><fpage>68</fpage><lpage>82</lpage><pub-id pub-id-type="pmid">24456268</pub-id></element-citation></ref><ref id="R4"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ary</surname><given-names>DV</given-names></name><name><surname>Duncan</surname><given-names>TE</given-names></name><name><surname>Duncan</surname><given-names>SC</given-names></name><name><surname>Hops</surname><given-names>H</given-names></name></person-group><year>1999</year><article-title>Adolescent problem behavior: The influence of parents and peers</article-title><source>Behaviour Research and Therapy</source><volume>37</volume><issue>3</issue><fpage>217</fpage><lpage>230</lpage><pub-id pub-id-type="pmid">10087640</pub-id></element-citation></ref><ref id="R5"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bauer</surname><given-names>NS</given-names></name><name><surname>Herrenkohl</surname><given-names>TI</given-names></name><name><surname>Lozano</surname><given-names>P</given-names></name><name><surname>Rivara</surname><given-names>FP</given-names></name><name><surname>Hill</surname><given-names>KG</given-names></name><name><surname>Hawkins</surname><given-names>JD</given-names></name></person-group><year>2006</year><article-title>Childhood bullying involvement and exposure to intimate partner violence</article-title><source>Pediatrics</source><volume>118</volume><issue>2</issue><fpage>e235</fpage><lpage>e242</lpage><pub-id pub-id-type="pmid">16882768</pub-id></element-citation></ref><ref id="R6"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Bandura</surname><given-names>A</given-names></name></person-group><year>1973</year><source>Aggression: A social learning analysis</source><publisher-name>Prentice-Hall</publisher-name></element-citation></ref><ref id="R7"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Bandura</surname><given-names>A</given-names></name><name><surname>Walters</surname><given-names>RH</given-names></name></person-group><year>1977</year><source>Social learning theory</source><publisher-loc>Englewood Cliffs, NJ</publisher-loc><publisher-name>Prentice- Hall</publisher-name></element-citation></ref><ref id="R8"><element-citation publication-type="book"><collab>Bureau of Just1ice Statistics</collab><year>2014</year><source>Violence by gang members</source><publisher-name>U.S. Department of Justice</publisher-name></element-citation></ref><ref id="R9"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Carlyle</surname><given-names>KE</given-names></name><name><surname>Steinman</surname><given-names>KJ</given-names></name></person-group><year>2007</year><article-title>Demographic differences in the prevalence, co- occurrence, and correlates of adolescent bullying at school</article-title><source>Journal of School Health</source><volume>77</volume><issue>9</issue><fpage>623</fpage><lpage>629</lpage><pub-id pub-id-type="pmid">17970866</pub-id></element-citation></ref><ref id="R10"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Copeland</surname><given-names>WE</given-names></name><name><surname>Wolke</surname><given-names>D</given-names></name><name><surname>Angold</surname><given-names>A</given-names></name><name><surname>Costello</surname><given-names>EJ</given-names></name></person-group><year>2013</year><article-title>Adult psychiatric outcomes of bullying and being bullied by peers in childhood and adolescence</article-title><source>JAMA Psychiatry</source><volume>70</volume><issue>4</issue><fpage>419</fpage><lpage>426</lpage><pub-id pub-id-type="pmid">23426798</pub-id></element-citation></ref><ref id="R11"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Cornell</surname><given-names>DG</given-names></name><name><surname>Brockenbrough</surname><given-names>K</given-names></name></person-group><year>2004</year><article-title>Identification of bullies and victims: A comparison of methods</article-title><source>Journal of School Violence</source><volume>3</volume><fpage>63</fpage><lpage>87</lpage></element-citation></ref><ref id="R12"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Cotter</surname><given-names>KL</given-names></name><name><surname>Wu</surname><given-names>Q</given-names></name><name><surname>Smokowski</surname><given-names>PR</given-names></name></person-group><year>2016</year><article-title>Longitudinal risk and protective factors associated with internalizing and externalizing symptoms among male and female adolescents</article-title><source>Child Psychiatry &#x00026; Human Development</source><volume>47</volume><issue>3</issue><fpage>472</fpage><lpage>485</lpage><pub-id pub-id-type="pmid">26341092</pub-id></element-citation></ref><ref id="R13"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Curran</surname><given-names>PJ</given-names></name><name><surname>Bauer</surname><given-names>DJ</given-names></name></person-group><year>2011</year><article-title>The disaggregation of within-person and between-person effects in longitudinal models of change</article-title><source>Annual Review of Psychology</source><volume>62</volume><fpage>583</fpage><lpage>619</lpage></element-citation></ref><ref id="R14"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Enders</surname><given-names>CK</given-names></name></person-group><year>2010</year><source>Applied missing data analysis</source><publisher-name>Guilford Press</publisher-name></element-citation></ref><ref id="R15"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Espelage</surname><given-names>DL</given-names></name><name><surname>Bosworth</surname><given-names>K</given-names></name><name><surname>Simon</surname><given-names>TR</given-names></name></person-group><year>2000</year><article-title>Examining the social context of bullying behaviors in early adolescence</article-title><source>Journal of Counseling and Development</source><volume>78</volume><issue>3</issue><fpage>326</fpage><lpage>333</lpage></element-citation></ref><ref id="R16"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Espelage</surname><given-names>DL</given-names></name><name><surname>Holt</surname><given-names>ML</given-names></name></person-group><year>2001</year><article-title>Bullying and victimization during early adolescence: Peer influences and psychosocial correlates</article-title><source>Journal of Emotional Abuse</source><volume>2</volume><issue>3</issue><fpage>123</fpage><lpage>142</lpage></element-citation></ref><ref id="R17"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Espelage</surname><given-names>DL</given-names></name><name><surname>Hong</surname><given-names>JS</given-names></name><name><surname>Rao</surname><given-names>M*</given-names></name><name><surname>Thornberg</surname><given-names>R</given-names></name></person-group><year>2015</year><article-title>Social-ecological factors associated with bullying perpetration among early adolescents across the elementary- middle school transition</article-title><source>Violence &#x00026; Victims</source><volume>30</volume><fpage>470</fpage><lpage>488</lpage><pub-id pub-id-type="doi">10.1891/0886-6708.VV-D-14-00046</pub-id><pub-id pub-id-type="pmid">26118267</pub-id></element-citation></ref><ref id="R18"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Espelage</surname><given-names>DL</given-names></name><name><surname>Low</surname><given-names>S</given-names></name><name><surname>Rao</surname><given-names>MA</given-names></name><name><surname>Hong</surname><given-names>JS</given-names></name><name><surname>Little</surname><given-names>TD</given-names></name></person-group><year>2014</year><article-title>Family violence, bullying, fighting, and substance use among adolescents: A longitudinal mediational model</article-title><source>Journal of Research on Adolescence</source><volume>24</volume><issue>2</issue><fpage>337</fpage><lpage>349</lpage></element-citation></ref><ref id="R19"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ferguson</surname><given-names>CJ</given-names></name><name><surname>San Miguel</surname><given-names>C</given-names></name><name><surname>Hartley</surname><given-names>RD</given-names></name></person-group><year>2009</year><article-title>A multivariate analysis of youth violence and aggression: The influence of family, peers, depression, and media violence</article-title><source>The Journal of Pediatrics</source><volume>155</volume><issue>6</issue><fpage>904</fpage><lpage>908</lpage><pub-id pub-id-type="pmid">19683724</pub-id></element-citation></ref><ref id="R20"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gifford-Smith</surname><given-names>M</given-names></name><name><surname>Dodge</surname><given-names>KA</given-names></name><name><surname>Dishion</surname><given-names>TJ</given-names></name><name><surname>McCord</surname><given-names>J</given-names></name></person-group><year>2005</year><article-title>Peer influence in children and adolescents: Crossing the bridge from developmental to intervention science</article-title><source>Journal of Abnormal Child Psychology</source><volume>33</volume><issue>3</issue><fpage>255</fpage><lpage>265</lpage><pub-id pub-id-type="pmid">15957555</pub-id></element-citation></ref><ref id="R21"><element-citation publication-type="web"><person-group person-group-type="author"><name><surname>Gladden</surname><given-names>RM</given-names></name><name><surname>Vivolo-Kantor</surname><given-names>AM</given-names></name><name><surname>Hamburger</surname><given-names>ME</given-names></name><name><surname>Lumpkin</surname><given-names>CD</given-names></name></person-group><year>2014</year><source>Bullying surveillance among youths: Uniform definitions for public health and recommended data elements, version 1.0</source><comment>Retrieved from <ext-link ext-link-type="uri" xlink:href="https://www.cdc.gov/violenceprevention/pdf/bullying-definitions-final-a.pdf">https://www.cdc.gov/violenceprevention/pdf/bullying-definitions-final-a.pdf</ext-link></comment></element-citation></ref><ref id="R22"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hong</surname><given-names>JS</given-names></name><name><surname>Espelage</surname><given-names>DL</given-names></name></person-group><year>2012</year><article-title>A review of research on bullying and peer victimization in school: An ecological system analysis</article-title><source>Aggression and Violent Behavior</source><volume>17</volume><issue>4</issue><fpage>311</fpage><lpage>322</lpage></element-citation></ref><ref id="R23"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hymel</surname><given-names>S</given-names></name><name><surname>Swearer</surname><given-names>SM</given-names></name></person-group><year>2015</year><article-title>Four decades of research on school bullying: An introduction</article-title><source>American Psychologist</source><volume>70</volume><issue>4</issue><fpage>293</fpage><pub-id pub-id-type="pmid">25961310</pub-id></element-citation></ref><ref id="R24"><element-citation publication-type="book"><collab>Institute of Behavioral Science</collab><year>1987</year><source>Youth Interview Schedule: Denver Youth Survey</source><publisher-loc>Boulder, Co</publisher-loc><publisher-name>University of Colorado</publisher-name></element-citation></ref><ref id="R25"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Karcher</surname><given-names>MJ</given-names></name></person-group><year>2000</year><article-title>Children with Adolescent Mentors Program (CAMP): The developmental mentoring trainer&#x02019;s guide</article-title><source>Unpublished manual</source><publisher-name>University of Wisconsin-Madison</publisher-name></element-citation></ref><ref id="R26"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Karcher</surname><given-names>MJ</given-names></name><name><surname>Davis</surname><given-names>C</given-names></name><name><surname>Powell</surname><given-names>B</given-names></name></person-group><year>2002</year><article-title>The effects of developmental mentoring on connectedness and academic achievement</article-title><source>School Community Journal</source><volume>12</volume><issue>2</issue><fpage>35</fpage><lpage>50</lpage></element-citation></ref><ref id="R27"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Karcher</surname><given-names>MJ</given-names></name></person-group><year>2009</year><article-title>Increases in academic connectedness and self-esteem among high school students who serve as cross-age peer mentors</article-title><source>Professional School Counseling</source><volume>12</volume><issue>4</issue><fpage>292</fpage><lpage>299</lpage></element-citation></ref><ref id="R28"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Knous-Westfall</surname><given-names>HM</given-names></name><name><surname>Ehrensaft</surname><given-names>MK</given-names></name><name><surname>MacDonell</surname><given-names>KW</given-names></name><name><surname>Cohen</surname><given-names>P</given-names></name></person-group><year>2012</year><article-title>Parental intimate partner violence, parenting practices, and adolescent peer bullying: A prospective study</article-title><source>Journal of Child and Family Studies</source><volume>21</volume><issue>5</issue><fpage>754</fpage><lpage>766</lpage></element-citation></ref><ref id="R29"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Little</surname><given-names>RJ</given-names></name></person-group><year>1988</year><article-title>A test of missing completely at random for multivariate data with missing values</article-title><source>Journal of the American Statistical Association</source><volume>83</volume><issue>404</issue><fpage>1198</fpage><lpage>1202</lpage></element-citation></ref><ref id="R30"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Low</surname><given-names>S</given-names></name><name><surname>Espelage</surname><given-names>DL</given-names></name></person-group><year>2014</year><article-title>Conduits from community violence exposure to peer aggression and victimization: Contributions of parental monitoring, impulsivity, and deviancy</article-title><source>Journal of Counseling Psychology</source><volume>61</volume><issue>2</issue><fpage>221</fpage><pub-id pub-id-type="pmid">24635595</pub-id></element-citation></ref><ref id="R31"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>McNeely</surname><given-names>C</given-names></name><name><surname>Falci</surname><given-names>C</given-names></name></person-group><year>2004</year><article-title>School connectedness and the transition into and out of health- risk behavior among adolescents: A comparison of social belonging and teacher support</article-title><source>Journal of School Health</source><volume>74</volume><issue>7</issue><fpage>284</fpage><lpage>292</lpage><pub-id pub-id-type="pmid">15493705</pub-id></element-citation></ref><ref id="R32"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Merrin</surname><given-names>GJ</given-names></name><name><surname>Davis</surname><given-names>JP</given-names></name><name><surname>Berry</surname><given-names>D</given-names></name><name><surname>D&#x02019;Amico</surname><given-names>EJ</given-names></name><name><surname>Dumas</surname><given-names>TM</given-names></name></person-group><year>2016</year><article-title>The longitudinal associations between substance use, crime, and social risk among emerging adults: A longitudinal within and between-person latent variables analysis</article-title><source>Drug and Alcohol Dependence</source><volume>165</volume><fpage>71</fpage><lpage>78</lpage><pub-id pub-id-type="pmid">27242288</pub-id></element-citation></ref><ref id="R33"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Musu-Gillette</surname><given-names>L</given-names></name><name><surname>Zhang</surname><given-names>A</given-names></name><name><surname>Wang</surname><given-names>K</given-names></name><name><surname>Zhang</surname><given-names>J</given-names></name><name><surname>Kemp</surname><given-names>J</given-names></name><name><surname>Diliberti</surname><given-names>M</given-names></name><name><surname>Oudekerk</surname><given-names>BA</given-names></name></person-group><year>2018</year><source>Indicators of School Crime and Safety: 2017 (NCES 2018-036/NCJ 251413)</source><publisher-name>National Center for Education Statistics, U.S. Department of Education, and Bureau of Justice Statistics, Office of Justice Programs, U.S. Department of Justice</publisher-name><publisher-loc>Washington, DC</publisher-loc></element-citation></ref><ref id="R34"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Muth&#x000e9;n</surname><given-names>LK</given-names></name><name><surname>Muth&#x000e9;n</surname><given-names>BO</given-names></name></person-group><year>1998&#x02013;2014</year><source>Mplus User&#x02019;s Guide</source><edition>7</edition><publisher-loc>Los Angeles, CA</publisher-loc><publisher-name>Muth&#x000e9;n &#x00026; Muth&#x000e9;n</publisher-name></element-citation></ref><ref id="R35"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Olweus</surname><given-names>D</given-names></name></person-group><year>1993</year><source>Bullying at school</source><publisher-loc>Oxford, England</publisher-loc><publisher-name>Blackwell</publisher-name></element-citation></ref><ref id="R36"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Olweus</surname><given-names>D</given-names></name></person-group><year>1997</year><article-title>Bully/victim problems in school: Facts and intervention</article-title><source>European Journal of Psychology of Education</source><volume>7</volume><fpage>495</fpage><lpage>510</lpage></element-citation></ref><ref id="R37"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Pellegrini</surname><given-names>AD</given-names></name><name><surname>Bartini</surname><given-names>M</given-names></name></person-group><year>2000</year><article-title>A longitudinal study of bullying, victimization, and peer affiliation during the transition from primary school to middle school</article-title><source>American Educational Research Journal</source><volume>37</volume><issue>3</issue><fpage>699</fpage><lpage>725</lpage></element-citation></ref><ref id="R38"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Pellegrini</surname><given-names>AD</given-names></name><name><surname>Long</surname><given-names>JD</given-names></name></person-group><year>2002</year><article-title>A longitudinal study of bullying, dominance, and victimization during the transition from primary school through secondary school</article-title><source>British Journal of Developmental Psychology</source><volume>20</volume><issue>2</issue><fpage>259</fpage><lpage>280</lpage></element-citation></ref><ref id="R39"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Pepler</surname><given-names>D</given-names></name><name><surname>Jiang</surname><given-names>D</given-names></name><name><surname>Craig</surname><given-names>W</given-names></name><name><surname>Connolly</surname><given-names>J</given-names></name></person-group><year>2008</year><article-title>Developmental trajectories of bullying and associated factors</article-title><source>Child Development</source><volume>79</volume><issue>2</issue><fpage>325</fpage><lpage>338</lpage><pub-id pub-id-type="pmid">18366426</pub-id></element-citation></ref><ref id="R40"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Resnick</surname><given-names>MD</given-names></name><name><surname>Ireland</surname><given-names>M</given-names></name><name><surname>Borowsky</surname><given-names>I</given-names></name></person-group><year>2004</year><article-title>Youth violence perpetration: What protects?what predicts? findings from the national longitudinal study of adolescent health</article-title><source>Journal of Adolescent Health</source><volume>35</volume><issue>5</issue><fpage>424</fpage><lpage>433</lpage></element-citation></ref><ref id="R41"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Salmivalli</surname><given-names>C</given-names></name></person-group><year>2010</year><article-title>Bullying and the peer group: A review</article-title><source>Aggression and Violent Behavior</source><volume>15</volume><issue>2</issue><fpage>112</fpage><lpage>120</lpage></element-citation></ref><ref id="R42"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Singer</surname><given-names>JD</given-names></name><name><surname>Willett</surname><given-names>JB</given-names></name></person-group><year>2003</year><source>Applied longitudinal data analysis: Modeling change and event occurrence</source><publisher-loc>New York</publisher-loc><publisher-name>Oxford University Press</publisher-name></element-citation></ref><ref id="R43"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Thornberry</surname><given-names>TP</given-names></name><name><surname>Krohn</surname><given-names>MD</given-names></name><name><surname>Lizotte</surname><given-names>AJ</given-names></name><name><surname>Smith</surname><given-names>CA</given-names></name><name><surname>Tobin</surname><given-names>K</given-names></name></person-group><year>2003</year><source>Gangs and delinquency in developmental perspective</source><publisher-loc>New York</publisher-loc><publisher-name>Cambridge University Press</publisher-name></element-citation></ref><ref id="R44"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Enders</surname><given-names>CK</given-names></name><name><surname>Tofighi</surname><given-names>D</given-names></name></person-group><year>2007</year><article-title>Centering predictor variables in cross-sectional multilevel models: a new look at an old issue</article-title><source>Psychological Methods</source><volume>12</volume><issue>2</issue><fpage>121</fpage><lpage>138</lpage><pub-id pub-id-type="pmid">17563168</pub-id></element-citation></ref><ref id="R45"><element-citation publication-type="web"><collab>United States Department of Justice</collab><year>2015</year><source>Domestic violence</source><comment>Retrieved July 19, 2016, from <ext-link ext-link-type="uri" xlink:href="http://www.justice.gov/ovw/domestic-violence">http://www.justice.gov/ovw/domestic-violence</ext-link></comment></element-citation></ref><ref id="R46"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Voisin</surname><given-names>DR</given-names></name><name><surname>Hong</surname><given-names>JS</given-names></name></person-group><year>2012</year><article-title>A meditational model linking witnessing intimate partner violence and bullying behaviors and victimization among youth</article-title><source>Educational Psychology Review</source><volume>24</volume><issue>4</issue><fpage>479</fpage><lpage>498</lpage></element-citation></ref></ref-list></back><floats-group><fig id="F1" orientation="portrait" position="float"><label>Figure 1</label><caption><p>Within-Person Family Violence and Within-Person Peer Deviance (Level 1 Interaction)</p><p>Simple Slopes: +1SD WP Peer Deviance: &#x003b2; = 0.09, SE = 0.02, <italic>p</italic> &#x0003c; .001; Mean Peer Deviance: &#x003b2; = 0.05, SE = 0.02, <italic>p</italic> &#x0003c; .001; &#x02212;1SD WP Peer Deviance: &#x003b2; = .01, SE = 0.02, <italic>p</italic> = .578.</p></caption><graphic xlink:href="nihms982012f1"/></fig><fig id="F2" orientation="portrait" position="float"><label>Figure 2</label><caption><p>Within-Person Peer Deviance and Between-Person Family Violence (Cross Level Interaction)</p><p>Simple Slopes: +1SD BP Peer Deviance: &#x003b2; = 0.14, SE = 0.02, <italic>p</italic> &#x0003c; .001; Mean Peer Deviance: &#x003b2; = 0.12, SE = 0.01, <italic>p</italic> &#x0003c; .001; &#x02212;1SD BP Peer Deviance: &#x003b2; = .10, SE = 0.02, <italic>p</italic> &#x0003c; .001.</p></caption><graphic xlink:href="nihms982012f2"/></fig><table-wrap id="T1" position="float" orientation="landscape"><label>Table 1</label><caption><p>Estimates of Fixed and Random Effects from a Series of Individual Multilevel Models Predicting Bullying Perpetration</p></caption><table frame="hsides" rules="groups"><thead><tr><th valign="bottom" rowspan="3" align="left" colspan="1"/><th colspan="5" valign="bottom" align="center" rowspan="1">Parameter Estimates <italic>(SE)</italic></th></tr><tr><th colspan="5" valign="bottom" align="left" rowspan="1">
<hr/></th></tr><tr><th valign="bottom" align="center" rowspan="1" colspan="1">Model 1</th><th valign="bottom" align="center" rowspan="1" colspan="1">Model 2</th><th valign="bottom" align="center" rowspan="1" colspan="1">Model 3</th><th valign="bottom" align="center" rowspan="1" colspan="1">Model 4</th><th valign="bottom" align="center" rowspan="1" colspan="1">Model 5</th></tr></thead><tbody><tr><td colspan="6" align="left" valign="bottom" rowspan="1"><bold><italic>Fixed Effects</italic></bold></td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">Intercept</td><td align="center" valign="bottom" rowspan="1" colspan="1">.435<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.014)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.338<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.026)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.369<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.025)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.413<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.023)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.408<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.023)</td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">Age</td><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1">.038<xref rid="TFN2" ref-type="table-fn">*</xref><break/>(.013)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.019<break/>(.013)</td><td align="center" valign="bottom" rowspan="1" colspan="1">&#x02212;.016<break/>(.012)</td><td align="center" valign="bottom" rowspan="1" colspan="1">&#x02212;.016<break/>(.012)</td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">Sex (Ref = Male)</td><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1">&#x02212;.034<break/>(.026)</td><td align="center" valign="bottom" rowspan="1" colspan="1">&#x02212;.085<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.025)</td><td align="center" valign="bottom" rowspan="1" colspan="1">&#x02212;.050<xref rid="TFN2" ref-type="table-fn">*</xref><break/>(.023)</td><td align="center" valign="bottom" rowspan="1" colspan="1">&#x02212;.049<xref rid="TFN2" ref-type="table-fn">*</xref><break/>(.023)</td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">Black (Ref=White)</td><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1">.206<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.09)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.197<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.027)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.099<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.025)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.100<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.026)</td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">Other (Ref=White)</td><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1">&#x02212;.011<break/>(.047)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.011<break/>(.044)</td><td align="center" valign="bottom" rowspan="1" colspan="1">&#x02212;.035<break/>(.041)</td><td align="center" valign="bottom" rowspan="1" colspan="1">&#x02212;.032<break/>(.041)</td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">WP Family Violence</td><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1">.075<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.016)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.050<xref rid="TFN3" ref-type="table-fn">**</xref><break/>(.016)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.050<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.016)</td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">BP Family Violence</td><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1">.201<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.013)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.117<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.013)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.116<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.013)</td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">WP Peer Deviance</td><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1">.204<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.023)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.212<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.032)</td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">BP Peer Deviance</td><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1">.319<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.020)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.315<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.020)</td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">WP Family Violence<xref rid="TFN2" ref-type="table-fn">*</xref> WP Peer Deviance</td><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1">.120<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.006)</td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">WP Peer Deviance<xref rid="TFN2" ref-type="table-fn">*</xref> BP Family Violence</td><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1">.063<xref rid="TFN2" ref-type="table-fn">*</xref><break/>(.032)</td></tr><tr><td colspan="6" align="left" valign="bottom" rowspan="1"><bold><italic>Random Effects</italic></bold></td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">BP Intercept</td><td align="center" valign="bottom" rowspan="1" colspan="1">.183<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.011)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.169<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.010)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.138<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.009)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.106<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.008)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.121<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.008)</td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">WP Intercept</td><td align="center" valign="bottom" rowspan="1" colspan="1">.165<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.006)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.165<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.006)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.159<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.006)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.152<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.006)</td><td align="center" valign="bottom" rowspan="1" colspan="1">.126<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.006)</td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">WP Peer Deviance</td><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1"/><td align="center" valign="bottom" rowspan="1" colspan="1">.142<xref rid="TFN4" ref-type="table-fn">***</xref><break/>(.036)</td></tr><tr><td colspan="6" align="left" valign="bottom" rowspan="1"><bold><italic>Fit Indices</italic></bold></td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">&#x02212;2LL</td><td align="center" valign="bottom" rowspan="1" colspan="1">4856.76</td><td align="center" valign="bottom" rowspan="1" colspan="1">4757.85</td><td align="center" valign="bottom" rowspan="1" colspan="1">4403.30</td><td align="center" valign="bottom" rowspan="1" colspan="1">4075.77</td><td align="center" valign="bottom" rowspan="1" colspan="1">4007.80</td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">AIC</td><td align="center" valign="bottom" rowspan="1" colspan="1">4862.76</td><td align="center" valign="bottom" rowspan="1" colspan="1">4771.85</td><td align="center" valign="bottom" rowspan="1" colspan="1">4421.31</td><td align="center" valign="bottom" rowspan="1" colspan="1">4097.77</td><td align="center" valign="bottom" rowspan="1" colspan="1">4035.80</td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">BIC</td><td align="center" valign="bottom" rowspan="1" colspan="1">4880.82</td><td align="center" valign="bottom" rowspan="1" colspan="1">4813.99</td><td align="center" valign="bottom" rowspan="1" colspan="1">4475.28</td><td align="center" valign="bottom" rowspan="1" colspan="1">4163.71</td><td align="center" valign="bottom" rowspan="1" colspan="1">4119.72</td></tr><tr><td align="left" valign="bottom" rowspan="1" colspan="1">#Parameters</td><td align="center" valign="bottom" rowspan="1" colspan="1">3</td><td align="center" valign="bottom" rowspan="1" colspan="1">7</td><td align="center" valign="bottom" rowspan="1" colspan="1">9</td><td align="center" valign="bottom" rowspan="1" colspan="1">11</td><td align="center" valign="bottom" rowspan="1" colspan="1">14</td></tr></tbody></table><table-wrap-foot><fn id="TFN1"><p><italic>Note:</italic> Model 1 is an unconditional null model. Model 2 added the control variables of age, gender, and race (M1 to M2; &#x00394;LR = 98.9, &#x00394;<italic>df</italic> = 4, <italic>p</italic> &#x0003c; .001). Model 3 added the main effects of within and between-person family violence (M2 to M3; &#x00394;LR = 354.55, &#x00394;<italic>df</italic> = 2, <italic>p</italic> &#x0003c; .001). Model 5 added the main effect of within and between-person time peer deviance (M3 to M4; &#x00394;LR = 327.54., &#x00394;<italic>df</italic> = 2, <italic>p</italic> &#x0003c; .001). Model 6 added the interactions of within-person family violence and within-person peer deviance, and within-person peer deviance and between-person family violence (M4 to M5; &#x00394;LR = 67.97, &#x00394;<italic>df</italic> = 3, <italic>p</italic> &#x0003c;.001).</p></fn><fn id="TFN2"><label>*</label><p><italic>p</italic> &#x0003c; .05,</p></fn><fn id="TFN3"><label>**</label><p><italic>p</italic> &#x0003c; 01,</p></fn><fn id="TFN4"><label>***</label><p><italic>p</italic> &#x0003c; .001.</p></fn></table-wrap-foot></table-wrap></floats-group></article>