NEIGHBORHOOD CONTEXT AND NONLINEAR PEER EFFECTS ON ADOLESCENT VIOLENT CRIME

NEIGHBORHOOD CONTEXT ANDNONLINEAR PEER EFFECTS ONADOLESCENT VIOLENT CRIME∗

GREGORY M. ZIMMERMANSchool of Criminology and Criminal JusticeNortheastern University

STEVEN F. MESSNERDepartment of SociologyUniversity at Albany, State University of New York

KEYWORDS: neighborhood, nonlinear, peer influence, violence

Although evidence of the strong correlation between deviant behaviorand exposure to deviant peers is overwhelming, researchers have yet toinvestigate whether a nonlinear functional form better captures this rela-tionship than does a linear form. Researchers also have yet to examinethe extent to which peer effects vary as a function of the neighborhoodcontext. To address these issues, we use data from the Project on HumanDevelopment in Chicago Neighborhoods (PHDCN) to examine 1) thefunctional form of the relationship between peer violence exposure andself-reported violent crime and 2) the extent to which the effect of ex-posure to violent peers on violence is ecologically structured. Estimatesfrom logistic hierarchical models indicate that the effect of peer violenceexposure on violent crime decreases at higher values of peer violence,as reflected in a nonlinear relationship (expressed in terms of log-odds).Furthermore, exposure to violent peers increases along with neighbor-hood disadvantage, and the effect of peer violence exposure on violentcrime is attenuated as neighborhood disadvantage increases, which isreflected in a cross-level peer violence/disadvantage interaction.

Evidence of the strong correlation between deviant behavior and ex-posure to deviant peers is overwhelming (see, e.g., Elliott, Huizinga, and

∗ This research uses data from the Project on Human Development in ChicagoNeighborhoods (PHDCN). We are grateful to Ryan King and the anonymousreferees for comments on an earlier draft of this article. Direct correspon-dence to Gregory M. Zimmerman, School of Criminology and Criminal Justice,Northeastern University, 204 Churchill Hall, 360 Huntington Avenue, Boston,MA 02215 (e-mail: [email protected]).

C© 2011 American Society of Criminology doi: 10.1111/j.1745-9125.2011.00237.x

CRIMINOLOGY Volume 49 Number 3 2011 873

874 ZIMMERMAN & MESSNER

Ageton, 1985: 71; Thornberry and Krohn, 1997: 218; Warr and Stafford,1991: 851). This relationship has been documented using self-reports, socialnetwork data, and official data; in studies examining a wide range of risky,delinquent, and criminal behaviors; and in various social contexts (forreviews, see Matsueda and Anderson, 1998; Warr, 1996). Moreover, “nostudy yet has failed to show a significant effect of peers on current and/orsubsequent delinquency” (Warr, 2002: 42).

Despite the evidence linking peer delinquency to adolescent delinquentbehavior, no published criminological studies, to our knowledge, havetheorized about or assessed empirically the possible nonlinearities in thisrelationship. The conventional approach has been to estimate a linearmodel. The attraction of the linear model is readily apparent; it is intuitivelyappealing and parsimonious. Nevertheless, without examining the natureof the causal effect of peers, research has implicitly assumed that changesin peer delinquency lead to proportional changes in delinquent behavior,which need not be the case (Tittle, 1995: 35).

Research on variability in the effect of peers across social contexts alsois sparse. Studies have examined mediating factors through which peer in-fluence functions and individual-level moderating factors (e.g., age, gender,peer attitudes, impulsivity, and perceived sanction threats) that influencethe strength of peer influence (Kung and Farrell, 2000; Liu, 2003; Marshaland Chassin, 2000; Musher-Eizenman, Holub, and Arnett, 2003; Pettit et al.,1999; Vitaro, Brendgen, and Tremblay, 2000; Vitulano, Fite, and Rathert,2010; Warr and Stafford, 1991; Zimmerman and Messner, 2010). Studiesalso have examined cross-cultural and structural variation in peer interac-tions (for a review, see Warr, 2002: 14–22). But researchers have yet toinvestigate the extent to which the peer effect varies as a function of theneighborhood context.

Our research contributes to the literature by investigating the functionalform of the relationship between exposure to violent peers and violence.We also examine whether the effect of exposure to violent peers on violenceis ecologically structured and, if so, explore why. To test our hypotheses(enumerated in a subsequent discussion), we use data from the Projecton Human Development in Chicago Neighborhoods (PHDCN), which isa data set particularly well suited for studying individuals in their localizedsocial environments.

NONLINEARITY IN PEER INFLUENCE

Tittle (1995: 35) has argued that one of the key weaknesses of the majortheories of crime and delinquency is their “neglect of the form of thesupposed causal effect.” As a result, these theories “leave the impressionthat any increment in their proposed causal variable leads to an equal or

PEER VIOLENCE AND NEIGHBORHOODS 875

proportional increment in the postulated effect.” Tittle (1995) illustratedthe problematic nature of the assumption of linearity with reference toSutherland’s (1934) differential association theory, a theory that serves asthe foundation for much of the research on peer influence and crime. Hechallenged the idea that ever increasing contact with “messages” of deviantbehavior will promote more and more deviant conduct, speculating that“messages too frequently conveyed can become boring and ineffective,sometimes even causing hostility and rejection” (Tittle, 1995: 36).

Following Tittle’s (1995) general line of reasoning, we suggest that anincrease in exposure to violent peers will significantly increase violent of-fending but only up to a certain point. Eventually, a “saturation” effectwill set in. That is, at low levels of exposure to violent peers, an increasein violent peers will have a considerable impact on violent offending, asthese contacts provide relatively novel “messages” that are supportive ofviolent behavior. At high levels of exposure to violent peers, however, thesame increase in violent peers will have a much less pronounced impact onviolent behavior because 1) a bountiful supply of such peers already existsand 2) any proviolence “messages” that additional peers might convey willbe somewhat redundant and, thus, not particularly consequential. Thesemessages might indeed become “boring and ineffective.”

Despite the large volume of research on peer effects and adolescentdelinquent behavior, the possibility of nonlinearities in this relationshiphas not been addressed. However, saturation or “ceiling” effects have beenfound in other lines of research. For example, Hannon (2002) found thatneighborhood poverty had a stronger effect on property crime at lowerlevels of neighborhood deprivation than at higher levels (see also Krivo andPeterson, 1996). Similarly, Thaxton and Agnew (2004) found that parentaland teacher attachments exhibited nonlinear effects on delinquency, suchthat negative attachments had a strong effect and neutral and positiveattachments had little effect. Furthermore, deterrence research has foundevidence of a ceiling effect, beyond which the certainty of punishmenthas little effect on crime (e.g., Yu and Liska, 1993). Other nonlinearfunctional forms also have been discovered in criminological research.Deterrence research has uncovered “tipping points” or “threshold” ef-fects, under which the certainty of crime has no effect, but over whichthe effect is substantial (e.g., Tittle and Rowe, 1974). Similar thresholdeffects have been found for the relationship between parental strictnessand delinquent behavior (e.g., Rankin and Wells, 1990) and the relation-ship between socioeconomic deprivation and criminal behavior (e.g., Blauand Golden, 1986). Finally, Warr (1993) found a curvilinear relationshipbetween age and exposure to delinquent peers, which is similar to thenonlinear age distribution of crime (Hirschi and Gottfredson, 1983: 554;Warr, 2002: 91).


Our research builds on these studies by examining whether the effectof peer violence exposure on adolescent violent crime is nonlinear, asreflected in a declining marginal effect of violent peer exposure at highlevels of peer violence. We also examine whether the effect of exposure toviolent peers on violence is ecologically structured, that is, if it varies by theneighborhood context and, if so, why. We explicate below the reasons forexpecting the effect of violent peers to be dependent on the neighborhoodcontext.

ECOLOGICAL STRUCTURING OF THE PEER EFFECT

Previous research examining variability in the relationship between peerdelinquency and adolescent delinquent behavior has focused on the mod-erating effects of individual-level characteristics. For example, studies haveexamined how adolescent and peer attitudes toward deviance affect theinfluence of those peers (e.g., Vitaro, Brendgen, and Tremblay, 2000; Warrand Stafford, 1991). Studies also have investigated the moderating effectsof emotional bonds with peers (Zimmerman and Messner, 2010), prosocialinvolvement (Kaufmann et al., 2007), and disinhibitive characteristics suchas attention-deficit hyperactivity disorder (Marshal, Molina, and Pelham,2003) and impulsivity (Vitulano, Fite, and Rathert, 2010). Most studies onthis topic, however, have examined how age, gender, and parenting prac-tices such as monitoring, discipline, and support moderate the peer effecton delinquent and criminal behavior (e.g., Dishion et al., 1995; Dishion,Nelson, and Bullock, 2004; Kung and Farrell, 2000; Marshal and Chassin,2000; Musher-Eizenman, Holub, and Arnett, 2003; Poole and Regoli, 1979).Only a small number of studies has examined the contextual moderators ofpeer influence. One such study aggregated individuals’ responses about sub-stance use to the school level and found that the correlation between adoles-cent and peer smoking and drinking behaviors increased when school-levelsmoking and drinking increased (Cleveland and Wiebe, 2003). The resultsreflected a selection process whereby adolescents who already smoke anddrink have more opportunities to affiliate with similar peers in a high-usecontext (Cleveland and Wiebe, 2003: 288–9).

The existing literature thus suggests that variability exists in the peereffect on delinquent and criminal behavior. However, multilevel analyses ofthe variability in peer influence across neighborhood contexts are conspic-uous by their absence. We address this issue by investigating whether theeffect of exposure to violent peers on violence is ecologically structured.We hypothesize that such ecological structuring will in fact be observed,such that the effect of exposure to violent peers on violence will be atten-uated in the more disadvantaged neighborhoods. This second hypothesisfollows logically from our initial hypothesis about the expected curvilinear


relationship between violent peers and violence, and from an additionalpremise about a contextual effect of neighborhood disadvantage on violentpeer exposure. Specifically, we expect that neighborhood disadvantage willexhibit a positive relationship with exposure to peer violence. Accord-ingly, neighborhoods with high levels of disadvantage will be more likelyto be populated by youths at the high end of the violent peer exposurecontinuum—the range of the distribution in which the effect of violent peerexposure on violence is attenuated.

We expect to observe a positive relationship between neighborhooddisadvantage and exposure to violent peers because disadvantage is likelyto affect both the relative size of the population of violent peers in theneighborhood and the likelihood that adolescents will select peers from theneighborhood into their social networks. Influential criminological theoriesand prior empirical research lend considerable credibility to the claimthat the relative size of the population of violent peers will be high inextremely disadvantaged neighborhoods. Indeed, neighborhood disadvan-tage has emerged as one of the strongest and most consistent predictorsof violent crime rates in macrolevel research (Pratt and Cullen, 2005).Of course, it is logically possible that a neighborhood could have a highviolent crime rate and few criminally prone residents, if the actual offenderswere to be “imported” from other neighborhoods. However, research hasindicated that offenders do not tend to travel large distances when selectingtheir targets for victimization (e.g., Brantingham and Brantingham, 1993;Chainey and Ratcliffe, 2005; Rengert and Wasilchick, 1985). That is, most“offending occurs along the normal, noncriminal travel patterns of offend-ers” (Ratcliffe, 2006: 264).

Moreover, we have good theoretical reasons to anticipate that individu-als residing in disadvantaged neighborhoods will be exposed to socializa-tion processes that encourage violent cultural orientations. For example,Wilson (1996) argued that socioeconomically disadvantaged areas isolateyouths from middle-class and upper-class norms and increase exposure toantisocial value systems. Anderson (1999) contended that a “code of thestreets” has developed in disadvantaged areas, which is a cultural frame thatvirtually requires engagement in risky and often violent behaviors to gainrespect and to avoid victimization. Similarly, Warr (2002: 132) maintainedthat in disadvantaged areas, the street is “the hangout of poor youth,” wherenonnormative cultural orientations prevail.

A series of studies also provides empirical evidence suggestive of a directlink between peer violence exposure and neighborhood disadvantage. Forexample, Simons et al. (1996) found that concentrated disadvantage has anindirect effect on adolescent boys’ conduct problems by increasing affilia-tion with deviant peers; Brody et al. (2001) found that community disadvan-tage positively and significantly predicts both parental and youth reports


of affiliation with deviant peers; and Stark (1987) surmised that becausedisadvantaged neighborhoods have a large concentration of deviant youths,adolescents living in these neighborhoods have little choice but to affiliatewith deviant peers. Furthermore, Haynie, Silver, and Teasdale (2006) foundthat adolescents residing in disadvantaged neighborhoods are more likely toassociate with peers who fight (and who have lower academic orientations).They also found that neighborhood disadvantage influences youth violenceindirectly by encouraging exposure to violent peer networks.

Recent ethnographic research by Harding (2009) further clarifies theunderlying processes that might link neighborhood disadvantage to expo-sure to violent peers. Harding (2009) proposed that violence becomes acritical element of the social organization of disadvantaged neighborhoods,thereby structuring the opportunities for peer socialization. He described aselection process through which youths coping with violence in disadvan-taged neighborhoods seek out older peers for protection. These cross-agepeer interactions, in turn, increase the likelihood of selecting older peerswho endorse violent behavioral models. Harding (2009) also highlightedthe importance of social and cultural isolation, which restrict the activityspace of lower-class youths to the neighborhood (more so than for middle-and upper-class youths). The constrained opportunity for interaction withpeers increases the likelihood that these youths will come into contact witholder, violent peers, who are the agents of socialization into unconventionalcultural frameworks in disadvantaged neighborhoods (also see Harding,2010).

Finally, using data from the PHDCN, Sharkey (2006) identified an in-tervening mechanism through which neighborhood disadvantage influencesexposure to violent peers. Sharkey (2006: 826) found that concentrateddisadvantage has a significant effect on “street efficacy” or the “perceivedability to avoid violent confrontations and to be safe in one’s neighbor-hood.” Street efficacy, in turn, has a significant effect on peer delinquency.The overall direct effect of neighborhood disadvantage on peer delinquencyin Sharkey’s (2006) analyses is positive, although it does not reach a levelof statistical significance (see the online supplement to the article). Thismight reflect Sharkey’s (2006) use of a general peer delinquency scalerather than a measure of violent peer delinquency (his six-item general peerdelinquency scale contains a single item pertaining to aggressive behavior).We expect to observe a stronger relationship between neighborhood disad-vantage and violent peer exposure.

In short, we propose that a nonlinear functional form will better repre-sent the effect of exposure to violent peers on violence than will a linearform. Furthermore, we expect the effect of exposure to violent peers onviolence to be attenuated in more disadvantaged neighborhoods becauseneighborhoods with high levels of disadvantage will be populated by youths


at the high end of the violent peer exposure continuum, where the effectof violent peer exposure is attenuated. Stated more formally, our principalhypotheses are stipulated as follows:

Hypothesis 1: The effect of peer violence on violent offending shouldbe nonlinear and decrease as levels of peer violence increase.

Hypothesis 2: The effect of peer violence on violent offending shouldbe attenuated as neighborhood disadvantage increases.

Hypothesis 3: Concentrated disadvantage should significantly increaseexposure to violent peers.

RESEARCH DESIGN AND METHODS1

DATA

We assess our hypotheses with data from the PHDCN, a multiwaveinterdisciplinary study of how individual, family, and contextual factors con-tribute to youth development. The PHDCN consists of several components,including a Community Survey (CS) and Longitudinal Cohort Study (LCS).The CS is a probability sample of 8,782 Chicago residents focused on as-sessing the social, economic, political, and cultural conditions in their com-munities. For the CS, Chicago’s 865 census tracts were combined into 343neighborhood clusters (NCs) based on spatial contiguity according to eco-logical boundaries and internal homogeneity with respect to race/ethnicityand SES. Each neighborhood cluster, averaging 8,000 people, was smallerthan the 77 community areas in Chicago, thereby approximating a local“neighborhood.” A three-stage sampling design was used to select cityblocks within NCs, households within blocks, and one adult (18 years orolder) per household. This design ensured that the number of cases perNC could generate meaningful results from residents’ aggregated responses(see Sampson, Raudenbush, and Earls, 1997).

The LCS, consisting of three waves of data, is a probability sample ofparticipants in seven cohorts defined by age at baseline (0, 3, 6, 9, 12, 15,and 18 years). A stratified probability sample of 80 NCs selected fromthe 343 NCs and a simple random sample of households within theseNCs identified eligible respondents in each cohort. Respondents and theirprimary caregivers were interviewed up to three times between 1994 and2002; the average time between interviews was 2.5 years. A total of 1,516subjects from cohorts aged 12 (n = 820) and 15 (n = 696) years wereinterviewed at wave I. Of these, 99.1 percent or 1,502 subjects (814 and

1. The discussion of data and methods draws on Zimmerman and Messner (2010).


688 from cohorts 12 and 15, respectively) who responded to at least oneviolent crime item over the three waves of data collection were includedin this study.2 Analysis of attrition revealed no significant differences onkey variables between the 1,502 subjects included in the study and the14 subjects excluded from the study. Although response rates for wave IIwere 86.2 percent and 82.7 percent for the 12- and 15-year-old cohorts,respectively, and response rates for wave III were 74.9 percent and 71.3percent, our modeling techniques allowed for the inclusion of all 1,502respondents (see the “Statistical Models” section that follows). Less than3 percent of respondents were missing valid data on exposure to peerviolence, and less than 5 percent of respondents were missing valid dataon background variables. For all respondent and family-level variables,we used multiple imputation techniques to address potential bias resultingfrom missing data (for details about multiple imputation procedures, seeAllison, 2001; Royston, 2005; for details about multiple imputation usingHLM software, see Raudenbush and Bryk, 2002).

At least one subject resided in 78 of the 80 sampled NCs. Nine NCshad less than five subjects and were collapsed by race/ethnicity and SESto yield a macrolevel sample size, N, of 70 and an average microlevelsample size within NCs, n, of 21. Despite differing views on the samplesizes needed to obtain unbiased cross-level interaction coefficients and tominimize the probability of type I errors, there is general agreement that themajor consideration should be the macrolevel sample size, and it is betterto have a large number of groups with a few people than a small number ofgroups with many people (see, e.g., Hox, 1995; Kreft and de Leeuw, 1998:199–226; Snijders and Bosker, 1999). The sample sizes in this study meetthese guidelines. In addition, we gain power by using multiple observationsacross participants. The dependent variable (see the “Statistical Models”section that follows) consists of up to 24 violent crime items per individualover the three waves of data collection (average = 20). Therefore, themodels have an average of 420 violent crime responses per neighborhood(21 people per neighborhood × 20 items per respondent).

VIOLENT BEHAVIOR

Respondents were administered a Self-Report of Offending question-naire (National Institute on Drug Abuse, 1991) at each wave of data col-lection to determine whether they had committed a series of violent crimes

2. The average ages of respondents at wave I, II, and III were 13.53, 15.53, and 18.12years, respectively. The youngest respondent at wave I was 10.80 years, whereasthe oldest respondent at wave III was 22.28 years. Despite the variation, these agescorrespond with the peak years of offending.


in the year preceding the interview. Self-reports were used because theyare independent of and capture a broader range of behaviors than officialmeasures of crime (Thornberry and Krohn, 2002). Eight items indicatingphysical aggression are considered violent crimes: hitting someone outsideof the house; attacking someone with a weapon; throwing objects such asrocks or bottles at people; carrying a hidden weapon; maliciously settingfire to a house, building, or car; forcefully snatching someone’s purse orwallet; using a weapon to rob someone; and being involved in a gang fight.Previous research with the PHDCN has used these items to measure violentbehavior (e.g., Raudenbush and Sampson, 1999; Sampson, Morenoff, andRaudenbush, 2005).

Violent crime is relatively rare in the sample. Although 2,380 violentcrimes were reported, the estimates of the prevalence of robbery (.5 per-cent), forceful purse snatching (.7 percent), arson (.9 percent), attackingsomeone with a weapon (4.2 percent), and gang fighting (6.3 percent) wereall less than 10 percent. These offenses were followed by carrying a hiddenweapon (10.7 percent) and throwing objects (13.3 percent). Even the mostprevalent offense, hitting someone (26.5 percent), was reported by less than30 percent of subjects (see appendix A). Although some of these crimes areinfrequent, the estimates are consistent with national norms (Brener et al.,1999).

NEIGHBORHOOD CONTEXT

Based on previous research, this study examines ten variables con-structed from the 1990 decennial census (Morenoff and Sampson, 1997;Sampson, Raudenbush, and Earls, 1997). These ten variables were com-bined into three indices of neighborhood structural differentiation based onfactor analysis: concentrated disadvantage, immigrant concentration, andresidential instability.

Concentrated disadvantage comprises the percent of families below thepoverty line, percent of households receiving public assistance, percentof nonintact families with children, percent of population unemployed,median household income in 1989, and percent of population non-White.These variables are highly interrelated and all load on a single factor (allloadings ≥ .83) using principal components analysis with oblique rotation.The variables were combined into a scale using a weighted factor regressionscore such that high levels reflect high levels of disadvantage. This is a well-established scale (Wikstrom and Loeber, 2000) that has been validated inChicago (see Sampson and Raudenbush, 1999: 640; Sampson, Raudenbush,and Earls, 1997: 920).

Immigrant concentration, constructed by the sum of z scores for per-cent Latino and percent foreign-born (r = .91), captures neighborhood


heterogeneity. Residential stability is operationalized by the percentage ofowner-occupied homes and the percentage of residents living in the samehouse as 5 years earlier (also constructed by summing the standardizedvariables; r = .89). These two variables serve as neighborhood-level controlsin the analysis.

We acknowledge a potentially problematic feature of our measurementstrategy in the assessment of the effects of neighborhood conditions, inparticular neighborhood disadvantage, on violence. The neighborhood-level variables are linked to individuals based on where they lived at waveI, approximately 3 and 5 years before the wave II and III measures ofviolence, respectively. Yet neighborhood conditions could have changedbetween the waves of the study, or respondents could have moved. Ourprincipal methodological strategy thus implies that neighborhood disadvan-tage exerts a contemporaneous effect on violence at wave I but also near-term and long-term enduring effects on violence at waves II and III. Recentwork by Sharkey and Sampson (2010) and Sampson and Sharkey (2008)using the PHDCN indicated that there is in fact appreciable mobility in thesample and that this mobility is consequential for youth outcomes, includingviolence. It is beyond the scope of this article, both conceptually and em-pirically, to model residential mobility and mechanisms of neighborhoodchange, but we consider the potential impacts of these factors in sensitivityanalyses reported as follows.

PEER VIOLENCE

On a scale ranging from one (“None of them”) to three (“All of them”),respondents reported how many of their friends engaged in each of fourviolent behaviors in the year preceding the baseline interview: getting into aphysical (fist) fight with schoolmates/coworkers or friends; hitting someonewith the idea of hurting them; attacking someone with a weapon with theidea of hurting them; and using a weapon or force to get money or thingsfrom people. These items were standardized and summed to form a peerviolence scale (α = .70) on which higher values represent higher levels ofpeer violence. To capture the hypothesized nonlinear relationship betweenpeer violence and self-reported violence, we constructed a quadratic peerviolence term, that is, the score on the standardized peer violence scalesquared.

We recognize that our measurement of exposure to violent peers is notideal. Respondents do not indicate the exact number of friends engagingin the types of violence in the enumerated list; therefore, the peer violenceexposure measure cannot be adjusted to account for the size of the respon-dent’s peer network. In addition, the PHDCN does not provide the agecomposition of the peer group. Therefore, we cannot measure cross-age


peer interactions. Moreover, a general limitation of self-reports of peer mis-conduct is same-source bias, or the possibility that respondents’ perceptionsof their friends’ behaviors may reflect their own behaviors (see Haynie,Silver, and Teasdale, 2006: 155-6). This measurement contamination claim(Gottfredson and Hirschi, 1990: 157) has received considerable attentionfrom scholars in the area of peer influence (e.g., Elliot and Menard, 1996;Haynie and Osgood, 2005; Matsueda and Anderson, 1998; Thornberry andKrohn, 1997: 222-3; Thornberry et al., 1994; Warr, 1993, 2002). Nonetheless,it is widely recognized that the number of delinquent friends is a robust pre-dictor of adolescent delinquency (Elliot, Huizinga, and Ageton, 1985; Warr,2002). In addition, unlike many previous studies, the scale contains violentcrime items that overlap with those comprising the dependent variable.

BACKGROUND VARIABLES

The following demographic variables were measured: age, gender,race/ethnicity, immigrant generational status (first, second, third, andhigher), internalizing (i.e., being anxious, depressed, and overcontrolled)and externalizing (i.e., being aggressive, hyperactive, noncompliant, andundercontrolled) problem behaviors, self-control, and IQ. Racial/ethnicgroups were categorized as Hispanic, African American, White, or “Other”(i.e., Asian, Pacific Islander, American Indian, or Other). Self-control is anindex defined by lack of inhibitory control, present-orientation, sensationseeking, and lack of persistence (see Gibson et al., 2010). IQ is measuredby the Wechsler Intelligence Scale for Children vocabulary test (Sampson,Morenoff, and Raudenbush, 2005; Wechsler, 1949).

Family-level variables include family size, primary caregiver (PC) maritalstatus (1 = married; 0 = not married), number of years living at current resi-dence, household socioeconomic status (SES), family structure, PC employ-ment status (1 = employed full time or part time; 0 = not employed), andnumber of siblings. Household SES was constructed as a standardized scaleof parent’s income, education, and occupational status. Family structurewas created with the following classification scheme: 1) two parents, bothbiological; 2) two parents, one/both nonbiological; 3) one parent, biological;and 4) one parent, nonbiological.

All individual- and family-level predictors are measured at the wave Iinterview. Some background variables are “fixed” and, thus, clearly ex-ogenous to violent offending (e.g., gender, race/ethnicity, and immigrantgenerational status). Others might conceivably be affected by involvementin violence, but given that they serve as control variables in the analysis,we measure them at wave I and treat them as exogenous to violence.We considered using a time-varying measure of peer violence given thelikelihood of reciprocal causal effects of peer delinquency and offending.


However, the wave II and III Deviance of Peers questionnaires in thePHDCN focus on less serious deviant behaviors (e.g., obeying school rules,property offending, and substance use) and include only one of the fourviolent offending behaviors in our peer violence index (i.e., the number offriends attacking someone with a weapon). This prevented us from creatinga reliable within-person measure of peer violence that varies across time.Appendix A reports descriptive statistics for all variables in the study.

STATISTICAL MODELS

Our analysis focuses on whether respondents reported involvement ineach violent crime item at each time point. This allows us to use a multi-variate, multilevel Rasch model, the simplest item response theory (IRT)model, to predict the odds of engaging in violent crime. Recent stud-ies have discussed the benefits of using item response theory to modelself-reported criminal behavior (Maimon and Browning, 2010; Osgood,McMorris, and Potenza, 2002; Raudenbush, Johnson, and Sampson, 2003;Sampson, Morenoff, and Raudenbush, 2005; Sharkey, 2006; Zimmerman,2010). We follow closely the methodology of Raudenbush, Johnson, andSampson (2003) and Sampson, Morenoff, and Raudenbush (2005) in ap-plying the multivariate, multilevel Rasch model to violent offending. Thismethod simultaneously uses the benefits of item response and hierarchicallinear models, applying item response theory to the dependent variablein a random-effects setting. It “takes into account (a) the fact that someviolent offenses are rarer than others, (b) changes over time within subjectsin propensity to violence, and (c) the dependence of violence on individ-ual, family, and neighborhood characteristics” (Sampson, Morenoff, andRaudenbush, 2005: 226). This model also avoids the loss of vast amountsof data that would result from missing data on the dependent variable(Osgood, McMorris, and Potenza, 2002). It allows us to use all 30,160violent crime item responses generated by the 1,502 respondents in oursample, as any subject responding to at least one violent crime item in atleast one of the three waves of data collection is included in the analysis.

The three-level logistic hierarchical model nests violent crime item re-sponses within persons within neighborhoods. Individual violent crime itemresponses are incorporated into a scale of violent offending in the level 1model. This model allows the violent crime items to vary as a quadraticfunction of age (over the three waves of study), criminal propensity, anditem severity and produces a latent variable (θ) representing each person’spropensity to engage in violent crime. This continuous variable is assumedto be normally distributed on a logit metric and serves as the outcomevariable for the person-level and neighborhood-level models (Osgood,McMorris, and Potenza, 2002). In the level 2 model, all individual and


family characteristics are used to predict violent offending within neigh-borhoods. The level 3 model predicts individual variation in violent offend-ing across neighborhoods with the neighborhood-level characteristics (seeRaudenbush, Johnson, and Sampson, 2003, for a detailed description of thestructure of the three-level logistic hierarchical model of violent offending).

To test our hypothesis that the effect of peer violence is better rep-resented by a nonlinear functional form than a linear form, we add aquadratic peer violence term to the full model.3 To test our hypothesis thatthe effect of exposure to violent peers on violence is attenuated in moredisadvantaged neighborhoods, we allow the slope of peer violence to varyrandomly across neighborhoods and then model the slope as a function ofconcentrated disadvantage. We also estimate a two-level hierarchical modelto examine whether concentrated disadvantage has a significant effect onexposure to violent peers (a normally distributed continuous variable). Allmodels are estimated using generalized estimating equations with robuststandard errors in the HLM 6 program.4

RESULTS

IS THE PEER EFFECT NONLINEAR?

Table 1 presents coefficient estimates from the three-level logistic hi-erarchical model discussed earlier. To reduce collinearity and make theresults interpretable for an average person in the sample, the continuousindependent variables were grand-mean centered (see Raudenbush andBryk, 2002: 31-5). We begin with an examination of the effects of individual-level characteristics on self-reported violent offending (model 1 intable 1). The results indicate that exposure to peer violence significantlypredicts self-reported violent crime (.70∗∗). In addition, individuals withlower levels of self-control are more likely to be violent (−.14∗∗); youthswith two nonbiological parents are more likely than youths with two bio-logical parents to be violent (.29∗∗); nontransient youths (−.02∗∗) and thosewith more siblings (−.07∗∗) are less likely to be violent; males are more

3. By adding a squared peer violence term to the model, we fit a quadratic logistichierarchical regression model to the data. This allows us to interpret the coeffi-cients on a log-odds metric and to discuss linearity and nonlinearity in terms of thelog-odds of violent crime while providing a more accurate fit to the data (Collett,2002: 118-121).

4. Two major assumptions of the model are 1) additivity–item severities and personpropensities contribute additively to the log-odds of a positive item response–and 2) local independence–item responses are independent Bernoulli randomvariables. These assumptions imply that the set of item responses taps a sin-gle construct, herein “the propensity to commit (violent) crime” (Raudenbush,Johnson, and Sampson, 2003: 177).


Table 1. Self-Reported Violent Offending Regressed on PeerViolence2 and a Cross-Level PeerViolence/Disadvantage Interaction

Model 1 Model 2 Model 3 Model 4Coefficient Coefficient Coefficient Coefficient

Variable (SE) (SE) (SE) (SE)

Intercept −1.22∗∗(.22) −1.19∗∗(.23) −1.07∗∗(.22) −1.15∗∗(.23)Peer Influence Variables

Peer violence .70∗∗(.04) .69∗∗(.04) .83∗∗(.06) .70∗∗(.04)Peer violence2 −.11∗∗(.03)Peer Violence ×Disadvantage

−.08∗ (.03)

Behavioral/CognitiveFactorsSelf-control −.14∗∗(.03) −.15∗∗(.03) −.14∗∗(.03) −.14∗∗(.03)Externalizing problemsscore

.00 (.00) .00 (.00) .00 (.00) .00 (.00)

Internalizing problemsscore

−.01 (.00) −.01 (.00) −.01 (.00) −.01 (.00)

Reading/verbal ability .00 (.01) .00 (.01) .00 (.01) .01 (.01)Family/HouseholdFactors

Two nonbio .29∗∗(.09) .29∗∗(.09) .28∗∗(.09) .29∗∗(.09)One bio .19 (.17) .17 (.17) .19 (.16) .17 (.17)One nonbio .45 (.25) .40 (.24) .38 (.24) .40 (.24)Family size .01 (.03) .01 (.02) .00 (.02) .01 (.02)Years living at currentaddress

−.02∗∗(.00) −.02∗∗(.00) −.02∗∗(.00) −.02∗∗(.00)

Number of siblings −.07∗∗(.02) −.07∗∗(.02) −.07∗∗(.02) −.07∗∗(.02)Family SES .00 (.03) −.01 (.03) −.01 (.03) −.01 (.03)PC marital status .02 (.14) .01 (.14) .01 (.13) .01 (.14)PC employment status −.14 (.08) −.14 (.08) −.14 (.08) −.14 (.08)

Demographic FactorsLinear age −.02 (.08) −.02 (.08) −.02 (.08) −.02 (.08)Quadratic age .01 (.02) .01 (.02) .01 (.02) .01 (.02)Male .64∗∗(.08) .63∗∗(.08) .62∗∗(.08) .64∗∗(.08)First−generationimmigrant

−.65∗∗(.15) −.62∗∗(.14) −.56∗∗(.14) −.60∗∗(.14)

Second-generationimmigrant

−.17 (.10) −.14 (.10) −.12 (.10) −.14 (.10)

Hispanic .09 (.14) .16 (.14) .12 (.14) .13 (.14)African American .23 (.12) .13 (.13) .10 (.14) .10 (.14)Other .03 (.21) −.01 (.21) −.02 (.21) −.05 (.21)

NeighborhoodCharacteristics

Concentrateddisadvantage

.02 (.04) .02 (.04) .04 (.05)

Immigrant concentration −.16∗∗(.06) −.16∗∗(.06) −.17∗∗(.06)Residential stability −.06 (.04) −.05 (.04) −.06 (.04)

NOTES: The level 1 model produces relative severities of the items in the scale of violence.Although these results are not presented in table 1, they are available from the authors uponrequest.ABBREVIATIONS: bio = biological parents; nonbio = nonbiological parents; PC = primarycaregiver; SE = standard error; SES = socioeconomic status.∗p < .05; ∗∗p < .01.


likely to be violent than females (.64∗∗); and first-generation immigrantsare less likely than third-generation immigrants to engage in violent crime(−.65∗∗). Model 2 adds the neighborhood-level characteristics and indicatesthat individuals living in neighborhoods with higher levels of concentratedimmigration are less likely to be violent (−.16∗∗). Note that the effectsof the individual-level characteristics are not substantially altered whenthe neighborhood-level variables are included in the model. Overall, thesefindings comport with previous research (e.g., Mears, Ploeger, and Warr,1998; Pratt and Cullen, 2000; Sampson, Morenoff, and Raudenbush, 2005;Sampson, Raudenbush, and Earls, 1997; Van Voorhis et al., 1988; Warr,2002).

Model 3 in Table 1 investigates the functional form of the peer vio-lence/violence relationship by adding a quadratic peer violence term (“PeerViolence2”) to the three-level logistic hierarchical model. The negative andsignificant quadratic peer violence term (−.11∗∗) indicates that the effectof violent peer exposure on the log odds of involvement in violent crimeis nonlinear. The Akaike information criterion (AIC) and a chi-squarelikelihood-ratio test (p < .001) indicate that the quadratic model (model 3in Table 1) fits the data better than the linear model (model 2 in Table 1).5

The sign of the coefficient supports our motivating hypothesis that there isa declining marginal effect of exposure to violent peers on violent offendingas peer violence increases.

Figure 1 illustrates the nonlinear effect of exposure to violent peers onviolent offending. The figure indicates that the peer violence/offendingrelationship exhibits a decreasing positive slope as peer violence increases.Table 2 shows the predicted slope for the peer violence effect on violentcrime at selected points along the curve. This slope is calculated as thepartial derivative of the peer influence equation. Referring back to model 3in Table 1, the peer influence equation is

.83 × (Peer Violence) − .11 × (Peer Violence)2 (1)

The partial derivative of this equation is

.83 − 2 × .11 × (Peer Violence) (2)

5. The AIC is calculated as AIC = 2k - 2ln(L), where k is the number of parametersin the estimated model and L is the value of the likelihood function of the model.The AIC does not rely on the sample size, and is used in lieu of the more restrictiveBayesian information criterion (BIC) (which relies on the sample size) because itis not clear in multilevel models which sample size should be used: the lower-levelsample size, the higher-level sample size, or some combination of the two.


Figure 1. Nonlinear Model of the Peer Violence Effect onSelf-Reported Violent Crime

–3.0

–2.5

–2.0

–1.5

–1.0

–.5

0

.5

1.0

–1.5 –1.0 –.5 0 .5 1.0 1.5 2.0 2.5 3.0

Standard Deviations from Mean of Peer Violence

Vio

lent

Cri

me

(Log

-odd

s)

NOTES: Peer violence ranges from –1.4 to 3.9 (see appendix A), but 98.5 percent(1,480/1,502) of sample respondents report peer violence in the displayed range. Theremaining respondents report values on the upper end of peer violence. Data points arescattered throughout the displayed range and ensure that the nonlinear functional form isnot attributed to a few outliers at either the upper end or the lower end of the continuum.

To illustrate, the marginal effect at the mean of peer violence is .83[.83 − 2 × .11 × (0)] (see Table 2); and the marginal effect at 1 standarddeviation above the mean of peer violence is .61 [.83 - 2 × .11 × (1)] (seeTable 2). Overall, Table 2 indicates that the effect of exposure to violentpeers on violent offending decreases as peer violence increases until itreaches nonsignificance at 2.8 standard deviations above the mean of peerviolence. Approximately 1.5 percent of subjects (22/1,502) have values ofpeer violence above this point. Thus, although the peer violence effectdecreases as exposure to violent peers increases, peer violence is indeedinfluential at almost all points along the curve.

DOES THE PEER EFFECT VARY BY LEVELS OFNEIGHBORHOOD DISADVANTAGE?

To examine whether the effect of exposure to violent peers on violenceis attenuated in more disadvantaged neighborhoods (hypothesis 2), we firstestimate a baseline model without level 2 or level 3 covariates to examine


Table 2. Predicted Slopes for the Nonlinear Peer ViolenceEffect on Self-Reported Violent Crime

Standard Deviations from Mean of Peer Violence Predicted Slope Coefficient (SE)

−1.5 1.17∗∗∗(.13)−1.0 1.06∗∗∗(.11)−.5 .94∗∗∗(.08)

.0 .83∗∗∗(.06)

.5 .72∗∗∗(.04)1.0 .61∗∗∗(.04)1.5 .49∗∗∗(.05)2.0 .37∗∗∗(.07)2.5 .25∗∗ (.09)2.6 .23∗ (.10)2.7 .21∗ (.10)2.8 .19 (.11)2.9 .16 (.11)3.0 .14 (.11)

ABBREVIATION: SE = standard error.∗p < .05; ∗∗p < .01; ∗∗∗p < .001.

how the variation in violence is apportioned (not shown). The model indi-cates that there is significant neighborhood-level variation in the peer effect(χ2 = 91.32; df = 69.00; p < .05). Approximately 22 percent, 73 percent, 3percent, and 2 percent of the reliable variation in self-reported violencelies between item responses, individuals, neighborhoods, and exposure toviolent peers, respectively. To investigate the source of the variability in thepeer effect across neighborhoods, we model the propensity of violence as afunction of a cross-level peer violence/disadvantage interaction. The coef-ficient for the “Peer Violence × Disadvantage” interaction term in model4 of Table 1 is negative and significant (−.08∗), indicating that a 1 standarddeviation increase in concentrated disadvantage reduces the slope of “PeerViolence” by .08 units. Consistent with our second hypothesis, the effectof peer violence on violent offending is attenuated in more disadvantagedneighborhoods.

Figure 2 depicts the relationship between peer violence and violent of-fending by level of concentrated disadvantage. Even though peer violenceis positively associated with violent crime at all levels of concentrated dis-advantage, the slope of the line is steeper at lower levels of disadvantage.

DOES CONCENTRATED DISADVANTAGE INFLUENCEEXPOSURE TO VIOLENT PEERS?

Our interpretation of the cross-level peer violence/disadvantage interac-tion (elaborated earlier) is predicated on 1) the premise that the effect ofpeer violence on violent offending is nonlinear, as reflected in a declining


Figure 2. The Peer Violence Effect on Self-Reported ViolentCrime, by Level of Concentrated Disadvantage

–2.5

–2.0

–1.5

–1.0

–.5

0

.5

1.0

1.5

–1.5 –1.0 –.5 0 .5 1.0 1.5 2.0 2.5 3.0

Standard Deviations from Mean of Peer Violence

Vio

lent

Cri

me

(Log

-odd

s)

1.5 < Disadvantage @ Disadvantage 1.5 > Disadvantage

NOTES: Peer violence ranges from –1.4 to 3.9 (see appendix A), but 98.5 percent(1,480/1,502) of sample respondents report peer violence in the displayed range. Theremaining respondents report values on the upper end of peer violence. Data points arescattered throughout the displayed range and ensure that the nonlinear functional form isnot attributed to a few outliers at either the upper end or the lower end of the continuum.

marginal effect of violent peer exposure at high levels of peer violence(established earlier); and 2) the hypothesis that neighborhoods with highlevels of disadvantage are populated by youths at the high end of the violentpeer exposure continuum, the range of the distribution in which the peereffect is attenuated (hypothesis 3).

Model 1 in Table 3 shows a preliminary analysis with the neighborhood-level characteristics as the sole predictors of exposure to violent peers.Consistent with our third hypothesis, the results indicate that concentrateddisadvantage positively and significantly predicts exposure to violent peers(.21∗∗). As levels of disadvantage in the neighborhood increase, exposureto violent peers also increases. The results also indicate that exposure toviolent peers is lower in neighborhoods with higher levels of immigrantconcentration (−.12∗∗). Model 2 in Table 3 introduces the person-level


Table 3. Peer Violence Exposure Regressed on ConcentratedDisadvantage and Neighborhood-Level andPerson-Level Covariates

Model 1 Model 2Variable Coefficient (SE) Coefficient (SE)

Neighborhood CharacteristicsConcentrated disadvantage .21∗∗(.03) .07∗ (.03)Immigrant concentration −.12∗∗(.03) −.02 (.03)Residential stability .05 (.04) .04 (.03)

Behavioral/Cognitive FactorsSelf-control −.16∗∗(.03)Externalizing problems score .00 (.00)Internalizing problems score .00 (.00)Reading/verbal ability −.03∗∗(.01)

Family/Household FactorsTwo nonbio .06 (.08)One bio .12 (.13)One nonbio .03 (.20)Family size .01 (.01)Years living at current address .02 (.00)Number of siblings −.01 (.02)Family SES .00 (.03)PC marital status −.05 (.11)PC employment status .01 (.06)

Demographic FactorsMale .21∗∗(.06)Age at wave 1 .07∗∗(.02)First-generation immigrant −.29∗∗(.07)Second-generation immigrant −.10 (.07)Hispanic .21∗∗(.07)African American .45∗∗(.09)Other .13 (.13)

ABBREVIATIONS: bio = biological parents; nonbio = nonbiological parents; PC = primarycaregiver; SE = standard error; SES = socioeconomic status.∗p < .05; ∗∗p < .01.

covariates to determine whether the effect of disadvantage on peer vio-lence persists when controlling for compositional differences across neigh-borhoods in the individual- and household-level variables. The effect ofdisadvantage decreases but is still significant (.07∗), net of the controlvariables, once again indicating that exposure to violent peers increases asconcentrated disadvantage increases. In contrast, the apparent contextualeffect of immigrant concentration becomes nonsignificant when controllingfor the individual-level characteristics.

SENSITIVITY ANALYSES

As noted, our principal analyses have been based on the static measure-ment of neighborhood context. That is, neighborhood conditions measured


at wave I predict violent offending at all three waves of the panel. It is notpossible to measure neighborhood conditions at each wave of the panel, butit is possible to replace the measures of concentrated disadvantage, ethnicheterogeneity, and residential instability at wave I with measures fromthe 2000 census, which are temporally proximate to the wave III violencemeasures. The measures of neighborhood disadvantage taken at wave I andwave III prove to be highly correlated (r = .88; p < .001). It is therefore notsurprising that the results presented earlier pertaining to the moderating ef-fects of neighborhood disadvantage are substantively unchanged when the2000 census neighborhood-level measures are substituted for the analogousvariables measured at wave I.

A second important methodological issue relevant to our assessment ofneighborhood effects pertains to the potential impact of respondents’ resi-dential mobility. Perhaps moving to a more disadvantaged neighborhoodcould increase the number of violent peers respondents associate with,thereby decreasing the peer effect (according to the saturation model dis-cussed earlier). Conversely, moving to a less disadvantaged neighborhoodcould decrease peer violence exposure, thereby increasing the effect ofaffiliating with violent peers. In either scenario, the impact of neighborhooddisadvantage might not be reflected faithfully for the sample at large, thatis, for both respondents who remained in the neighborhood recorded atwave I and respondents who moved. However, it is likely that poor in-dividuals “select” impoverished neighborhoods in which to live, whereasaffluent families “select” high-class neighborhoods. This type of selectionbias (see Sampson and Sharkey, 2008) suggests that individuals in our sam-ple likely moved to neighborhoods with roughly the same neighborhood-level characteristics as their original neighborhoods, which would limit themeasurement error associated with the neighborhood-level factors.

To assess the potential impact of residential mobility on our substantiveconclusions, we reestimated all regression models with a dummy variabledifferentiating between respondents who moved over the course of thestudy and respondents who were residentially stable (1 = moved; 0 = didnot move). Youths whose neighborhoods changed during the study areno more or less likely to engage in violence than youths who lived in thesame residence throughout the study (β = .12; SEβ = .07; p > .05). Inaddition, the nonlinear relationship between violent peer exposure andviolent offending is replicated with the control for residential mobility,as is the cross-level interaction between neighborhood disadvantage andviolent peer exposure.6 These supplementary analyses lend confidence to

6. We also created a cross-level product term between the residential mobilityvariable and the neighborhood disadvantage index. This product term is nega-tive and significant in all regression models. There are various interpretations of


our general conclusions about the nonlinear effect of exposure to violentpeers and the ecological structuring of this effect.

SUMMARY AND DISCUSSION

Our research contributes to the literature by examining 1) the functionalform of the well-established, individual-level relationship between peerviolence exposure and self-reported violent crime; and 2) the extent towhich the effect of exposure to violent peers on violence is ecologicallystructured. The results of multilevel regression analyses support our mo-tivating hypothesis that a nonlinear functional form better represents theviolent peers/violence relationship than does a linear form. Specifically, aquadratic peer violence term negatively and significantly predicts violentoffending, indicating that the effect of peer violence exposure on violentcrime decreases as peer violence increases. Consistent with our secondhypothesis, the effect of peer violence exposure on violent crime is at-tenuated as neighborhood disadvantage increases, which is reflected in across-level peer violence/disadvantage interaction. Furthermore, this cross-level interaction is observed because neighborhoods with high levels ofdisadvantage are populated by youths at the high end of the violent peerexposure continuum (consistent with hypothesis 3), where the effect ofviolent peer exposure is attenuated.

We recognize that some limitations are associated with our analyses.First, as discussed, our measurement of exposure to violent peers is notideal. Unfortunately, we cannot address same-source bias or measure theexact size or age composition of a respondent’s peer group using thePHDCN. In addition, the measurement of neighborhood context is prob-lematic. The neighborhood-level variables are linked to individuals basedon where they lived at wave I, but neighborhood conditions could havechanged between the waves of the study, or respondents could have moved.We have conducted sensitivity analyses pertaining to these concerns, whichshould lend confidence to our results, but it would be preferable to have aprecise temporal match between the measurement of neighborhood contextand behavior. Moreover, a general issue confronting the “neighborhood ef-fects” research on crime is determining the appropriate geographical unit toattach to individuals, that is, the neighborhoods in which offenders reside or

this interaction. Perhaps the interaction reflects measurement error. Or perhapsmobility could be suppressing an association between disadvantage and violentoffending. This would be the case if the mobile respondents in our sample movedto less criminogenic neighborhoods. Although the interpretation of the interactionremains a puzzle for future research, the results presented earlier are substantivelyunchanged when controlling for the cross-level mobility/disadvantage interaction,once again substantiating the robustness of the findings.


the neighborhoods in which their offenses occur (Sampson, Morenoff, andGannon-Rowley, 2002: 469). The PHDCN data do not include informationon location of offenses; yet knowing where individuals offend is importantfor interpreting the mechanisms underlying any observed neighborhoodeffects (see Sampson, 2006: 157).

With these limitations in mind, our analyses have several implicationsfor future research. We have offered a rationale for the nonlinear rela-tionship between violent peer exposure and violence with reference to a“saturation” effect and have cited evidence of other nonlinearities in thecriminological literature. However, a more formal and rigorous theoreticalexplanation for the observed nonlinear peer effect is called for, one that isimbedded in existing criminological theory. Accounting for the functionalform of the peer delinquency/delinquency relationship would seem to bea critical task for future research given that the correlation between peerbehavior and delinquent behavior is one of the most widely demonstratedfindings in the criminological literature (Warr, 2002).

Furthermore, our analyses have focused on a single dimension of neigh-borhood context: disadvantage. However, given the centrality of collectiveefficacy in neighborhood-level research, we also considered the possibilitythat collective efficacy mediates the effect of concentrated disadvantageon exposure to violent peers. It seems plausible to speculate that violentpeer exposure would be lower in neighborhoods with a high degree ofcollective efficacy. Yet in supplementary analyses (available upon request),collective efficacy did not predict exposure to violent peers. We also con-sidered the possibility that the somewhat surprising null effect of collectiveefficacy on violent peer exposure might reflect countervailing processes.Recent research by Maimon and Browning (2010) indicated that collectiveefficacy positively predicts unstructured socializing. To the extent that un-structured socializing fosters exposure to violent peers, any negative effectof collective efficacy on violent peer exposure (e.g., via supervision andmonitoring) might be suppressed by its positive effect through unstructuredsocializing. However, collective efficacy did not have a significant effecton violent peer exposure even when a measure of unstructured socializingsimilar to that used by Maimon and Browning (2010) was included in themodel. The lack of any relationship between collective efficacy and violentpeer exposure thus remains a puzzle for future research.

In supplementary analyses, we also examined 1) whether collective effi-cacy interacted with exposure to violent peers to produce violent offending;and 2) whether moral/legal cynicism (Sampson and Bartusch, 1998) pre-dicted exposure to violent peers or interacted with peer violence when pre-dicting violent offending. None of these supplementary analyses producedsignificant results. Still, we encourage researchers to continue to examinehow peer influence varies across different dimensions of the neighborhoodcontext.


Our analyses also have been limited to violent offending. Perhapsthe nonlinear functional form of peer influence and the cross-levelpeer/disadvantage interaction also emerge for other types of crime.Researchers should continue to unpack the mechanisms through whichpeers influence various delinquent and criminal behaviors.

Our analyses also highlight the need to integrate different lines of the-oretical and empirical inquiry. For example, recent work on violent peerexposure has found that females are more influenced by their violentpeers than are males (Zimmerman and Messner, 2010). Future researchshould incorporate gender, neighborhood-level characteristics, and func-tional form into the study on peer influence to produce an accurate model ofthe peer effect on offending behavior. For it is possible that nonlinearity inthe peer effect and cross-level peer/context interactions are gender-specific.

Finally, we note that our analyses highlight a dimension of “neighbor-hood effects” that, for the most part, has been neglected in the crimino-logical literature. For a long time, researchers have been interested in the“contextual effects” of neighborhoods, that is, the possibility that a vari-able measured at the neighborhood-level might exhibit a causal effect onindividual variation in crime net of individual-level predictors. Researchersalso have searched for the “moderating effects” of neighborhood charac-teristics, whereby the strength of individual-level relationships depends onthe neighborhood context. Yet we do not interpret the observed cross-level interaction between disadvantage and violent peers as a “moderatingeffect” as commonly understood in the literature. Instead, the observedcross-level interaction evidently exists because of an underlying nonlinearindividual-level effect of exposure to violent peers on violence and of acontextual effect of disadvantage on peer violence. As we have argued,neighborhood disadvantage increases exposure to violent peers, and asresult, disadvantaged neighborhoods are populated by youths at the highend of the violent peer exposure continuum, where the effect of violentpeer exposure is closer to its limit (as reflected in the nonlinear peerviolence/violence relationship). Thus, the observed cross-level interactionbetween neighborhood disadvantage and exposure to violent peers is es-sentially a different mathematical way of detecting the curvilinear effect ofpeer violence exposure on violence, given the contextual effect of disad-vantage on violent peer exposure. Our results, therefore, reveal a differentkind of neighborhood effect and, in doing so, once again underscore theimportance of the neighborhood context. Our analyses also affirm Tittle’s(1995) claims about the utility of moving beyond linear theorizing and mod-eling in criminology. We encourage continued research on processes thatinterrelate features of the neighborhood context with nonlinear relation-ships between theoretically relevant individual characteristics and criminaloffending.


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Appendix A. Descriptive StatisticsVariable Mean SD Range

Individual Data (N = 1,502)Behavioral/cognitive factors

Peer violence 0 1.0 −1.4 – 3.9Self-control 2.7 .6 .7 – 4.9Externalizing problems score 10.4 8.5 0 – 66.0Internalizing problems score 10.2 9.0 0 – 63.0Reading/verbal ability 7.1 3.0 1.0 – 19.0

Family/household factorsFamily structureTwo bio (reference) 43.7 49.6 0 – 1.0Two nonbio 21.4 41.1 0 – 1.0One bio 30.5 46.1 0 – 1.0One nonbio 4.4 20.5 0 – 1.0Family size 5.8 2.0 .6 – 14.0Years at current address 6.7 7.3 0 – 59.0Number of siblings 2.2 1.7 0 – 10.0Family SES −.1 1.4 −3.0 – 3.8PC marital status 53.9 49.9 0 – 1.0PC employment status 63.2 48.2 0 – 1.0

Demographic factorsAge at wave 1 13.5 1.5 10.8 – 16.9Male 48.9 .5 0 – 1.0Immigrant generationFirst 13.2 33.8 0 – 1.0Second 29.3 45.5 0 – 1.0Third or higher (reference) 57.5 49.4 0 – 1.0

Race/ethnicityHispanic 44.7 49.7 0 – 1.0African American 36.9 48.3 0 – 1.0White (reference) 14.3 35.0 0 – 1.0Other 4.1 19.9 0 – 1.0

Violent crime item responsesHitting someone 26.5 44.1 0 – 1.0Attacking with a weapon 4.2 20.0 0 – 1.0Throwing objects 13.3 34.0 0 – 1.0Carrying a hidden weapon 10.7 30.9 0 – 1.0Arson .9 9.6 0 – 1.0Forceful purse snatching .7 8.3 0 – 1.0Robbery .5 7.1 0 – 1.0Being in a gang fight 6.3 24.3 0 – 1.0

Neighborhood Data (N = 70)Concentrated disadvantage 0 1.0 −1.8 – 2.1Immigrant concentration .4 1.1 −1.0 – 3.0Residential stability −.1 1.0 −2.1 – 2.0

NOTES: All person-level data were obtained at wave 1. Binary and nominal variables arereported as percentages.ABBREVIATIONS: bio = biological parents; nonbio = nonbiological parents; PC = primarycaregiver; SD = standard deviation; SES = socioeconomic status.

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NEIGHBORHOOD CONTEXT AND NONLINEAR PEER EFFECTS ON ADOLESCENT VIOLENT CRIME