Clarity from Violence? Intragroup Aggression and the Structure of Status Hierarchies
Abstract
Status hierarchies are fundamental forms of social order that structure peer interactions like intragroup aggression. The reciprocal relationship, however, remains unclear. Does intragroup aggression strengthen, or weaken, status hierarchies? Under what conditions? To answer these questions, I analyze an original dataset containing victimization and directed friendship networks of 8,229 adolescents across 256 classes and three semesters. Measuring the strength of status hierarchies by how likely friendship nominations are characterized by hierarchical triads, I show that peer aggression weakens status hierarchies, and temporal sequences indicate the results are unlikely to be explained by reverse causality. I theorize that clear status hierarchies emerge through coordinated reallocations of esteem, and peer aggression engenders hierarchy primarily by giving onlookers shared opportunities to coordinate. Peer aggression, however, is frequently ambiguous, and onlookers arrive at inconsistent interpretations, fragmenting how they assign esteem and reducing the clarity of status distinctions. Additional analyses confirm that whether peer aggression strengthens or weakens status hierarchies depends on the consistent perceptions of onlookers. Taken together, this research demonstrates the significance of third-party onlookers and their ability to consistently interpret interactions, while offering new explanations for when peer aggression is self-limiting or persistent.
Does peer aggression clarify a group’s status hierarchy? Or does aggression weaken status hierarchies, leading to greater ambiguity? Under what conditions? Status hierarchies are a foundational and ubiquitous form of social order. Patterned differences in the receipt of respect almost always emerge whenever humans form social groups (Bendix 1980; Blau and Scott 2003; Gould 2002; Magee and Galinsky 2008; Ridgeway 2019). A rich line of social science research investigates how status hierarchies structure the intensity, frequency, and targets of peer aggression and conflict (e.g., Faris and Felmlee 2014; Gould 2003; Papachristos 2009).1 Here, I invert this traditional emphasis. My goal is to investigate how peer aggression affects the structure of status hierarchies, and, in doing so, better understand when and how peer interactions like aggression contribute to this fundamental form of social order (Benard, Berg, and Mize 2017; Fararo and Skvoretz 1986; Kawakatsu et al. 2021; Lynn, Podolny, and Tao 2009; Manzo and Baldassarri 2015).
One way to approach this question is to imagine peer aggression produces dyads of winners and losers, wherein deference flows upward from losers to winners. Individuals use aggression to compete with one another to establish status differences, and dominant individuals win respect (Lorenz 2002; see also Lee and Ofshe 1981; Levi Martin 2009; Mazur 1973). As intuition would suggest, and as I will illustrate through formal simulations, these dyadic encounters clarify status hierarchies. Individuals occupy increasingly differentiated and rank-ordered positions, aligning with their individual capacity for aggression (see Bonabeau, Theraulaz, and Deneubourg 1996; Miyaguchi, Miki, and Hamada 2020). This perspective, which might be termed the dyadic framework, supposes that peer aggression contributes to clear status hierarchies.
An amendment to this dyadic framework introduces third-party audiences and audience judgment. In this view, “the essential relationship is not dyadic but triadic”: the judgment of third-party others in the group is what constitutes status, not the deference of victims per se (Goode 1978:22; see also Black 1990). The premise of an audience framework is that status hierarchies are the product of consistent allocations of respect among group members, informed through sequences of interactions that are visible to onlookers (Chase 1980). This idea permeates scholarship on aggression as a signal of strength or competence to others, rather than primarily about forcing deference from victims (Benard 2015; Cheng and Tracy 2014; Gambetta 2009; Halevy, Chou, and Galinsky 2011).
Audience judgments of aggression are contextual. In settings where aggression is valued (e.g., gangs; Papachristos 2009), onlookers may react to peer aggression by denigrating victims and reallocating respect to aggressors. In other settings, audiences may negatively judge aggression, and aggressors may lose respect in the eyes of others (see Anderson and Kilduff 2009; Ridgeway and Diekema 1989). As I will show in simulations, however, the theory implies that peer aggression clarifies a status hierarchy, regardless of whether it is negatively or positively evaluated. Whether aggressors or victims are lauded or denigrated by audiences, as long as reactions are coordinated, they rewire a network of directed esteem (i.e., respect) to produce rank-ordered positions. If aggression is negatively judged, then individual aggressors will occupy clear, lower-status positions, but the structure of the esteem network trends toward differentiated, rank-ordered roles. Hence, the audience framework predicts that peer aggression engenders hierarchical clarity when it is a visible interaction that helps audiences coordinate in allocating respect to members.
Whether someone is joking or behaving aggressively toward another, however, is often ambiguous. For instance, research suggests that instrumental aggressors may deliberately obscure whether they are behaving aggressively or not (see Leifer 1988; Padgett and Ansell 1993). As smeared text on a page elicits multiple interpretations, aggression may be visible without necessarily being legible to audiences, who draw diverse interpretations as to what is occurring. Some perceive the interaction as a playful exchange of solidarity, others perhaps mistake the victim for an aggressor. Additionally, audiences do not always share in their understanding of what constitutes aggression or how to respond to it. The resulting multiplicity means that reallocations of respect are uncoordinated, and, in simulations, I show that status hierarchies are weakened when audiences are uncoordinated in how they allocate respect. This suggests a further amendment of the dyadic and audience frameworks, where the link between aggression and hierarchical clarity is contingent on the degree to which aggression is legible to audiences.
Empirical tests of these nested accounts require data that are challenging to collect. The first challenge is that status hierarchies are a group-level, rather than individual-level, phenomenon. Prior research has shown that individual aggressors generally occupy higher-status positions in later time periods (e.g., Callejas and Shepherd 2020; Cheng et al. 2013). Additionally, research on instrumental aggression posits that people rely on aggression to move within a status hierarchy (Faris 2012). Individual ascent and descent on a status ladder, however, is about mobility. Mobility takes the structure of the hierarchy for granted, assuming there is a ladder with rungs to climb. Showing that aggression helps people move up on a status ladder does not tell us about the structure of the ladder, such as whether the rungs are secure. Indeed, sufficiently well-powered analyses of group structure require full network data on actors embedded in discrete groups that also vary in their frequency of intragroup aggression.
A second empirical challenge is the problem of reciprocal causes and effects. Research shows that ambiguous status distinctions engender peer aggression, as individuals are more likely to attack one another to clarify and protect their status positions (Gould 2003; Kilduff, Elfenbein, and Staw 2010; Piezunka et al. 2018). In other words, the clarity of a status hierarchy affects the overall rates and targets of aggression. To disentangle these reciprocal effects, one approach is to manipulate the frequency of peer aggression in a field experiment and assess how this exogenous change affects group structure. The next best solution is to rely on longitudinal data to establish temporal sequences and show how these sequences differ by initial levels of intragroup aggression, which means we need detailed network data not only from multiple groups, but also from multiple groups over time.
To collect a dataset that satisfies these criteria, I tracked directed friendship nominations and victimization patterns among a cohort of 8,229 Chinese middle school students over three semesters and across 256 classes. The coverage of the data is remarkable, with effectively all students participating and 93.3 percent of students completing all three survey waves (N = 7,672). Researchers have questioned the assumption that friendship nominations are proxies for directed esteem or respect (e.g., Kitts and Leal 2021; Vörös, Block, and Boda 2019). I rely on an alternative, weaker assumption. When friendship nominations, which are usually characterized by closure and reciprocity, are instead hierarchically structured, this indicates the existence of a strong status hierarchy to coordinate the observed network. Under this assumption, one measure of the strength of status hierarchies is the extent to which hierarchical triads are observed in the friendship nominations more than would be expected by chance. To further control for social structures that are correlated with but separable from hierarchy, such as network closure, mutuality, and density, I also model tie formation using exponential random graph models (ERGM) with a term—traditionally called “tau”—that represents the sum of hierarchical triads (following McFarland et al. 2014).
I then examine how levels of classroom aggression in one semester predict levels of hierarchical clarity in the next, while accounting for differences in precision in these estimated parameters (following the multilevel approach suggested by Snijders and Baerveldt 2003). Critically, the data contain a rich set of time-varying measures of mental health, individual-level predictors of victimization, and predictors of tie formation identified in prior research. These are controlled for in the analyses. Additionally, because friendship nominations in these adolescent groups are characterized by extraordinary levels of gender homophily2 and often even consist of disconnected gender subgroups, I also explore gender heterogeneity in the results.
Results show that higher overall rates of intragroup peer aggression in one semester weaken status hierarchies in the next. To address concerns about reverse causality, I show that results are robust when analyzed with cross-lagged panel models with fixed effects, supporting the claim that peer aggression generates more ambiguity in the status hierarchy (Allison, Williams, and Moral-Benito 2017). Empirical tests support key mechanisms of the legibility framework. For instance, by comparing the frequency of aggression reported by victims versus that of onlookers, I show that aggression erodes hierarchy in contexts where the group cannot consistently identify whether aggression is occurring or not. By contrast, aggression clarifies and strengthens status hierarchies when it is also identified as such by other group members.
The findings enrich our understanding of how aggression among individuals contributes to social structure at the group level. Third-party audiences come into focus as key players: group structure is a consequence of audience judgment of visible dyadic interactions. Yet, the findings also highlight the importance of shared interpretation. For aggression to strengthen status hierarchies, group members must share their understanding of aggression and coordinate how they allocate respect. Aside from elucidating how peer aggression contributes to a fundamental form of social order, this research sheds light on substantively important problems, such as how and when aggression produces clear social structures that arrest further escalation.
How Peer Aggression Shapes Status Hierarchies
Whether in the form of barbed comments, rumor-spreading, social exclusion, or physical attacks, peer aggression is understood here as violent actions perceived by victims as intentionally hurtful (see Deutsch 1949). Given the interpersonal harms of peer aggression, it appears antisocial on the surface. Aggression, however, is often a relational act par excellence, embedded within social networks and motivated by social concerns about status positions (Coser 1964; Faris 2012; Faris and Felmlee 2014; Fiske and Rai 2020; Magee and Galinsky 2008; Merten 1997). For instance, when a status hierarchy is strong and the positions that everyone occupies are clear, peer violence and aggression are less likely to occur or escalate (Bendersky and Hays 2012; Gould 2003; Kilduff et al. 2010; Piezunka et al. 2018). Nevertheless, how does peer aggression affect hierarchical clarity?
To review and develop theory around this question, I begin by demarcating scope conditions and conceptual definitions. To facilitate group coordination, organizational leaders frequently differentiate members into formal, rank-ordered roles that constitute a hierarchy (Anderson and Brown 2010; Goode 1978). The scope of the theories introduced here, however, is bounded to groups with status hierarchies that are not fully determined by formal positions. Moreover, I assume sufficiently small groups where individuals can develop “working knowledge” about one another (Faris 2012:1209). These are groups where members know about and interact with one another.
Under the scope conditions of informal peer groups and working knowledge, I assume status hierarchies are primarily defined by the network structure of directed esteem. From here, I define the clarity of status hierarchies as the extent that peer allocations of respect are consistently directed and produce rank-ordered positions (Bunderson et al. 2016). For instance, a hierarchy is so weak as to be nonexistent if all individuals occupy structurally equivalent positions in a network of directed esteem, such as a fully connected and reciprocal graph. It is impossible to discern distinct positions, and there is no communally agreed-upon rank-ordering of positions by respect. As defined here, ambiguity and weakness in a status hierarchy are synonymous, as ambiguous roles are poorly distinguished. By contrast, a clear status hierarchy is intersubjective, characterized by distinct rank-ordered positions that emerge from consistently directed allocations of respect in the group.
This structural definition of a strong status hierarchy as consisting of rank-ordered positions in a network of peer esteem accords with sociological notions of status as positional, rather than a resource held by individuals (e.g., Gould 2002). To illustrate this conceptual distinction, consider how each might be measured. A resource-based operationalization of status, such as a Gini coefficient, represents asymmetries in the distribution of esteem within the group (Allison 1978). Yet, such a measure lacks any information about the network structure of how esteem is allocated and, critically, whether there is acyclicity and consensus about positions (Bunderson et al. 2016). Structural operationalizations of hierarchical clarity, by contrast, directly estimate the extent to which rank-ordered positions are present in a network of esteem. Scholars have created such measures by focusing on the building blocks of networks: triads (Faust 2007). A directed network has 16 possible triads, and combinations of triads that are “forbidden” (or complementarily, allowed) define distinctive network structures, such as perfectly balanced networks (Cartwright and Harary 1956; Rawlings and Friedkin 2017). Research has shown that five triadic building blocks define the rank-ordered positions that align with the definition of hierarchical clarity here (McFarland et al. 2014; Moody et al. 2011). Following triad naming conventions of labeling the number of mutual, asymmetric, and null (MAN) edges in each triad, these triads are called 021D, 021U, 030T, 120D, and 120U. Each of these triads uniquely captures consistent directionality in allocations of esteem (see Figure 7 for visualizations of each).3 When these five building blocks are observed together, they imply consensus about rank-ordered status positions: a clear status hierarchy (Bunderson et al. 2016).
The Dyadic Framework
Given these scope conditions and definitions, a simple theory to explain how peer aggression affects the clarity of status hierarchies might be called a dyadic framework. In this framework, peer aggression creates a dominant winner and deferential loser (see Lee and Ofshe 1981; Lorenz 2002; Mazur 1973). Each instance of peer aggression redirects respect from losers (typically the victims) to winners (typically the aggressors). If individuals in a group have different capacities for dominance, intuition suggests each episode of dyadic aggression contributes to a clear status hierarchy. To formalize this intuition, I program key propositions of this framework in a simulation to assess resulting group-level consequences.
Following research on agent-based models (Humon and Fararo 1995; Stadtfeld and Amati 2021), each simulation begins by drawing a random, directed network of esteem allocations based on real-world peer groups. I do so by sampling a random network among 32 actors, the average size of peer groups in my sample, using ERGM coefficients from the mean calculated from all networks in my dataset. Once the network is drawn, I randomly assign a different latent capacity for dominance to each actor according to a standard normal distribution (mean 0, standard deviation of 1). This is a simple group where individuals have varying capacities to dominate others. In each round, two individuals are randomly drawn, and a winner and loser are resolved based on who is more dominant. The more dominant individual is presumed to “win” deference from this encounter, represented conceptually by replacing the edge between those two actors with a directed edge from loser to winner. This is repeated for R rounds. For each round, I calculate hierarchical clarity as the extent to which the five hierarchical triads are observed more than what would be expected by chance (McFarland et al. 2014). All simulations were conducted in R Studio, using the R programming language.
Clearly, the real world is more complex, but the simplicity of this simulation enables formal articulation of the fundamental parameters of a dyadic framework and their group-level implications. Results from n = 100 simulations are shown in Figure 1, Panel A. In this figure, simulated measures of hierarchical clarity are plotted for each round. Predicted values from a locally weighted scatterplot smoothing (LOESS) model are shown, with 95 percent confidence intervals. The simulation shows that hierarchical clarity increases monotonically with each round of aggression. The primary empirical prediction of a dyadic framework, then, is that the frequency of intragroup aggression leads to greater hierarchical clarity.
Figure 1. Simulation Results Based on Different Theoretical Propositions for How Peer Aggression Relates to Hierarchical Clarity
Note: Panels show simulated levels of hierarchical clarity (A) as a function of 1,800 rounds of peer aggression, under a dyadic framework; (B) after 40 rounds, under four different audience reactions to peer aggression, with legend ordered by the average magnitude of hierarchical clarity achieved in round 40; (C) after 40 rounds, when audience esteems aggressor, when visibility (V) is .5 or 0; and (D) after 40 rounds, when legibility (L) is .2. N = 100 simulations are displayed, with predicted values and 95 percent confidence intervals from a locally weighted scatterplot smoothing (LOESS) model.
The Audience Framework
An amendment to the dyadic framework imagines that aggression contributes to hierarchical clarity by coordinating how third-party onlookers reallocate their esteem, rather than merely creating winners and losers within dyads. In an audience framework, aggression is a signal: a symbolic act performed for an audience (Anderson and Bushman 2002; Benard 2013; Goode 1978). Gambetta (2009:80), for instance, observes that prisoners publicly attack others as a costly signal of their status positions. Social psychologists have also observed that behaving aggressively toward others can lead to status by signaling confidence and competence (Anderson and Kilduff 2009; see also Cheng et al. 2013). In this model, cumulative patterns of interactions establish social rank primarily through a triadic process, whereby onlookers reallocate their esteem in response to observed episodes of aggression (see Chase 1980).
Critically, when aggression is understood as a signal, interpretation of this signal can vary from context to context. Rather than imagining that dominant winners are always more respected, there are at least four possibilities for how onlookers reallocate esteem in response to observed aggression. An audience may (a) withdraw esteem from aggressors, (b) withdraw esteem from victims, (c) allocate more esteem to aggressors, or (d) allocate more esteem to victims. Each corresponds to a different normative possibility in group settings, where (a) attacking others is an illegitimate way to obtain status, (b) victims who are too weak to defend themselves are unworthy, (c) aggression is valued in the group and is thus a legitimate way to assert status, or (d) those who are attacked are considered deserving of esteem. Whether aggression contributes to upward status mobility for aggressors depends on which possibility prevails. For instance, in groups where explicit displays of dominance are illegitimate, research shows that individuals who dominate victims lose, rather than gain, status (Anderson, Ames, and Gosling 2008; Anderson and Brown 2010; Fragale et al. 2012). However, would the theory produce different predictions about how aggression affects the clarity of status hierarchies, depending on which audience response prevails?
To investigate the relevant predictions that emanate from variations in audience judgment, I program these possibilities in the simulation. As before, two individuals are randomly chosen each round, with the aggressor being the more dominant actor. During each round R, each onlooker has some probability V of observing this event. If they see the event, each actor takes one of the four actions mentioned above: they may withdraw esteem from an aggressor or victim (coded as adding –1 to the weight of the appropriate directed edge or adding this negatively weighted edge if it does not yet exist), or they can allocate esteem to an aggressor or victim (coded as the addition of +1 weight to the appropriate directed edge and adding said edge if it does not yet exist). Edges with a weight of 0 are removed. Because this is a signed graph, I calculate hierarchical clarity separately for subgraphs with negative and positive ties, before taking the mean.
Remarkably, results from n = 100 simulations of each possibility show hierarchical clarity increases whether aggressors or victims are denigrated or esteemed (see Figure 1, Panel B). This remains true when onlookers do not deterministically react the same way, but only have a higher probability of doing so. On the surface, this pattern is puzzling. Consider triads consisting of a victim, aggressor, and onlooker (see also Chase 1980:910). As in the dyadic framework, we assume the aggressor has forced deference from the victim. If so, a hierarchical triad is produced only when onlookers also esteem the aggressor (for a visual illustration, see Figure 2). What this surface intuition misses, however, is that the coordinated reallocation of esteem among onlookers toward a common actor generates multiple hierarchical triads involving each pair of onlookers and either the victim or aggressor. Hence, whether aggressors or victims are denigrated or esteemed, there will be increasing consensus about rank-ordered positions in the group whenever audiences see public interactions that help them coordinate how to allocate status.
Figure 2. Triad Transitions Under Different Audience Reactions
Note: A represents aggressor, V represents victim, O represents an onlooker. Dashed edges designate denigration, or the allocation of disrespect. Solid edges represent deference, or the allocation of respect.
These results imply that the audience framework arrives at a similar prediction as a dyadic one with respect to the relationship between aggression and hierarchical clarity. Yet, there are two important differences. First, the audience framework predicts that each act of aggression contributes to hierarchical clarity more efficiently, as each onlooker has some probability of reallocating esteem during each round. For instance, in groups of N = 32, each additional round of aggression contributes 40 times more to hierarchical clarity if audiences are allowed to react, compared to a simple dyadic framework. Second, the effect of aggression flows primarily through what the audience observes, rather than deference within aggressor-victim dyads. Thus, in an audience framework, the effect of aggression on hierarchical clarity varies by visibility. In simulations where onlookers only have a 50 percent chance of seeing and reallocating esteem to aggressors, each round of aggression contributes half as much to hierarchical clarity. Additionally, if there are no observers of aggression, any effect on hierarchical clarity ought to be negligible (see Figure 1, Panel C).
The Legibility Framework
Critically, the theoretical perspectives developed thus far do not predict that aggression erodes the clarity of a hierarchy. One way to permit this possibility is to consider that, as a public signal, aggression is itself subject to ambiguity. Consider the following account of intragroup aggression (Gould 2003:73):
One evening, Jehan, along with Pierot Malet, Brenardin Delecroix, Jean Wastiel, and a few others went to the Au Beau Regard tavern following an afternoon of tennis. As dinner was being cleared away, one of the above (possibly Wastiel) tossed a piece of bread at Jehan, striking him on the lapel of his jacket. The latter countered this by throwing a half-full glass of wine into Wastiel’s face. Wastiel good-naturedly cried, “Now I can see better,” poured wine into his own glass, and declaring: “Eye for an eye!” threw the contents at Jehan. Jehan was no longer amused: furious, he drew his dagger and dealt a thrust at Wastiel.
From the audience’s perspective, it was unclear why or when the putatively good-natured throwing of food transformed to an insult. Did Wastiel intend to insult Jehan by throwing a piece of bread at him? Was Jehan behaving aggressively when he threw a glass of wine into Wastiel’s face, or was it playful repartee? Up to the moment the dagger was drawn, the onlookers could not be certain whether the interaction signified peer aggression.
The difficulty audiences have in classifying interactions as peer aggression is central to what I term the legibility framework. Rather than observing and responding to aggression as victims experience it, audiences see peer interactions that are difficult to comprehend, which engenders diverse interpretations and reactions. Misinterpretation can occur when a signal is encoded and decoded, so legibility depends on both the performer and the audience. Performances of aggression may be ambiguous because humans are, in the main, clumsy users of violence (Collins 2008). Aggression may be spontaneous and ambiguous, rather than rehearsed, such that audiences struggle to interpret what is happening. Additionally, skilled social actors have good reasons to deploy aggression ambiguously (Leifer 1988; Padgett and Ansell 1993). They may commit to unambiguous attacks only after a series of successful dry runs and trial balloons to determine whether audiences will support them. Rather than public displays of dominance, they may attack others in ways that can be plausibly denied, deploying barbed comments or “pranks” that could be deemed jokes or innocuous games (see Teräsahjo and Salmivalli 2003). Additionally, even if aggressors have no motive to behave ambiguously, peer aggression could still be ambiguous if audiences do not share understandings of what aggression entails or if many interactions resemble, but do not signify, harmful intent or aggression. If the exchange of “trash talk” is commonplace and understood to be friendly, then onlookers might find it difficult to ascertain when a given insult ought to be understood as peer aggression.
The notion of legibility is distinct from visibility. Under the scope conditions of informal peer groups with working knowledge, interactions are unlikely to be totally invisible to onlookers, but seeing an interaction does not mean it can be accurately categorized. If strategic actors mean to gauge how onlookers react, then—as those who have been the subject of passive-aggressive or micro-aggressive comments might observe—aggression is visible but open to multiple interpretations. In some cases, audiences may even struggle to “disentangle aggressors from defenders” (Leifer 1988:869). Conversely, aggression that is coordinated with others, such as false gossip or ostracism, may be invisible to teachers. However, these acts of aggression are both visible and legible to the many peers who share the understanding that they are denigrating someone else (Adler and Adler 1998; Eder and Enke 1991; Garandeau and Cillessen 2006). In these cases, aggression flows through the peer network, recruiting onlookers directly to participate in an aggressive act, making such forms of aggression highly legible and especially potent in clarifying status distinctions.
The primary prediction from this framework, then, is that peer aggression clarifies status hierarchies when aggression is legible, but it erodes status hierarchies when it is not. To illustrate this, I encode a parameter for legibility in the agent-based model. As above, each round consists of an aggressor attacking a victim, with audience members having some probability V of observing the event and reacting (in this case, by esteeming the aggressor). If an audience member observes the event, however, they now have probability L of interpreting and reacting to the interaction consistently. If not, then the audience member randomly chooses how to reallocate esteem (or takes no action at all). The simulation results are identical to the audience models when legibility is 100 percent. However, as legibility decreases toward 0, the simulation reveals that each round of aggression essentially introduces uncoordinated rewiring in the esteem network and decreases hierarchical clarity (see Figure 1, Panel D).
To be clear, this simulation is not meant to generate networks that would appear in the real world, in that it omits significant factors that explain the formation of hierarchical triads (e.g., ex ante variation in individual status characteristics). In focusing on the implications of specific theories, however, the simulations reveal that the coordinated reallocation of esteem among onlookers is necessary and sufficient to produce clear status hierarchies. By contrast, inconsistent interpretation of peer interactions implies uncoordinated rewiring of an esteem network, which erodes the clarity of status hierarchies by introducing noise into the network.
Data and Methods
Context and Sample
To test these theoretical perspectives, I use data from adolescent peer groups. Aside from meeting the scope conditions, peer victimization in adolescent groups is important because it wreaks considerable damage on group and individual welfare, sometimes making life so unbearable as to compel victims to take their own lives (Carney 2000; Espelage and Swearer 2004; Juvonen, Graham, and Schuster 2003; National Academies of Sciences 2016). The prevalence of victimization in the United States ranges from 17.9 to 30.9 percent (National Academies of Sciences 2016:32). Moreover, peer aggression is observed in virtually every educational context in the world. The World Health Organization (WHO) has been fielding the Health Behavior in School-aged Children Survey (HBSC) across 40 countries since 1983. The median of students reporting themselves as either victims or perpetrators of aggression across these countries was 23 percent among boys and 16 percent among girls (WHO 2012).
I conducted a longitudinal survey among 8,229 7th- and 8th-grade students in 256 classrooms located in a prefecture in Shaanxi province, China. The sample was randomly drawn from a sampling frame of all middle schools in this prefecture, excluding (a) any school with a total enrollment of fewer than 100 students, as the local bureau of education noted that such schools were in the process of being merged with other schools, and (b) any school with selective entrance requirements (i.e., elite schools).4 Random sampling ensures the analysis represents the real-world range of peer aggression across adolescent groups. Within each school, up to two 7th- and 8th-grade classes were randomly chosen, and all students in those classes were surveyed. In each sampled class, all students were invited to privately complete paper-based surveys, and all surveys were placed into opaque, sealed envelopes when complete. To further reduce the probability of individual identification, each student was assigned a de-identified ID number at the beginning of the study that was used throughout each wave of data collection. All survey procedures were reviewed and approved by an Institutional Review Board.
Nearly all the adolescents (99 percent) assented to participate, and 93.3 percent of the adolescents completed all waves of the survey (N = 7,672). As with all longitudinal studies, some students (6.7 percent, or 557) could not be tracked.5 Of these, 325 students dropped out (58 percent of 557), 128 transferred to another school (24 percent), and 100 were sick, absent, or declined to participate in the follow-up surveys (18 percent). Because the unit of analysis in this study is the group, attrition that occurs because a student transfers or drops out from the class does not introduce bias and instead is part of the social process I seek to investigate. For instance, aggression may affect the departure of these individuals, and individuals who exit a group affect hierarchical clarity. Nevertheless, for transparency, Appendix Table A1 shows a t-test of differences in baseline characteristics between individuals who stayed for all three waves versus those who could not be tracked for one or more waves.
On average, these groups consist of 32 students and cannot have more than 60 students. The classes sampled in this data collection are the primary social context that students inhabit on a day-to-day basis. Relations among these students are further concentrated because approximately 70 percent of students in my sample live at school (see Table 1). Students spend their entire day with the same group of peers, and there is a greater-than-chance likelihood of living with their peers. These classes, therefore, constitute comparable groups that meet the scope conditions of the theoretical perspectives I seek to test.
| Variables | Mean | SD | Min. | Max. |
|---|---|---|---|---|
| Independent Variables | ||||
| Proportion Students Reporting Victimization | ||||
| T1 | 37.5% | 12.7% | 0 | 73% |
| T2 | 18.9% | 12.2% | 0 | 65% |
| T3 | 25.7% | 13.4% | 0 | 77.8% |
| Perceived Proportion of Students Victimized | ||||
| T1 | 20.2% | 12.7% | 0 | 100% |
| T2 | 17.7% | 10.9% | 0 | 86% |
| T3 | 17.8% | 13.6% | 0 | 100% |
| Dependent Variables | ||||
| Clarity of Status Hierarchy (Tau) | ||||
| T1 | –.064 | .521 | –1.267 | 2.354 |
| T2 | .828 | .607 | –.629 | 4.687 |
| T3 | 1.305 | .684 | –1.326 | 3.044 |
| Status Hierarchy (AME of ERGM Tau) | ||||
| T1 | –.007 | .010 | –.0626 | .056 |
| T2 | .006 | .010 | –.0322 | .055 |
| T3 | .008 | .063 | –.692 | .057 |
| Time-Varying Classroom-Level Covariates | ||||
| Perceived Teacher Care | ||||
| T1 | –.025 | .766 | –2.351 | 1.877 |
| T2 | –.671 | .826 | –2.495 | 1.817 |
| T3 | –.760 | .766 | –2.847 | 2.102 |
| Mental Health Risk Score (Anxiety) | ||||
| T1 | 38.49 | 3.547 | 28.52 | 48.81 |
| T2 | 37.43 | 3.860 | 23.67 | 50 |
| T3 | 36.88 | 4.390 | 24.12 | 47.83 |
| Time-Invariant Covariates (in Semester 1) | ||||
| Average level of asset PCA | –.255 | .656 | –1.734 | 1.553 |
| Proportion boys | 53.4% | .093 | 26.3% | 81.8% |
| Average age | 12.99 | .618 | 11.77 | 14.12 |
| Proportion living in dormitories | 70% | .235 | 0 | 100% |
| Proportion from single-parent families | 7.7% | .062 | 0 | 36.7% |
| Proportion with parents who are migrants | 17.5% | .103 | 0 | 50.9% |
| Proportion with parents who completed high school | 52.9% | .134 | 20% | 96.6% |
| Proportion with parents with agricultural occupations | 29% | .198 | 0 | 77.5% |
| Average academic achievement | –.033 | .490 | –1.569 | 1.186 |
Source: Author’s survey.
Note: N = 256. Semester 1 survey conducted in Fall 2012–13 school year. For information on student composition, see Appendix Table A1 for description of control variables and tests of how attritors compare to those who completed all follow-up questionnaires. Average class size = 32 students (8,229 students/256 classrooms).
Measures
Group-level measures of peer aggression
All respondents were asked to report the number of times they were victimized, where these events generally occurred, and how many people attacked them the last time they were attacked. Students were also asked to report how many of their classmates were victimized by other classmates. Enumerators verbally instructed students that any behavior personally experienced as playful or joking did not count as victimization. (Translated wordings for all relevant questions are provided in Part A of the Appendix.) During the second survey wave, respondents were also asked to further distinguish how many times they experienced verbal, relational, or physical aggression from the above aggressors.
One limitation in data collection is that students were not asked to report their aggressors, as this information was sensitive and had high rates of non-response in pilot testing: adolescents were reluctant to indicate whom they attacked or who attacked them. Aside from accuracy concerns, there was a high risk of harm of any accidental revelation of responses, especially in a closed classroom setting like China. The existing data, however, still permit me to measure the aggregate level of aggression in any classroom (as reported by victims), and the degree to which onlookers accurately perceived the level of aggression occurring within each class.
Measuring the strength of status hierarchies
During each survey wave, students were asked to self-report the names of up to nine friends. Although name-generator approaches to collecting network data can be biased by censoring, only 4 percent of students filled out all nine blanks. Additionally, with average class sizes of 32, nine names would consist of 28 percent of an average class. Students were asked to select these individuals from within their classrooms. This restriction ensures that complete friendship networks can be constructed for 256 separate classrooms across three semesters.6
I use triadic patterns in student friendship nominations to measure the strength of status hierarchies in each class. In adolescent peer groups where members spend most of their time together, friendships are highly valued. Nevertheless, whether friendship nominations are a suitable proxy of esteem is debated (Kitts and Leal 2021; Vörös et al. 2019). Friendship nominations, for instance, are typically characterized by reciprocity, rather than signifying asymmetric flows of esteem. Here, I rely on a different, weaker assumption: the extent to which friendship nominations are structured hierarchically indicates the strength of a status hierarchy. Put differently, I assume it is unlikely to observe a friendship nomination network characterized by acyclic triads and rank-ordered positions in the absence of a clear status hierarchy. In fact, closure and reciprocity would tend toward erasing any acyclic triads. If hierarchical friendship nominations are observed, this suggests the presence of a status structure that organizes how students are making nominations in the aggregate. “In the aggregate” is a key qualifier, because any randomly chosen individual in the group may have many reasons for nominating friends. Yet, at a group level, it is difficult to imagine a hierarchically structured nomination network forming in the absence of a status hierarchy.
To capture the degree to which friendship nominations are structured hierarchically, beyond what would be expected in a group with the same number of nodes and directed edges (e.g., in- and out-degree), I compute “tau” statistics. This statistic compares the observed distribution of hierarchical triads in a network to a sample of randomly generated networks generated from the same dyadic features of the observed network. The first step is to conduct a triad census, which enumerates all triads that occur within a group. These 16 different possible arrangements, ranging from closed triads where all ties are mutual (300) to triads where ties are all null (003), are placed in a vector T. Then, I calculate tau using the following equation:
where T is a vector of observed counts for each of the 16 triad arrangements; W is a vector assigning weight only to the five hierarchical triads; μ is the expected count of triads based on a draw of 4,000 randomly generated networks with the same number of mutual, asymmetric, and null dyads as the observed network; and ∑T indicates the variance/covariance matrix of the randomly generated networks. The intuition here is that the numerator is the difference between the observed number of hierarchical triads and what would be expected given the dyadic structure of the group. The denominator is the standard error: the standard deviation of a distribution of the tau statistic calculated from the randomly generated networks. The tau statistic is, therefore, parallel in construction to z-scores, where zero indicates that the observed graph is no more hierarchical than would be expected by chance. Higher values indicate that the hierarchical structure in the friendship nominations is greater than expected.
Covariates
An unadjusted regression of tau on peer aggression would be confounded by several factors. For instance, if the proportion of girls in a class predicts the prevalence of peer aggression and the strength of a status hierarchy, results would be biased if gender were not included as a covariate. To reduce the plausibility of this and other competing accounts, I include as a control variable any characteristic that might reasonably be correlated with both the dependent and independent variables of interest.
I first include basic measures to account for the composition of students in each class, such as the proportion of girls and average age (in years). Because the proportion of students who live in dormitories structures the frequency of group interactions, I control for the proportion of students who live in dormitories. I also include the mean level of academic achievement in the class. During the first and third waves of the survey, students took a proctored, 30-minute standardized math test based on items collected from the Chinese national curriculum. Students and teachers could not prepare for the test because it was administered and printed by the research team. No one in the sample schools knew the questions beforehand. The scores were scaled into z-scores by subtracting the mean and dividing by the standard deviation of the distribution of all students tested.
To account for socioeconomic status differences that may confound my analysis, I control for the average household socioeconomic status of the class by including the proportion of students who are from a single-parent family and whose parents graduated from high school, migrated for work in the cities, and primarily work in agriculture. I also control for the average level of wealth in students’ households. To do so, I asked students to report whether their household owned certain common items, livestock, and small businesses; the material used to construct their home; and the size of their home. The construction of continuous measures for household wealth is more reliable when using indicators of assets than using self-reported wealth (for a review, see Kolenikov and Angeles 2009). Most responses to household asset–ownership variables in the dataset were dichotomous and therefore not normally distributed. As such, I used the first component from a polychoric principal components analysis to construct a standard index for household wealth (Kolenikov and Angeles 2009).
The above covariates do not vary meaningfully with time, but certain time-varying factors confound the analysis. Two key factors are perceived teacher care and the level of stress and anxiety that students experience. Attentive homeroom teachers (i.e., those who directly oversee the class) may encourage social processes that clarify the informal social interactions of the class while also taking action to reduce peer aggression. To address this concern, I collected a 12-item scale with questions pertaining to students’ perceptions of their homeroom teacher during each semester. I use the first principal component of these 12 items as a composite for teacher care. Similarly, students may experience differing levels of anxiety from semester to semester, which may explain both the frequency of peer aggression and hierarchical clarity, thus confounding the analysis. I therefore also collect several time-varying covariates, including a measure from a variation of the Child Manifest Anxiety Scale (CMAS) called the Mental Health Test (MHT), which was administered to all respondents during each study wave. This 100-question scale, which forms a composite measure of anxiety that is standardized with mean 0 and standard deviation of 1, is widely used to measure the anxiety and mental health of students in China (Yao et al. 2011; Zhou 1991). Because higher scores on this scale signify worse mental health, I label this a “mental health risk score” in the tables and figures presented here.
Analytic Strategy
This study presents four sets of analyses. First, I analyze descriptive patterns in aggression, including the type of aggression occurring within the classrooms, where it is occurring, and among whom. I also examine the network structure of friendship nominations and how hierarchical clarity changes over time. These descriptive analyses contextualize all subsequent analyses, for instance, by revealing the high level of gender homophily observed in the classes and motivating the need to explore heterogeneous effects by gender.
In the second analysis, I model the strength of status hierarchies as a function of peer aggression—the key relationship of interest in this study. A feature of this analysis is that I include fixed effects for both school and semester. This means classes are being compared within school and within semester. Taking these elements together, the fixed-effects linear regression model is as follows:
where τijt is the tau coefficient for class i in school j and time t. Tijt–1 is the proportion of students who report being victimized in class i in the preceding semester. Lagging this independent variable means a third of the observations are dropped, as there is no lagged measure available at the first semester. Nevertheless, this is a critical first step in ruling out reverse causality. The term
is a vector of time-invariant covariates discussed in the measures section above;
refers to time-varying covariates.
is a fixed-effects term for each school j, and
is a fixed-effects term for each semester t. To account for the clustered nature of standard errors, I report bootstrap standard errors adjusted for clustering at the class level. As a robustness check, I also fit alternative models that include fixed effects for class i in lieu of fixed effects for school and time. In these alternative models, all class-level, time-invariant covariates, whether observed or unobserved, are held constant.
Despite the inclusion of lags for the independent variable, three-wave fixed-effects models are sensitive to the specification of lags (Bellemare, Masaki, and Pepinsky 2017; Vaisey and Miles 2017). Moreover, to further address concerns about reverse causality, I would ideally include a lagged dependent variable, but this can introduce serious biases in a fixed-effects model (e.g., Nickell bias; Keele and Kelly 2006). To address these problems, I re-estimate the results using cross-lagged fixed-effects models, which have been shown to circumvent problems of mis-specified lags and the biases associated with lagged dependent variables in fixed-effects models (Leszczensky and Wolbring 2022). A cross-lagged panel model uses structural equation models to estimate the reciprocal relationship between the dependent and explanatory variables.
Another concern is that the analysis does not account for alternative network processes that generate friendship nominations, such as mutuality or closure (the degree to which individuals form clusters). To further control for these processes, I investigate whether the results are consistent when using tau statistics estimated through exponential random graph models (ERGM), where the conditional probability of observing a network is specified as follows:
The left side of the equation,
refers to the probability that a randomly drawn network from the distribution of random graphs, Y, is the observed network y, given a set of estimated coefficients θ. g(y) is a vector of network statistics for network y, and
refers to a transposed vector of coefficients for these statistics. Aside from a network statistic for tau, I include edges, which accounts for the total number of ties in the network; dyad mutuality, which refers to the number of dyads where there is both a tie from i to j and vice versa; and “geometrically weighted edgewise shared pairs,” which captures transitivity, or the tendency to form clustered or connected triads. The intuition for this transitivity measure is that it reflects how much “a friend of a friend is a friend” (see Goodreau et al. 2009), and the geometric weighting is necessary to counter degeneracy, where the model encounters infinite regress situations (see Hunter et al. 2008). Because the equation is a probability, it must be divided by the total number of possible networks, indicated by the normalizing constant
This model enables me to identify whether there is a higher probability for friendship nominations to form hierarchical triads (tau), independent of preferences for mutuality, closure, and mere density (see Hunter et al. 2008; McFarland et al. 2014).
The ERGM model is fit to each of the observed networks (256 classes x 3 semesters) using a Markov Chain Monte Carlo (MCMC) method. The intuition is that the ERGM model begins with a set of parameter coefficients, generates networks that are compared to the observed network, and iteratively tunes these parameters until it finds a set of parameters that generates networks that are like the observed one. The resulting vector of parameter estimates θ consists of coefficients that can be interpreted as the log-odds of observing a network with tie configurations corresponding to the network statistic, net of the other statistics in the model. To address the scaling problem, I estimate average marginal effects of the tau statistic (Duxbury 2021). These average marginal effects for each class, in each semester, serve as the dependent variables of interest in subsequent analyses. Moreover, instead of treating estimates from models equally, I weight estimates by the inverse of its standard error. Following standard meta-analysis practices ensures that more precise estimates have greater weight (Raudenbush and Bryk 2002). Because ERGM models are estimated via numeric approximation, I also check the MCMC estimation for convergence for each model run.
The third analysis tests specific mechanisms that are theorized by a legibility account. To test whether audiences are relevant in driving the relationship between peer aggression and hierarchical clarity, I examine the relative effect size of victim-reported or audience-reported levels of peer aggression when both are included in the model. Additionally, I investigate whether the effects of peer aggression depend on the accuracy of audience perceptions (i.e., the degree to which victim-reported and audience-reported levels overlap). This interaction effect between victim-reported and audience-reported levels of peer aggression is a direct test of key claims of legibility, whereby peer aggression erodes status hierarchies when the aggression is ambiguous and hence inaccurately perceived. As a further robustness check, I investigate whether variability in audience perceptions of peer aggression, which indicates inconsistency in how individuals interpret peer aggression, negatively predicts hierarchical clarity. I also investigate alternative interpretations of the results, such as a threshold model whereby the relationship between aggression and hierarchical clarity is nonlinear.
Fourth, the high degree of gender homophily (segregation) implies that each class consists of two distinct subgroups, perhaps with their own distinct hierarchies, just as one school is a group characterized by subgroups of grades and classes. Additionally, boys and girls are known to rely on different forms of aggression, with different direct implications to the legibility framework. Hence, I assess how the main effects vary by gender and forms of aggression. To do so, I recalculate the average marginal effects for the tau statistic across each of the ERGMs above, separately for subgroups of boys and girls. For consistency, I also recalculate all covariates and independent variables by gender subgroups. I then test for gender differences in the relationship between peer aggression and the strength of status hierarchies. As part of this analysis, I also test whether observed gender differences are consistent with the legibility framework.
Results
Descriptive Patterns
How prevalent was peer aggression? How much aggression occurred among classmates versus outside of class? And what type of aggression did students experience? As shown in Table 1, in the first semester, 37.6 percent of students reported experiencing some form of peer aggression. In the next semester, only 19.1 percent of students reported being victimized. At the start of the next school year (the third semester), the rate of victimization rose to 25.4 percent. These results show that peer aggression was more likely to occur at the start of school years, perhaps because students were first meeting or getting reacquainted with one another.
To identify the extent to which peer aggression was occurring among classmates, I summarize data collected during the second wave of the survey, when students were asked to indicate whether they experienced aggression from people outside of their school, from those within their school but outside of their class, or from their classmates. Table 2 displays these results: 15 percent of girls and 16 percent of boys reported being victimized by classmates, 6.2 percent of girls and 7 percent of boys reported being victimized by students within the same grade (but not classmates), and 4.7 percent of girls and 6.2 percent of boys were victimized by individuals outside of that grade or school. These results indicate that most victimization occurred among classmates. Indeed, when accounting not merely for prevalence (whether the student was victimized or not) but also the frequency of occurrences, 72 percent of all victimization events occurred among classmates. Spatially, 54 percent of victimization events occurred within the classroom, 27 percent occurred within dormitories (which still consisted of classmates), and the remainder occurred in other locations. These findings indicate that most aggression occurred among classmates and within the classroom.
| Overall Incidence (% Reporting Victimization) |
Decomposed by Type (Conditional on Reporting Any Victimization) |
|||||
|---|---|---|---|---|---|---|
| Relational | Physical | Verbal | ||||
| Aggressor | Classmate | Girls | 15.4% | 34% | 20.5% | 55.4% |
| Boys | 16.1% | 26% | 30.6% | 42.2% | ||
| Person within grade, but not classmate | Girls | 6.2% | 12.4% | 6% | 19.6% | |
| Boys | 7% | 11.5% | 10% | 16.9% | ||
| Other person outside grade or school | Girls | 4.7% | 10% | 4.5% | 14.3% | |
| Boys | 6.2% | 9% | 8.6% | 13.8% | ||
| Example | Cannot play ping pong or jump-rope |
Fist fight in dormitory | “Why are you so stupid?” | |||
Note: These categorizations are based on self-reports among respondents who completed all three waves of the study. N = 7,672. Of victimization episodes, 88 percent were between people of the same gender. Among all victimization events, 54 percent occurred in the classroom, 27 percent in dormitories, and 18 percent in other locations (e.g., school track, canteen, bathroom).
What was the network structure of friendship nominations? Figure 3 displays a randomly chosen network from my sample. A key feature of this network is that it displays gender segregation. To investigate the extent to which gender homophily is a general finding, I calculate an assortativity coefficient for gender across all networks and all three time periods. This coefficient can be interpreted similarly to a Pearson correlation coefficient, as it ranges from –1 to 1 and corresponds to the degree to which friendship nominations are likely (positive values) or unlikely (negative values) to occur between same-gender individuals. In this case, the mean assortativity coefficient for gender was .92 across all classes in the first semester, .81 in the second semester, and .72 in the third semester.
Figure 3. Example of Friendship Nomination Network from Randomly Selected Class
Note: Nodes are students. Squares are boys, circles are girls. Arrows indicate the student nominated the other individual as a friend.
To confirm high levels of gender segregation, I fit an ERGM with terms for mutuality, edges, the propensity to send and receive ties by gender, and gender homophily for each of the 256 classes and for each period. I then calculate second difference average marginal effects for gender homophily, weighted by the inverse of standard errors observed for each network (see Duxbury 2022). Results show the probability of a friendship nomination between individuals of the same gender was 2.7 percentage points more likely to occur than a nomination between individuals of differing genders, even after accounting for processes like mutuality and the propensity for girls to send more ties than boys. This is six times larger in magnitude than comparable studies of homophily in other adolescent settings (e.g., .4 percentage points; see Goodreau et al. 2009). A critical fact that follows from this high level of gender segregation is that boys and girls occupy discrete social circles, especially at the beginning of their time in junior high school. Hence, the scope condition of working knowledge in the group may only hold within gender subgroups, motivating the need for analyses relating peer aggression to hierarchical clarity for boys and girls separately, even as they formally occupy the same class.
Figure 4 shows how hierarchical clarity changes over time, demonstrating that status hierarchies generally grow stronger as individuals spend more time interacting with one another.7 While these results do not elucidate the specific role of peer aggression, they support claims that status hierarchies emerge organically as individuals interact with each other (e.g., Gould 2002). To help provide intuition for what “strength” or “clarity” entails, Figure 4 shows two example networks: one where the status hierarchy is weak (A) and the other where it is strong (B). To ease interpretability, simplified blockmodels of extreme cases within the observed networks are plotted. The blockmodels show that groups with high tau have roles that can be rank-ordered and clearly distinguished. By contrast, when tau is low, there is no consistent way to identify roles that are rank-ordered by esteem. These temporal changes are also confirmed in descriptive statistics shown in Table 1, which show the tau statistic increases in magnitude over the three semesters.
Figure 4. Boxplots Showing Distribution of Hierarchical Clarity by Time and Gender, with Example Reduced-Form Networks
Note: Examples A and B are drawn from the distribution of networks among women in the third semester. Examples were chosen to match on basic features like number of vertices (20) and edges. Reduced-form blockmodels (k = 7) are shown to illustrate the basic network structure. Loops are removed to enhance interpretability. The width of the edges corresponds to the number of ties sent. The y-axis represents the ratio of in-directed and out-directed ties (normalized by the number of individuals in each block).
Main Effects of Aggression on Hierarchical Clarity
For data transparency, Figure 5 consists of a raw scatterplot between hierarchical clarity and peer aggression, indicating the two measures are negatively associated. This evidence supports the need for something like the legibility framework to explain how aggression erodes status hierarchies. Still, a more plausible explanation for this correlation is reverse causality: strong status hierarchies reduce aggression. To disentangle this causal relationship, I investigate temporal sequences in these data.
Figure 5. Scatterplot of Hierarchical Clarity as a Function of Proportion of Students Victimized
Note: Each circle represents one class, with size representing the number of students in that class. N = 768 (256 classes × 3 semesters).
Column 1 in Table 3 shows the results from a school and semester fixed-effects regression, where the class-level prevalence of peer aggression is lagged. The results show that tau, a measure for hierarchical clarity, decreases by .473 when moving from a hypothetical class where 0 percent of students report being victimized to a class where 100 percent of students report being victimized in the prior semester (p = .063). Or, placed on a more interpretable scale, a 10-percentage-point increase in the proportion of students who report being victimized correlates with a .0473 decrease in tau. Column 2 shows this result is robust to the inclusion of a rich set of covariates pertaining to the composition of these classes (p = .029). Column 3 shows results when we use class fixed effect, which removes the confounding effects of any time-invariant covariates at the class level. Across these columns, the overall direction of the effect remains unchanged, and the magnitude increases to .725 in the class fixed-effect model (p = .037). Given that the average level of tau observed across the entire sample is 1.05, this corresponds to a 69 percent decrease in hierarchical clarity.8
| Tau Statistic | AME of Tau, from ERGM | ||||
|---|---|---|---|---|---|
| (1) | (2) | (3) | (4) | (5) | |
| Unadjusted | Adjusted | Peer-Group Fixed Effect | Adjusted | Peer-Group Fixed Effect | |
| Last sem. peer aggression prevalence | –.473 (.252) |
–.567* (.258) |
–.725* (.346) |
–.017* (.008) |
–.029** (.019) |
| Average age of class | .234 (.180) |
–.004 (.004) |
|||
| Prop. identifies as boy | .308 (.383) |
.003 (.012) |
|||
| Prop. lives in dorm | .061 (.321) |
.005 (.011) |
|||
| Prop. single-parent | 1.589** (.654) |
.020 (.018) |
|||
| Average asset value | .027 (.163) |
.007 (.004) |
|||
| Average academic achievement level | .085 (.121) |
.000 (.002) |
|||
| Prop. parents are migrant workers | .517 (.511) |
.010 (.014) |
|||
| Prop. parents w/ high school degree | –.679 (.394) |
–.026* (.013) |
|||
| Prop. parents are farmers | –.262 (.482) |
–.001 (.018) |
|||
| Average perceived care from teacher | .049 (.051) |
.009 (.102) |
.001 (.001) |
–.001 (.003) |
|
| Average anxiety and stress levels | .022** (.009) |
–.005 (.018) |
.000 (.000) |
.000 (.001) |
|
| Semester fixed effect | ✓ | ✓ | ✓ | ||
| School fixed effect | ✓ | ✓ | ✓ | ||
| Class (peer group) fixed effects included | ✓ | ✓ | |||
| Constant | 1.006*** (.107) |
–4.365 (2.785) |
.184 (1.084) |
.065 (.055) |
.017 (.031) |
| Observations | 512 | 512 | 512 | 320 | 320 |
| R-squared | .225 | .404 | .280 | .466 | .286 |
| Number of classes | 256 | 256 | 256 | 209 | 209 |
Source: Author’s survey.
Note: Robust standard errors, adjusted for clustering by classes, are in parentheses. N = 320 for tau statistics derived from ERGM models because the model failed to converge in classes/semesters where gender segregation was nearly absolute.
*
p < .05; **p < .01; ***p < .001 (two-tailed tests).
How do the results change when we account for confounding network-generating processes? Columns 4 and 5 in Table 3 repeat these analyses for the average marginal effect (AME) of the tau statistic estimated from the exponential random graph models. Column 4 shows that peer aggression reduces the probability that a new tie would create a hierarchical triad by 1.7 percentage points (p = .029). Column 5 supports this conclusion, with results from the peer-group fixed-effect model indicating that peer victimization reduces tau by 2.9 percentage points (p = .003). Given that the base probability of any tie formation is 7.1 percent, this is a 41 percent decrease. Although results using the ERGM-derived measures of hierarchical clarity are more persuasive, the ERGM model failed to converge in cases where gender segregation was nearly absolute, which explains why the total number of observations in columns 4 and 5 is 320, as opposed to 512. This problem motivates the need to investigate gender subgroups.
The inclusion of lags accounts for temporal sequence, but as noted above, stronger evidence against reverse causality would incorporate cross-lagged fixed effects. The results of such a model, estimated using maximum likelihood, are shown in Table 4. The frequency of peer aggression in the prior semester reduces hierarchical clarity, even with the inclusion of lagged hierarchical clarity and regardless of whether clarity is measured through a dyad-conditioned tau statistic (column 1: β = –.845, p = .009) or the average marginal effect of the tau statistic estimated in an ERGM (column 2: β = –.043, p = .001). In sum, the direction and statistical significance of the results remain unchanged, and the magnitude of the effects are comparable to those estimated using models without cross-lagged fixed effects.
| Dependent Variable: Self-Reported Victimization (1 = yes) | Tau Statistic (1) |
AME of ERGM Tau (2) |
|---|---|---|
| Last sem. peer aggression prevalence | –.845** (.322) |
–.043** (.013) |
| Lagged tau | .167 (.098) |
.821** (.206) |
| Covariates included | ✓ | ✓ |
| Constant | .131 (.497) |
.340 (.125) |
| Number of classes | 256 | 209 |
Source: Author’s survey.
Note: Dynamic panel model estimated using structural equation models (see Allison et al. 2017). Number of classes is 209 when tau statistics are derived from ERGM models because the model failed to converge in cases where gender segregation was nearly absolute.
*
p < .05; **p < .01; ***p < .001 (two-tailed tests).
Why Did Peer Aggression Reduce Hierarchical Clarity?
Taken together, the results show that peer aggression erodes the clarity of status hierarchies. This finding rules out the dyadic or audience perspectives but leaves specific predictions of the legibility framework untested, and other alternatives could explain the results. Hence, before testing key claims of the legibility framework, I highlight and rule out three competing possibilities. For instance, one possibility is that each act of aggression introduces ambiguity as to the social rank of other actors until people in the group have seen enough information to decide on individuals’ positions. When such a threshold of aggression is reached, we might see the hierarchy shift, perhaps rapidly, into a state of clarity. This threshold explanation suggests the effect of peer aggression reverses when a sufficiently high level is reached (Biggs 2005; Granovetter 1978). Similarly, an Aristotelean “golden mean” hypothesis suggests an inverse U-shaped functional form, where too little and too much aggression erodes status hierarchies, but middling levels of aggression strengthen them. Is there a nonlinear functional form that relates peer aggression to the strength of status hierarchies? To uncover nonlinear relationships, I decompose the peer aggression variables into five quintiles and include this categorical variable as the primary independent variable. Figure 6 shows predicted levels of tau based on this analysis: the marginal effect of peer aggression on the strength of status hierarchies appears to be linear, with little evidence of nonlinear effects.
Figure 6. Hierarchical Clarity Is a Linear, Decreasing Function of Peer Aggression
Note: 95 percent confidence intervals shown. For each quintile, the percent of students reporting victimization is in parentheses.
Second, perhaps peer aggression erodes group structure more generally, reducing the likelihood of all triadic structures, not just hierarchical ones. Similarly, the choice of five triadic building blocks to represent hierarchical structure is based on prior research (Cartwright and Harary 1956; Faust 2007; Moody et al. 2011; Rawlings and Friedkin 2017), but perhaps the effects are driven by a subset of these triads, representing an alternative type of network structure. To resolve these possibilities, Figure 7 shows every triad in the census and its likelihood of being observed in each network, as a function of different levels of observed peer aggression. To check for nonlinear relationships, I also show boxplots of the distribution of tau statistics for each quartile of peer aggression. Correlation coefficients (and whether they are statistically significant at the .05, .01, or .001 level) are provided to help evaluate whether each triad appears/disappears when aggression increases in prevalence. A visual representation of each triad is also provided to help illustrate what each triad means (beyond the customary MAN label).
Figure 7. Correlations of Peer Aggression Frequency and Individual Triads
Note: Pearson correlation coefficient calculated in subset boxes.
*p < .05; **p < .01; ***p < .001 (two-tailed tests).
The results show that the frequency of peer aggression is correlated with a statistically significant increase in the probability of six triads {012U*,012C,111D,030C,201, 120C}, whereas eight triads decrease in probability {012,102,021D*,030T*,120D*,120U*,210,300}. The hierarchical triads are labeled with an asterisk, showing that all hierarchical triads decrease in probability except for 012U. Additionally, all cyclic triads (triads labeled with “C”) are also positively correlated with the prevalence of peer aggression. This can be understood as a further robustness check. Rather than hierarchical clarity, I could have measured “hierarchical confusion” as the proportion of cyclic triads that occur in the group, that is, triads that directly contradict rank-ordered positions. The results show that this measure increases as a function of peer aggression. Hence, it is unlikely that peer aggression simply erodes all triadic network structures, and its effects appear to be specific to hierarchical clarity.
Third, perhaps peer aggression reduces hierarchical clarity because it reflects attempts from lower-status students to redistribute esteem in the classroom. Put more colorfully, aggression might reflect insurrection against the existing status order, whereby group members rely on peer aggression to disrupt the hierarchy and redistribute esteem from the “haves” to the “have nots.” If so, high-status students would be expected to lose esteem more than low-status students as peer aggression increases in frequency. With the caveat that friendship nominations are a weak proxy for status, I test for how peer aggression affects friendship nominations to higher- versus lower-status individuals. I do so by including a node-level characteristic in the ERGM model, corresponding to the ratio of in- to out-degree ties received in a previous time-period (a measure of status). The coefficient in the ERGM model indicates the degree to which high-status actors receive more ties. The previous time-period lag is included to avoid circularity.
Once these ERGM coefficients are calculated, I investigate how this is moderated by the prevalence of peer aggression. In classrooms where there is more peer aggression, do the (initially) high-status actors lose or receive more ties? As before, I translate the ERGM coefficients to average marginal effects to avoid problems of scaling and weight by the inverse of the standard error. The results (Table 5, column 1) show no conclusive pattern, suggesting that levels of aggression in a classroom do not change whether formerly high-status actors receive more or fewer ties. In other words, there is no clear evidence that aggression is redistributive of esteem, either toward those who already have it, or those who do not. If status inequalities are not being undone, how can hierarchical clarity diminish? This is possible because hierarchy is not solely a function of whether there are millionaires and mendicants in the world of esteem, and the clarity of a hierarchy is not only about inequality in resources. Rather, the structural definition of hierarchical clarity encompasses consensus about status positions, which is a feature of both asymmetry and acyclicity in esteem.
| AME of Status from Last Sem. | AME of Tau, from ERGM | |||||
|---|---|---|---|---|---|---|
| (1) | (2) | (3) | (4) | (5) | (6) | |
| Last sem. peer aggression prevalence | –.009 (.007) |
–.010 (.006) |
–.042** (.016) |
–.026** (.008) |
–.043** (.017) |
|
| Perceived prevalence of peer aggression | –.013** (.004) |
–.030** (.010) |
.011 (.014) |
.103* (.041) |
||
| Perceived × actual prevalence of peer aggression | .076* (.031) |
.119** (.040) |
||||
| Subgroup consists of boys | .000 (.002) |
.009 (.006) |
–.002 (.003) |
|||
| Std. dev. in perceived prevalence of peer aggression | .001 (.002) |
|||||
| Std. dev. × perceived prevalence of peer aggression | –.011 (.006) |
|||||
| Average # of aggressors per victimization event | –.011 (.006) |
|||||
| Avg # of aggressors × last sem. peer aggression prevalence | .031* (.013) |
|||||
| Covariates included? | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
| Semester fixed effect? | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
| School fixed effect? | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
| Constant | .187** (.084) |
.066 (.056) |
.043 (.060) |
–.014 (.057) |
.078 (.164) |
–.007 (.062) |
| Observations | 512 | 320 | 320 | 1,024 | 1,024 | 1,024 |
| R-squared | .320 | .274 | .463 | .327 | .407 | .306 |
Source: Author’s survey.
Note: Robust standard errors, adjusted for clustering by classes, are in parentheses. Dependent variable in Model 1 is the average marginal effects calculated from the node-level ERGM coefficient for the ratio of in- versus out-degree in the prior semester. Observations for Model 1 refer to 256 classes observed over two semesters (256 × 2 = 512). Observations in Models 2 and 3 are lower than 512 because estimates of the ERGM tau statistic did not converge in cases with near absolute gender segregation. Observations in Models 4, 5, and 6 refer to gender subgroups within classes, across two time periods.
*
p < .05; **p < .01; ***p < .001 (two-tailed tests).
These analyses, which rule out alternative possibilities, imply the need for an explanation like the legibility framework, which posits that uncoordinated audience perceptions and reactions to peer aggression are what erodes hierarchical clarity. To directly test this explanation, I investigate whether audience perceptions matter in translating aggression to hierarchical clarity, and whether peer aggression strengthens status hierarchies if audiences accurately interpret aggression. I begin by assessing whether audience perceptions of aggression affect hierarchical clarity, even when controlling for victim-reported levels of peer aggression. Table 5, column 2, shows that the effect of aggression on hierarchical clarity is carried by perceived aggression, where moving from a class where nobody is perceived to have been a victim to one where everyone is reduces the probability that a new tie would create a hierarchical triad by 1.3 percentage points (p = .003). Additionally, the effect of victim-reported aggression nearly halves, from 1.73 percentage points when perceived victimization is omitted from the model (p = .029), to .98 percentage points when perceived victimization is included (p = .130). These results show that audience perceptions matter in predicting hierarchical clarity.
More importantly, I assess whether the effect of aggression depends on whether audiences can accurately identify it. Table 5, column 3, shows that, conditional on being accurately perceived by audience members, the likelihood of hierarchical ties forming increases by 7.59 percentage points when the proportion of people reporting being victimized shifts from 0 to 100 percent (p = .014). By contrast, when decoupled from perceptions, peer aggression erodes the clarity of status hierarchies (p = .009). If the effect of peer aggression on group structure is driven primarily by audience reactions, then how would victim-reported peer aggression erode hierarchical clarity when decoupled from audience perceptions? One reason is that these are tightly knit groups of approximately 32 students, interacting across multiple semesters. This implies that the misalignment between victim-reported and audience-reported aggression is not solely because people did not see the interactions, but at least in part because they did not accurately interpret it as aggression.
Although these two tests conform with the predictions of a legibility framework, significant analytic concerns remain. One concern is that statistics for tau did not converge in groups with high degrees of gender segregation, resulting in a smaller sample that is no longer representative of adolescent groups in this context. Are the results robust when tau is recalculated using ERGMs for gender subgroups within classes? Not only do high levels of homophily in friendship nominations imply that the relevant peer groups for these 7th- and 8th-graders are their same-gender classmates, convergence and model fit improve when we consider each class as consisting of two subgroups, one comprising boys and the other girls. Using this robustness check, the overall finding remains consistent: hierarchical clarity increases when perceived and victim-reported victimization are aligned (column 4).
To help visualize the results, Figure 8 visualizes the model in column 4 in a contour plot. The z-axis corresponds to average marginal effects of the tau statistic as calculated in ERGMs. As noted earlier, these values can be interpreted as the percentage point increase in the baseline probability of tie formation between two individuals (in this sample, 7.1 percent), conditional on a tie completing a hierarchical triad. For instance, a value of .01 is a 1 percentage-point change, implying an 8.1 percent chance of ties forming that complete hierarchical triads, relative to the baseline of 7.1 percent. The x-axis corresponds to the percent of adolescents in each class who reported experiencing peer aggression, and the y-axis corresponds to the percent of people in each class who experienced aggression, as perceived by onlookers. The dashed line corresponds to perfect accuracy, where members of the group perceive exactly as much aggression as is being reported by victims. The overlaid scatterplot provides the region of support, that is, the distribution of classes in the sample. Any areas of the plot where there are no points are extrapolations of the model. The scatterplot illustrates that audience estimates of aggression in the class are correlated with victim-reported rates of aggression. Nevertheless, the scatterplot shows these estimates are inaccurate, and the slope of a line of best fit is lower than .5, indicating the perceived proportion of adolescents experiencing aggression is generally downwardly biased. In other words, onlookers generally underestimate how much peer aggression is happening in the class.
Figure 8. Hierarchical Clarity as a Function of Perceived versus Actual Percent of Students Victimized
Note: Scatterplot represents region of support (i.e., raw distribution of classes); dotted line represents perfect concordance between perceived versus actual prevalence of peer aggression in the class. Hierarchical clarity is measured by the average marginal effect of a term for hierarchical triads, calculated from an exponential random graph model.
When it comes to hierarchical clarity, the results first show that increasing aggression (as perceived by victims) predicts weaker status hierarchies. The marginal effect of peer aggression is negative, that is, if we fix the mean position on the y-axis and move toward the right on the x-axis, predicted levels of hierarchical clarity decrease. This is consistent with the main effects discussed in the previous section. Status hierarchies, however, are stronger when actual and perceived aggression increase simultaneously—that is, if each move on the x-axis corresponds with a move on the y-axis. These results support the key predictions of a legibility framework: when group members fail to accurately perceive interactions as aggression, it erodes the status hierarchy, but aggression that is legible to onlookers increases the clarity of the status hierarchy.
A remaining concern is whether alignment between perceived and victim-reported victimization is a comprehensive operationalization for legibility. When audiences accurately identify peer aggression in a way that matches how victims experienced aggression, legibility is likely to be high. Yet, it is possible to imagine audiences sharing consistent interpretations of peer aggression that are systematically different from victims. Put differently, consistency implies low variance rather than accurate means, and peer aggression could be legible to audiences without necessarily implying alignment with victims’ perceptions. Indeed, if the effects of peer aggression operate primarily through audience perceptions, then what victims report may be irrelevant. To address this concern, I further test whether the results are robust when legibility is operationalized as the standard deviation in onlookers’ perceptions of aggression. Table 5, column 5, shows the results for this additional test. The effect of peer aggression as perceived by audiences on hierarchical clarity is positive and statistically significant (p = .012), but, as predicted, as variability in audience estimates of aggression increases (which operationalizes low levels of legibility in a group), this effect reverses and begins to erode hierarchical clarity (p = .073).
As a final test of the legibility framework, I investigate whether aggression that is coordinated with others contributes to greater hierarchical clarity. As predicted, the key underlying condition that needs to be met for individual interactions to strengthen status hierarchies is whether audiences are coordinated in how they reallocate esteem. Hence, peer aggression that draws multiple actors together to attack a victim ought to clarify a status hierarchy. In Figure 9, I plot the marginal effect of increased peer aggression on hierarchical clarity as a function of the average number of people who participated (shown in Table 5, column 6). The figure shows that when only a single individual was an aggressor, peer aggression generally erodes hierarchical clarity. As predicted, as more individuals participate, the marginal effect of peer aggression reverses and begins to increase hierarchical clarity.
Figure 9. Predicted Average Marginal Effects of Peer Victimization, as a Function of Increasing Number of Aggressors
Note: Mean number of people attacking a victim together was 1.27.
Heterogeneity by Gender, Type of Aggression Deployed, and Number of Aggressors
High levels of gender segregation observed among the classes in my sample necessitated additional analyses that considered gender subgroups separately. Were the effects of peer aggression on hierarchical clarity different for boys and girls? Figure 10 plots predicted margins from Table 6. For data interpretability, I include a histogram that shows the distribution of victimization prevalence in the data, which bounds the range of values the model could extrapolate to. Figure 10 reveals that the effect of peer aggression on hierarchical clarity not only differs but also reverses for adolescents who identify as boys, compared to those who identify as girls. Among girls, the increasing incidence of peer aggression in the prior semester is correlated with increasing probability that ties form hierarchical triads. By contrast, peer aggression appears to decrease the formation of hierarchical triads among boys. These gender differences are statistically significant (p = .009, see Table 6, column 1, row 3). In summary, the results show marked gender differences in how aggression relates to hierarchical clarity: aggression weakens status hierarchies among boys while modestly strengthening it among girls.
Figure 10. Hierarchical Clarity as a Function of Proportion of Students Victimized, by Gender
Note: 95 percent confidence intervals displayed. All other variables held at mean.
| AME from ERGM Tau | Perceived Prevalence of Peer Aggression | AME from ERGM Tau | |||
|---|---|---|---|---|---|
| (1) | (2) | (3) | (4) | (5) | |
| Last sem. peer aggression prevalence | .006 (.006) |
.136** (.042) |
–.017 (.001) |
||
| Subgroup consists of boys | .004 (.003) |
–.004 (.016) |
.004 (.003) |
.001 (.004) |
|
| Boys × last sem. peer aggression prevalence | –.019** (.007) |
–.106* (.043) |
–.011 (.008) |
||
| Perceived prevalence of peer aggression | .016 (.014) |
||||
| Perceived × actual prevalence of peer aggression | .101* (.043) |
||||
| Last sem. relational aggression prevalence | .001 (.011) |
–.005 (.024) |
|||
| Last sem. verbal aggression prevalence | –.003 (.008) |
–.003 (.017) |
|||
| Last sem. physical aggression prevalence | –.009 (.011) |
.005 (.023) |
|||
| Covariates included? | ✓ | ✓ | ✓ | ✓ | ✓ |
| Semester fixed effect included? | ✓ | ✓ | ✓ | ||
| School fixed effect included? | ✓ | ✓ | ✓ | ✓ | ✓ |
| Constant | –.024 (.061) |
–.308 (.317) |
–.014 (.057) |
–.012 (.040) |
–.036 (.087) |
| Observations | 1,024 | 1,024 | 1,024 | 209 | 512 |
| R-squared | .307 | .330 | .327 | .767 | .392 |
Source: Author’s survey.
Note: Robust standard errors, adjusted for clustering by classes, are in parentheses. Dependent variable in Model 2 is perceived prevalence of peer aggression from onlookers. Observations in Models 1, 2, 3, and 5 refer to gender subgroups within classes, across two time periods. Observations in Model 4 refer to classes, which is lower than 256 because of non-convergence of ERGM coefficients for tau statistic. Observations in Models 4 and 5 are halved, and semester fixed effects are not included, because types of aggression were collected only in the second semester.
*
p < .05; **p < .01; ***p < .001 (two-tailed tests).
Although I did not have ex ante predictions about gender differences, the legibility framework advanced here helps to explain this gender difference. In particular, Table 6, column 2, investigates whether there were gender differences in how accurate audiences were at predicting victim-reported levels of aggression. If the coefficients in the model were 1, then this would imply maximal accuracy, or perfect correlation between victim- and audience-reported levels of aggression. Among girls, the correlation was .136, and correlations were statistically significantly weaker for boys (p = .001, Table 6, column 2, row 3). This implies boys were less accurate than girls at interpreting aggression occurring among themselves.
Additionally, Table 6, column 3, shows that gender differences in the effect of peer aggression on hierarchical clarity are no longer statistically significant (p = .123) when models include audience perceptions of aggression, and the difference in coefficient magnitude when compared to a model where perceived aggression is omitted is statistically significant (p = .0018). In short, the results suggest one reason peer aggression strengthened status hierarchies among girls, yet had the opposite effect for boys, is that aggression is more legible among girls.
Why might peer aggression be more legible among girls than among boys? One possibility is that boys and girls experience different forms of aggression. Girls were 8 percentage points more likely than boys to experience relational exclusion, and 13 percentage points more likely to experience verbal aggression. Boys, by contrast, were about 10 percentage points more likely to experience physical aggression (see Table 2). To investigate whether these three forms of aggression affected hierarchical clarity differently, I include all three forms of aggression in a model predicting hierarchical clarity in the following semester. As noted earlier, one limitation here is that respondents were only asked to report on the type of aggression they experienced in the second wave of the survey, meaning the sample size of groups is halved. In a class-level analysis, Table 6, column 4, shows no clear differences by type of aggression. Similarly, in a gender-subgroup analysis, column 5 also shows no clear differences. Thus, although boys and girls experienced different forms of aggression, there is insufficient evidence to conclude that this explains why aggression had divergent effects on hierarchical clarity by gender.
Discussion and Conclusions
Status hierarchies emerge nearly universally across a wide range of contexts and structure significant human behaviors—including who people obey, how rewards are allocated, and how violence and aggression unfold (Gould 2002:1143). Yet, even as status hierarchies confront people as social facts and shape our interactions, they are simultaneously constructed and restructured through peer interaction. The present study investigated how one important class of peer interaction, intragroup aggression, affects the clarity of status hierarchies, or the degree to which a group exhibits discernable roles that are rank-ordered in terms of esteem. I advanced a framework that hinges on the legibility of peer aggression.
This framework sought to amend shortcomings from two theoretical precursors. A dyadic framework posits that aggression generates winners and losers in a dyad, and the sum of these dyadic relations clarifies a hierarchy. In an audience framework, peer aggression instead shapes group structure primarily by helping onlookers coordinate their allocation of esteem. I used simulations to identify group-level implications for the structure of hierarchy, showing that the audience and dyadic frameworks predict that peer aggression strengthens the clarity of a status hierarchy whenever audiences react to interactions consistently. A legibility framework, however, suggests peer interactions often present as garbled signals to onlookers, rendering the interactions open to multiple interpretations. These varied interpretations lead onlookers to reallocate esteem in different ways, introducing noise into the network and undermining consensus in the positions of different actors.
How well did this framework hold up to empirical validation? Although research has shown that aggressive and dominant individuals are upwardly mobile in a status hierarchy (e.g., Faris 2012), prior findings have been unable to identify whether the hierarchy itself becomes more clear. In fact, mobility may be more attainable through aggression when status hierarchies are weak, but the positions are prone to subsequent challenges. The original data collected here enabled me to investigate temporal sequences in the hierarchical structure of hundreds of adolescent peer groups. Access to complete networks at each point in time allowed me to measure hierarchical clarity in terms of acyclic network structure, rather than solely in terms of inequality or asymmetry, as if status were a fungible resource.
By measuring the strength of status hierarchies by the likelihood of triadic patterns in longitudinal friendship nominations across 256 discrete classes, I discovered that classes where peer aggression was more prevalent had weaker status hierarchies in a subsequent time period. The results were robust even when accounting for network-generating processes (e.g., closure or mutuality) that confound estimates of hierarchical clarity. Using a cross-lagged fixed-effects model, I showed that the results are robust to concerns about reverse causality. Results were robust even when a rich set of covariates are included, such as student achievement, mental health, socioeconomic status, and perceived teacher care. In this sense, the analyses constitute one of the best-identified tests of the causal relationship between peer aggression and hierarchical structure in a naturalistic setting. Prior work has lacked sufficient variation across groups to measure how interpersonal dynamics shape hierarchical structure (e.g., Faris and Felmlee 2014). Similarly, studies that have had sufficient cross-cluster variation have relied on cross-sectional survey data that cannot account for the reverse causal influence of hierarchical structure in conditioning peer aggression (e.g., Bunderson et al. 2016).
Critically, the legibility framework also held up to direct tests of its mechanisms. Results confirmed that peer aggression increased hierarchical clarity when aggression was accurately perceived by audiences. Peer aggression reduced hierarchical clarity when there was significant variance in audience estimates of aggression. Results also revealed that peer aggression strengthened hierarchical clarity when the aggression was coordinated with others. Competing possibilities were ruled out. There do not appear to be nonlinear threshold effects; the effects of peer aggression are specific to hierarchical triads, and not triads in general; and peer aggression does not reduce hierarchical clarity because low-status actors are using aggression to redistribute esteem. Finally, a legibility framework is useful even in explaining gender differences that emerged inductively during the analysis. In analyses that subdivided classes by gender, intragroup aggression among boys eroded the status hierarchy but had the opposite effect among girls. These differences are largely explained by legibility: onlookers were more accurate in identifying whether girls were behaving aggressively toward other girls, compared to their perceptions of boys.
Taken together, the results suggest that peer aggression contributes to hierarchical structure when third-party onlookers see and interpret peer aggression as such, allowing them to coordinate how they allocate esteem. Yet, aggression is often ambiguous, such as when aggressors seek to plausibly deny they were dominating victims, or groups lack a shared understanding of what constitutes aggression in the first place. Moreover, people are generally clumsy at communicating through aggression. The most unambiguous forms of intragroup aggression—the playground beatdown or the public duel—capture widespread attention, but these ritualized (and hence, highly legible) interactions do not constitute all examples of intragroup aggression. In cases such as the adolescent groups studied here, peer aggression is often ambiguous to onlookers and its effect on hierarchical clarity is, on average, negative. Put another way, the social network tradition this study is embedded within recognizes that relations can be interpreted differently: what “friendship” means differs from person to person (Kitts and Leal 2021). The present article extends this insight to interactions. If one person punches another, should this interaction be categorized as “aggression” or “playful?” In some contexts, this interaction is legible and unambiguous. It fits squarely as one or the other. In other contexts, a multiplicity of interpretations lead to uncoordinated allocations of esteem, thus undermining hierarchical status structures.
A legibility perspective implies new answers to substantively important problems. For instance, conflict and peer aggression remain at chronically high levels or escalate in some peer groups while diminishing in frequency over time in others. What explains the difference? The present study suggests the legibility of aggression occurring in these groups might help explain these dynamics. Research has shown that the clarity of status hierarchies helps limit the frequency and escalation of peer conflict and aggression (e.g., Faris and Felmlee 2011; Piezunka et al. 2018). This is also true in the present study. To demonstrate this, I use fractional logistic regression to model the proportion of peer aggression in a class as a function of hierarchical clarity in a prior semester, again with a fixed effect for semester, a school fixed effect, and all covariates included in other models. As other research predicts, hierarchical clarity reduces subsequent aggression: a one-unit increase in hierarchical clarity (tau) decreases peer aggression in a later semester by 1.43 percentage points. Because of this fact, when the legibility of aggression is low and peer aggression erodes hierarchical clarity, it also weakens the structures that would otherwise limit it. When legibility is high, peer aggression contributes to the clarity of a status hierarchy, which in turn limits subsequent aggression. Hence, if aggression is coordinated with others or grounded in established institutions (e.g., collectively oriented rites like gossip or duels), then we would expect peer aggression to diminish over time. For instance, aggression is more likely to be legible in contexts with clear meanings of what constitutes a status challenge (e.g., idiocultures like a street code or even “code of the tweet” that governs social media use among gangs; Fine 1979; Stuart 2020). In settings like these, peer aggression will likely decline in frequency or severity as group members interact with one another.
To what extent are the findings specific to the Chinese adolescent context? Students had few outside connections or activities; they interacted consistently with one another in groups over three semesters. Their participation in the survey was high, with remarkably low levels of attrition. These features enabled me to empirically disentangle the relationship between peer aggression and status hierarchies across these groups. People in other settings may interact with less intensity, and groups are likely more porous. Additionally, peer aggression is ubiquitous in adolescence. The high rate of peer aggression enabled sufficient variation for the empirical analyses. Other settings where peer aggression is observed (Aquino and Thau 2009), however, may be characterized by lower levels of aggression, or perhaps aggression is more legible outside the confines of a middle school.
Yet if scope conditions of informal hierarchies formed through interaction hold, it is unclear why these differences would undermine theoretical claims about the role of third-party onlookers and legibility in relating peer aggression to group structure, as the theoretical propositions are not obviously bound to the specifics of China, adolescence, or schools. Indeed, one feature of the present framework is that it directly acknowledges how culture and context affect the relationship between peer aggression and group structure. Peer aggression may have evolutionary underpinnings and, to some modest extent, clarify status hierarchies regardless of context, but a legibility framework posits that its effects are largely contingent on the subjective interpretations of third-party onlookers. Whether onlookers can consistently respond to peer aggression is deeply contextual, contingent on the degree to which understandings of what aggression entails and how to respond are shared.
To be clear, the framework does not predict that aggression is the only relevant factor in determining the strength of status hierarchies. Indeed, as a secondary contribution, the article empirically validated that hierarchical clarity increases as groups interact over time, thus supporting predictions from formal models (e.g., Manzo and Baldassarri 2015), much as recent work has empirically tested whether predictions from balance theory are supported by data from sentiment networks (Rawlings and Friedkin 2017). The theoretical claims tested here are that we would see more hierarchy in a parallel world where aggression is legible, not that the strength of status hierarchies is a sole function of aggression. It is also possible for status hierarchies to increase over time but for the marginal effect of peer aggression to be negative.
Additionally, the claim that interactions strengthen group hierarchies only when they are legible to audiences is not specific to aggression and could be applicable to other interpersonal interactions. Consider, for instance, an interaction meant by one individual to signal deference to another (e.g., bowing). This creates a status difference within that dyad, and if an audience sees and consistently categorizes this act as “deference,” then this peer interaction will generate greater consensus about status positions in the group. Yet, if onlookers are unable to interpret this action consistently, then this interaction may erode consensus about status positions. Such a general theory about the legibility of peer interactions demands more extensive empirical validation. For instance, future work could ask members of a group to offer their interpretations of specific interactions, including interactions that were perceived by others as aggression or deference. The degree to which these interpretations are shared should moderate whether these interactions strengthen or erode the group’s status hierarchy.
Another line of research could investigate how peer aggression affects victims, and how the severity varies by the legibility of aggression. A “micro-aggression” may be ambiguous for onlookers, but it is perceived as derogatory and hostile by the victim. On the surface, the degree of hostility experienced from a subtle insult seems modest when compared to an open insult. Yet, open insults give victims opportunities to publicly defend their status claims, and for onlookers to coordinate their rejection of aggressors’ attempts to derogate victims. Compared to an instance where an aggressor can plausibly deny they are attacking a victim, a situation where aggression is legible and can be challenged may lead to lower overall levels of harm for the victim. In a related vein, although the present study offers strong evidence that peer aggression erodes status hierarchies (and the conditions under which this is true), it was not possible to collect network data on aggressors. If such data can be collected, an important question is how different targeting patterns might contribute to or erode status hierarchies. Finally, the results show gender differences in the effect of peer aggression on hierarchical clarity, and some of this difference could be explained by the greater legibility of peer aggression among girls, compared to boys. Further development and testing of theories to explain adolescent gender differences in the legibility of peer aggression (or perhaps even peer interactions at large) may be a productive opportunity for future research.
At the broadest level, this research elucidates how hierarchies co-evolve with intragroup aggression, offering a framework to theorize how micro-level interactions can aggregate to reshape group structures. Unlike prior research, which emphasized the consequences of peer aggression for individual outcomes like status mobility, the present study investigates how peer aggression affects the clarity of a group’s structure. In doing so, this work inverts a traditional emphasis in social science research, which generally investigates how hierarchies structure peer aggression. Results show that the structure of status hierarchies cannot be induced by aggregating outcomes at the dyadic level (e.g., Ridgeway and Diekema 1989). Instead, the way individual episodes of aggression accrete to affect status hierarchies is dependent on the reactions of third-party onlookers, and the degree to which these peer interactions are legible to them.
Acknowledgments
I would like to thank Cameron Anderson, Peter Bearman, Matt Brashears, Dan McFarland, Govind Manian, Mario Small, Woody Powell, Andy Walder, and Robb Willer for helpful comments on earlier versions of the manuscript. I would also like to thank the respondents in this project for their time and willingness to participate.
Funding
Funding for this project was provided by the Ford Foundation. James Chu was also supported by the National Science Foundation Graduate Research Fellowship under grant number DGE-114747. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the Ford Foundation or National Science Foundation.
ORCID iD
James Chu https://orcid.org/0000-0003-2702-470X
Footnotes
1. For examples of research on how status hierarchies structure peer aggression in social psychology, social networks, and public health, see Cillessen and Rose 2005; Ellwardt, Labianca, and Wittek 2012; Fiske 2011; Fujimoto, Snijders, and Valente 2017; Rubineau, Lim, and Neblo 2019.
2. As I will discuss in more depth, exponential random graph models reveal that the probability of a friendship nomination between individuals of the same gender, relative to individuals of differing genders and controlling for density, mutuality, and transitivity, is nearly six times higher here than in U.S. middle schools (which already demonstrate high levels of gender homophily; Goodreau, Kitts, and Morris 2009).
3. For instance, 120D corresponds with an actor directing esteem at a pair of mutually esteemed actors, creating a rank order of two positions. Two individuals equally occupy a higher position, and another occupies a lower one. In 030T, actors occupy three rank-ordered positions. Compare these examples with 030C, where actors form a cycle that directly contradicts consensus about rank-ordered positions, or 111D, where only one of the two equally matched actors receives esteem, creating confusion and inconsistency in the rank-ordering of these positions.
4. Middle schools in China enroll the equivalent of 7th- through 9th-graders in the United States. The name of the prefecture is omitted for confidentiality reasons.
5. Other comparable panel studies of adolescents, such as Add Health, have attrition rates more than three times as large (approximately 20 percent; Faris and Felmlee 2014:235; Harris et al. 2019:1415b).
6. Students were also invited to nominate friends who were not necessarily within the class, such as students in a different grade or outside of school. Among all friendship nominations, 90.7 percent were within the same class.
7. In line with this claim, the average number of friendship nominations received increases from 1.6 in the first semester to 3.5 and 3.6 in the second and third semesters. The total proportion of isolates also declines from 23 percent to 11 and 13 percent in the second and third semesters, respectively. These differences are accounted for in the calculation of tau, which is conditioned on the dyad census.
8. If reductions in hierarchical clarity are driven by peer aggression, and if these reductions are concentrated among triads that include victims, then we might expect to see null results if the same models are repeated when tau is calculated on triads that exclude victims of peer aggression. These analyses are presented in Appendix Table A2. The unadjusted and adjusted models are substantively similar to those presented in Table 3, but the null hypothesis that peer aggression has no effect cannot be rejected in the class fixed-effect model.
Appendix
Part A. Translated Wording of Key Survey Questions
Survey Questions about Friendship Nominations
| Please write down the names of people you consider friends in your current class | 1. | 2. | 3. |
| 4. | 5. | 6. | |
| 7. | 8. | 9. |
Survey Questions about Peer Victimization
How many times did you experience peer victimization during this semester? Please indicate 0 if you did not experience peer victimization.
How many people in your class do you think were attacked by other classmates during this semester?
The last time you were attacked by others, how many people attacked you at the same time?
In what places have you experienced peer victimization?
A – the classroom
B – dorms
C – school canteen
D – school track
E – bathrooms
F – some other place within the school
G – some place outside the school
H – I have never experienced peer victimization
(The following questions were only asked in second semester.)
In the following table, please estimate how many times you experienced relational, physical, or verbal aggression in this semester. Please write 0 if you did not experience this form of aggression.
| Primarily Relational Exclusion | Primarily Physical Attack | Primarily Verbal Attack | |
|---|---|---|---|
| Classmate | ( ) times | ( ) times | ( ) times |
| Someone from same grade, different class | ( ) times | ( ) times | ( ) times |
| Someone from outside of my school | ( ) times | ( ) times | ( ) times |
| (1) | (2) | ||||||
|---|---|---|---|---|---|---|---|
| Variables | Sample Mean | Sample SD |
Min. | Max. | Leavers Mean |
Leavers SD |
Diff. (1)–(2) |
| Semester 1 Variables | |||||||
| Individual Measures | |||||||
| Victimized, semester 1 (1 = yes) | .371 | .483 | 0 | 1 | .397 | .490 | –.025 |
| Male (1 = yes) | .518 | .500 | 0 | 1 | .641 | .480 | –.124*** |
| Age (in years) | 14.90 | 1.076 | 10.83 | 19 | 15.37 | 1.141 | –.473*** |
| Lives in dormitory at school (1 = yes) | .704 | .457 | 0 | 1 | .706 | .456 | –.002 |
| Math achievement (in SDs) | .053 | .997 | –2.643 | 2.610 | –.277 | .951 | .331*** |
| Mental health risk index level (in SDs) | –.053 | .982 | –2.796 | 3.447 | .095 | 1.013 | –.149*** |
| Household Measures | |||||||
| Single-parent family (1 = yes) | .071 | .256 | 0 | 1 | .106 | .308 | –.035** |
| Family household asset score (in SDs) | –.243 | 1.261 | –3.394 | 3.415 | –.378 | 1.257 | .133* |
| Mother is a migrant worker over four months each year (1 = yes) | .06 | .238 | 0 | 1 | .077 | .267 | –.017 |
| Father is a migrant worker over four months each year (1 = yes) | .150 | .357 | 0 | 1 | .176 | .381 | –.026 |
| Mother graduated from junior high (1 = yes) | .260 | .439 | 0 | 1 | .241 | .428 | .020 |
| Father graduated from junior high (1 = yes) | .450 | .498 | 0 | 1 | .409 | .492 | .041 |
Source: Author’s survey.
Note: Analytic sample refers to n = 7,672 students who participated across all three semesters. Attritors refer to n = 557 students who left the sample by Semester 3 (Fall 2013–14 school year).
*
p < .05; **p < .01; ***p < .001. Significance tests based on two-tailed t-test of differences between means of the analytic sample and attrition sample.
| Tau Statistic | |||
|---|---|---|---|
| (1) | (2) | (3) | |
| Unadjusted | Adjusted | Peer-Group Fixed Effect | |
| Last sem. peer aggression prevalence | –.654** (.264) |
–.626** (.275) |
–.189 (.351) |
| Average age of class | .142 (.192) |
||
| Prop. identifies as boy | .411 (.391) |
||
| Prop. lives in dorm | .045 (.327) |
||
| Prop. single-parent | 1.038 (.717) |
||
| Average asset value | –.029 (.166) |
||
| Average academic achievement level | .056 (.141) |
||
| Prop. parents are migrant workers | .299 (.534) |
||
| Prop. parents w/ high school degree | .015 (.405) |
||
| Prop. parents are farmers | .059 (.423) |
||
| Average perceived care from teacher | .157*** (.056) |
.100 (.107) |
|
| Average anxiety and stress levels | .020** (.010) |
–.007 (.019) |
|
| Semester fixed effect | ✓ | ✓ | |
| School fixed effect | ✓ | ✓ | |
| Class (peer group) fixed effects included | ✓ | ||
| Constant | 1.006*** (.107) |
–4.365 (2.785) |
.184 (1.084) |
| Observations | 512 | 512 | 512 |
| R-squared | .285 | .328 | .110 |
| Number of classes | 256 | 256 | 256 |
Note: Robust standard errors, adjusted for clustering by classes, are in parentheses.
*
p < .05; **p < .01; ***p < .001 (two-tailed tests).
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Biographies
James Chu is an Assistant Professor of Sociology at Columbia University. He studies social stratification, economic and organizational sociology, and political polarization.
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