Prioritise Propensity: A multimethod analysis of peer influence and school-based aggression

ABSTRACT This study examines the situational role of aggressive peers in the explanation of school-based aggression. Using data from the multimethod Peer Relations and Social Behavior (PEERS) study, it tests hypotheses derived from Situational Action Theory (SAT) to investigate whether the effect of aggressive peers is greater for high propensity adolescents. The PEERS study used a cross-sectional survey followed by adapted Space-Time Budget (STB) interviews with a randomly selected subsample of participants. This paper presents situational analyses of STB data alongside additive analyses of survey data to demonstrate both situational convergence and statistical dependence. Results showed that the effect of aggressive peers was greatest amongst adolescents with high aggression-relevant propensity (i.e. weak morality and a poor ability to exercise self-control). Whilst high propensity adolescents were situationally vulnerable to the influence of aggressive peers, low propensity adolescents were situationally resistant to criminogenic peer effects. These findings suggest that targeting aggression-relevant propensity may be more fundamental than reducing exposure to aggressive peers for preventing aggressive behavior in schools. The theoretical, methodological, and empirical contributions in this study can be applied to advance future research on peer influence, aggression, and SAT.


Introduction
School-based aggression is a major public health problem that directly impacts more than 246 million children and adolescents internationally each year (UNESCO, 2017).Numerous systematic reviews and meta-analyses have found that aggression and victimization is associated with adverse health and behavioral outcomes across the life course including depression (Farrington et al., 2012;Ttofi et al., 2011), suicidal ideation (Holt et al., 2015;Van Geel et al., 2014), and criminal behavior (Farrington et al., 2012).Whilst effective interventions are urgently needed, the success of existing programs remains limited (see e.g., Castillo-Eito et al., 2020;Gaffney et al., 2019aGaffney et al., , 2019bGaffney et al., , 2021;;Jimenez-Barbero et al. 2016;Ttofi & Farrington, 2011;Yeager et al., 2015).Many interventions are primarily risk-focused insofar as they aim to identify and address established risk factors which may be symptoms or markers which lack causal efficacy (Farrington, 2006).In order to be effective, interventions need to target causally relevant factors and processes instead of risk factors that lack explanatory power (Wikström & Treiber, 2008, 2017).Consequently, there is an urgent need for a theoretically informed approach to the prevention of school-based aggression that identifies and targets the underlying causes and causal processes.
It is widely accepted that understanding the role of peers in the causation of aggressive events is critical for developing effective intervention programs (Hymel et al., 2015; see also Pepler et al., 2010;Swearer et al., 2010).One of the most robust findings in the criminological and psychological literature is that aggressive youth are significantly more likely to associate with aggressive friends (e.g., Cairns et al., 1988;Espelage et al., 2003;Xie et al., 1999; for a review, see Crick et al., 2009). 1 Peers are often present during incidents of aggression and bullying in schools (Atlas and Pepler 1998;Craig & Pepler, 1997;Hawkins et al., 2001) and this has led to the view of bullying as a "group process" (O'Connell et al., 1999;Sutton & Smith, 1999; for a review, see Salmivalli, 2010) in which individuals adopt a range of participant roles (Salmivalli et al., 1996; see also Salmivalli & Voeten, 2004;Salmivalli et al., 2011).Moreover, adolescence is characterized by hypersensitivity to peer acceptance (Foulkes & Blakemore, 2016;Sebastian et al., 2010;Somerville, 2013), increased vulnerability to peer influence (Albert et al., 2013;Foulkes & Blakemore, 2016;Knoll et al., 2015), and the desire to avoid social risk (Blakemore 2018; see also Andrews et al. 2020;Tomova et al., 2021).A growing body of research has investigated how peers guide and control aggressive behavior by contributing to social norms and enacting bystander responses (e.g., Berger and Caravita 2016;Dijkstra et al., 2008;Menesini et al., 2013;Salmivalli et al., 1996;Salmivalli & Voeten, 2004).However, existing research on peer influence is limited due to the lack of (i) a situational model which integrates individual and environmental factors and provides plausible causal mechanisms, and (ii) suitable data and methodologies capable of capturing person-environment interactions at the situational level.
The aim of this study is to address these problems by elaborating and testing the situational role of aggressive peers in the explanation of school-based aggression.First, this study applies and develops a robust analytical framework -Situational Action Theory (SAT; Wikström, 2006Wikström, , 2010Wikström, , 2014Wikström, , 2017Wikström, , 2019b) ) -to theorize the mechanisms and conditions of situational peer influence.This application of SAT's situational model closely mirrors Hardie's (2017Hardie's ( , 2021) ) application of SAT to the study of parental influence in the context of crime.Second, this study pioneers an innovative adaptation of the Space-Time Budget (STB) method (Hardie & Wikström, 2021;Wikström, Oberwittler et al. 2012;Wikström et al., 2012) to capture real-world situational data on the types of peers present in the setting for the first time.Finally, this study presents situational and individual-level findings from the Peer Relations and Social Behavior (PEERS) study which was designed to test key hypotheses derived from SAT.

School-based aggression and SAT
This paper proposes that SAT (Wikström, 2004(Wikström, , 2006(Wikström, , 2010(Wikström, , 2014(Wikström, , 2017(Wikström, , 2019) is a valuable theoretical framework for explaining the situational role of peer influence in school-based aggression.As a "general, dynamic, and mechanism-based" theory of moral action (Wikström, 2017: 510), 2 SAT addresses the theoretical limitations in the aggression and peer influence literature.First, SAT provides a situational model that specifies the relevant person-environment interactions that influence the action decision-making process leading to the rule-breaking event (Wikström & Treiber, 2016). 31 More broadly, deviant peer affiliation is one of the strongest predictors of problem behavior amongst adolescents (Vitaro et al., 2018) and peer delinquency is a powerful predictor of criminal behavior (Gallupe et al., 2019;Hoeben et al., 2016;Pratt et al., 2010).Some scholars have claimed that the peer-delinquency association results from processes of social and self selection (e.g., Cairns et al., 1988;Glueck & Glueck, 1950;Gottfredson & Hirschi, 1990, 2020;Hirschi, 1969).However, normative influence researchers have argued that the peer-delinquency relationship is a product of peer influence processes (e.g., Akers et al. 1979;Burgess & Akers, 1966;Sutherland, 1947).After decades of research, it is generally accepted that the peer-delinquency association results from a combination of selection and influence processes (McGloin & Thomas, 2019;Ragan, 2020; for a detailed discussion, see Kennedy, 2022: 38-45).
2 Moral actions are defined in SAT as "actions (including intentional inactions) guided by value-based and emotionally-grounded rules of conduct about what is the right or wrong thing to do in particular circumstances" (Wikström, 2019b: 262).For a discussion of the nature of morality in SAT, see Barton-Crosby (2022).
Second, SAT theorizes plausible causal mechanisms and distinguishes the situational causes (which result from the person-environment interaction) from the social 'causes of the causes' (which involve emergent processes of development and selection) (Wikström, 2017;Wikström & Treiber, 2019; see also Treiber, 2017).The application of SAT's situational model presented in this paper aims to explain why acts of aggression occur rather than why individuals develop different aggression-relevant propensities or why environments develop different aggression-relevant inducements. 4 Although criminological researchers have recognized the need to integrate peer influence research with models of action decision-making, they often assume that rational choice theory (Cornish & Clarke, 2008, 2014, 2017) is the optimum framework for this integration (e.g., Hoeben & Thomas, 2019;McGloin & Thomas, 2019).However, rational choice perspectives are limited for modeling action decision-making as they typically require the erroneous assumption that humans are fundamentally driven by self-interest and they overlook the role of automated processes of choice (Wikström & Treiber, 2016; for further criticisms, see Kroneberg, 2014;Wikström & Kroneberg, 2022).Moreover, these perspectives confine their attention to downstream processes of choice and ignore the preceding subprocesses of motivation and perception (see e.g., Van Gelder & Nagin, 2023) which are critical for explaining rule-breaking behavior.
Applying SAT (Wikström, 2006, 2010, 2011, 2014, 2017, 2019b, Wikström, Oberwittler et al., 2012, Wikström & Treiber, 2016), the basic hypothesis is that aggression results from a perception-choice process that is initiated and guided by the spatio-temporal interaction between relevant individual characteristics and setting features (Figure 1).First, adolescents differ in their propensity to engage in aggressive behavior.Aggression-relevant propensity refers to the tendency to see and choose aggression as an action alternative in response to a motivation.This propensity is dependent on personal aggression-relevant morality (moral rules and supporting moral emotions) and the ability to exercise self-control (i.e., the capacity to act in accordance with personal morality when externally pressured to do otherwise) (Wikström & Treiber, 2007).Second, school settings differ in the extent to which they encourage or discourage aggressive behavior. 5This tendency is dependent on the moral context of the setting which comprises aggression-relevant moral norms (perceived shared rules of conduct and their degree of homogeneity) and the perceived level and efficacy of enforcement in relation to frictions and opportunities (Wikström, 2019b).There is growing empirical support for the application of SAT's situational model to a range of rule-breaking behaviors (for a review, see Pauwels et al., 2018).

5
The setting is defined as "the part of the environment (the configuration of objects, persons, and events) that, at any given moment in time, is accessible to a person through his or her senses" (Wikström, Oberwittler et al., 2012: 15).
The perception-choice process is the action mechanism that links individuals and their environments to their actions (Wikström, 2010).This action decision-making process is primarily automatic or deliberate (Wikström, 2017) and consists of three key elements: (i) motivation, which initiates the action decision-making process, (ii) the moral filter, which determines the range of action alternatives the adolescent must choose between in response to a motivation, and (iii) external and internal controls, which manage conflicting rule-guidance during rational deliberation.Applying SAT, the basic argument is that adolescents are aggressive because they see aggression as an acceptable action alternative (and there is no effective deterrent) or they are unable to adhere to their personal morality (i.e., they fail to exercise self-control) when externally pressured to engage in aggression (Kennedy, 2022, forthcoming).This action decision-making process is elaborated in the situational model of peer influence presented below.

The situational model of peer influence
This paper presents a novel application of SAT's situational model to study the role of peers in the explanation of school-based aggression.This application focuses on the situational role of aggressive peers in motivating, guiding, and constraining the action decision-making process that produces aggressive behavior.Aggressive peers are defined in this paper as friends who advocate, encourage, or demonstrate aggressive behavior.This application focuses on aggressive friends because peer influence processes are assumed to be stronger in intimate and proximal relationships (Brechwald and Prinstein 2011;Crick et al., 2009).It also restricts its focus to aggressive peers and assumes that peer presence is not necessarily conducive to aggressive behavior.Whilst this assumption challenges Osgood et al.'s (1996) unstructured socializing perspective, 6 it is supported by a large body of research on bystander intervention (e.g., Kärnä et al., 2011;Polanin et al., 2012) and the prosocial effects of peers during adolescence (e.g., Ahmed et al. 2020;Chierchia et al., 2020;Foulkes et al., 2018;Maxwell, 2002;van Hoorn et al., 2016).
Finally, this application focuses on the physical (rather than the psychological) presence of peers to avoid conflating situational and developmental processes.Arguably, the psychological presence of peers is largely captured in situational models of peer influence by the construct of aggression-relevant propensity.Peer experiences play a central role in the development of aggression-relevant attitudes which are internalized through (generally long-term) psychosocial processes of moral education (Wikström, 2005; see also Wikström & Treiber, 2019;Wikström, 2019a). 7Whilst psychological presence may influence salience cues and anticipated social rewards (Hirtenlehner & Schulz, 2020), research has found that close friends are physically present in school contexts most of the time (Kennedy, 2022).Consequently, the situational model presented in this paper prioritizes the direct peer influences in the setting at the point of action.This application provides a foundation for guiding peer influence research and it may be expanded in future research to include the role of prosocial peers, the psychological presence of peers, and other types of peer relationships.
Applying SAT, the presence of aggressive peers increases the likelihood of aggression in the action context in three main ways.First, the presence of aggressive peers increases aggressionrelevant motivators (opportunities and frictions) and activates individual characteristics (desires, commitments, and friction sensitivities) involved in motivational subprocesses.Second, the presence of aggressive peers weakens the moral filter which increases the likelihood that aggression is 6 The central argument in Osgood et al.'s (1996) unstructured socializing perspective (see also Haynie & Osgood, 2005;Osgood & Anderson, 2004) is that situations characterized by unstructured socializing with peers in the absence of authority figures are particularly conducive to deviant behavior.As noted by Haynie andOsgood (2005: 1112), "[f]rom this opportunity perspective, peer relations are not connected to delinquency by the types of friends that one chooses.Instead, what matters is the amount of time spent with peers engaged in a common type of activity that is not inherently deviant."7 For instance, Wikström (2019b: 269) has said "it is the (perceived) moral norms of the setting that are directly action-relevant" and "[i]f moral norms more generally influence people's actions they do so as having become part of their personal morals through past processes of internalization." perceived as an action alternative.This is because aggressive peers weaken the perceived aggression-relevant moral norms of the setting and temporarily weaken personal morality (moral rules and emotions).Finally, the presence of aggressive peers activates the need for -and weakens the efficacy of -internal and external controls (i.e., the ability to exercise self-control and deterrence).
Aggressive peers can also enforce pro-aggression norms and increase social sanctions for failing to engage in aggressive behavior.For a detailed discussion of how the presence of aggressive peers influences the perception-choice process in SAT, see Kennedy (2022: 80-106, forthcoming).

Hypotheses
The aim of this study is to test hypotheses about how and why the presence of aggressive peers influences aggressive behavior in the action context.These hypotheses are derived from SAT's situational model and they focus on the spatio-temporal convergence between the presence of aggressive peers and individual aggression-relevant propensity (morality and the ability to exercise self-control).This person-environment interaction is central to the application of SAT's situational model and it is likely to be critical for explaining and intervening in schoolbased aggression.As causal mechanisms are imperceptible (Bunge, 2004) and cannot be tested directly, these hypotheses outline the effects that would be observed if the situational model was operating as expected.
Hypothesis 1: The presence of aggressive peers increases the likelihood of aggression (relative to the presence of non-aggressive peers).
Applying SAT, the presence of aggressive peers weakens the moral context of the setting and increases the likelihood of aggression by: (i) increasing the likelihood of experiencing aggression-relevant motivators (opportunities and frictions), activating aggression-relevant desires or commitments, and heightening individual friction sensitivities; (ii) weakening the perceived aggression-relevant moral norms of the setting and temporarily weakening personal morality (moral rules and emotions); and (iii) increasing the need for, and compromising the operation of, internal and external controls (deterrence and the ability to exercise self-control) in deliberate processes of choice.To summarize, there are multiple situational mechanisms through which the presence of aggressive peers increases the likelihood of aggression.
Hypothesis 2: The likelihood of aggression is greater for high propensity adolescents than low propensity adolescents.
According to SAT, high propensity adolescents are more likely to perceive and choose aggression as an action alternative in response to a relevant motivation.Aggression-relevant propensity consists of aggression-relevant morality (moral rules and emotions) and the ability to exercise self-control.
Adolescents with weak aggression-relevant morality are more likely to perceive aggression as an acceptable action alternative when tempted or provoked by a relevant motivator.Adolescents with a poor ability to exercise self-control are more likely to choose an aggressive response when managing external pressure -such as "peer pressure" (Wikström, 2019b) -during deliberate choice processes (provided that aggression is perceived as an action alternative).It follows that the likelihood of aggression should be greater for high propensity adolescents than low propensity adolescents.
Hypothesis 3: The effect of the presence of aggressive peers is greater for high propensity adolescents than low propensity adolescents. 8 The central claim derived from SAT is that aggressive behavior is produced by the spatio-temporal interaction between aggression-relevant propensity (morality and the ability to exercise self-control) and exposure to aggressive peers.This means that high propensity adolescents are more situationally vulnerable to the influence of aggressive peers and low propensity adolescents are more situationally resistant.It follows that the effect of aggressive peers on aggression should be greater for aggressionprone adolescents and minimal or non-existent for aggression-averse adolescents.

Materials and method
This study uses data from the multimethod Peer Relations and Social Behavior (PEERS) Study.The PEERS study was conducted with 396 randomly selected adolescents aged 13-14 at six schools in Cambridgeshire and Peterborough, UK (2019 -2020). 9This specialist study was designed to test hypotheses derived from SAT's situational model and advance knowledge about the situational dynamics of peer influence and school-based aggression.Testing situational models and hypotheses requires the collection of individual-level and situational data that are uniquely suited to this task (Hardie, 2020(Hardie, , 2021;;Wikström & Kroneberg, 2022).Inspired by the Peterborough Adolescent and Young Adult Development Study (PADS+), the PEERS study employed a cross-sectional survey and adapted PADS+ STB interviews to collect these distinct types of data. 10The major methodological contribution of the PEERS study was the adaptation of the innovative PADS+ STB method (Wikström et al., 2012;Wikström, Oberwittler et al., 2012;Hardie & Wikström, 2021) to facilitate the collection of unique situational data on the types of peers present in the setting.
The first stage of the PEERS study captured individual-level survey data on aggression-relevant propensity (morality and the ability to exercise self-control), association with aggressive peers, and aggression frequency over the previous month. 11Many empirical tests of SAT's interactive propositions have employed individual-level data and this can provide valuable insights when the necessary assumptions are clearly highlighted (Hardie, 2020;Wikström & Kroneberg, 2022).The second stage of the study used PEERS STB interviews with a randomly selected subsample (n = 90)12 to collect realworld situational data on the presence of aggressive peers and corresponding aggressive outcomes.Unlike individual-level data, situational data is structured so that the situation (person-environment interaction) and the associated behavioral outcome is the unit of analysis.It is increasingly recognized that empirical tests of situational models should primarily be based on situational data that evidences the assumed convergence between behavioral outcomes and particular person-environment interactions (Hardie, 2020;Wikström & Kroneberg, 2022); however, this data is rarely collected and analyzed in criminological research due to cost and misunderstandings about the unique benefits it provides (Hardie, 2020;Hardie & Wikström, 2021;Wikström & Kroneberg, 2022).
One of the major challenges for peer influence research is the need to develop new methodologies which are capable of adequately testing situational models of peer influence.Many researchers have called for methodological advancements to improve the study of aggression (e.g., Fontaine & Dodge, 2006;Eisner & Malti, 2015;Murray et al., 2022) and peer influence (e.g., Cairns & Cairns, 1994;McGloin & Thomas, 2019;Warr, 2002).The PEERS study responds to this call by adapting the PADS+ 8 This two-way interaction can be interpreted reciprocally (see Barnes et al., 2020;Hardie, 2020).As individuals are the source of their actions (Wikström, 2014), this study interprets the peer-propensity interaction using individual aggression-relevant propensity as the moderating variable (Hardie, 2020: 68). 9 The response rate for the PEERS study was 81.6%.
10 For a detailed discussion of the PEERS methodology and how the study tools interrelate, see Kennedy (2022: 112-141). 11 Individual-level data captures generalized personal characteristics, the amount of environmental exposure experienced over a particular period, and behavior counts aggregated to individuals (Hardie, 2020: 54).
STB method (Hardie & Wikström, 2021;Wikström, Oberwittler et al., 2012;Wikström et al., 2012) to study the situational dynamics of peer influence in the explanation of school-based aggression.The most unique benefit of the STB method is its ability to capture situational interaction (Hardie & Wikström, 2021) by collecting detailed situation-level data that enables the analysis of the spatiotemporal convergence between relevant aspects of people and environments (Hardie & Wikström, 2021;Wikström, Oberwittler et al., 2012;Wikström et al., 2012).However, previous STB datasets have lacked detailed situational data on the types of peers present in the setting (Beier, 2018) 13 and the collection of this data has been identified as a priority for the development of this method (Hirtenlehner et al., 2021;Kleinewiese, 2020;Kroneberg & Schulz, 2018).By capturing this complex situational data, the PEERS STB represents a significant methodological development that can support future research on the situational dynamics of peer influence.
The retrospective PEERS STB interview captured detailed time diary data in 15-minute intervals spanning the previous four school days.These time intervals are more finely grained than the hourly data collected in the PADS+ study and are better suited to the purpose of the current study. 14 Participants reported what they did (primary activity), where they were in the school (functional location), who they were with (nominated friends and guardians), and whether they engaged in aggressive behavior (aggressive outcome).The major methodological innovation of the PEERS STB was the development of an innovative peer nomination technique to record the presence of specific nominated friends at the situational level and link this to perceptual data on the aggression-relevant attitudes of each friend. 15This facilitated the creation of complex constructions of the types of friends who were present in the action context when aggressive behavior occurred (or did not occur) and provides multiple analytical possibilities.For a detailed discussion of how the PEERS STB adapted the PADS+ STB to facilitate the study of peer influence and school-based aggression, see Kennedy (2022: 130-6).
The collection of PEERS survey and STB data was sequential and integration occurred at the data analysis stage.The PEERS study captured data on aggression and exposure to aggressive peers at both the individual and the situational level, and individual-level survey data on aggression-relevant propensity (morality and the ability to exercise self-control) was applied to situational STB data units. 16Each STB data unit captured a situation (person-environment interaction) and associated behavioral outcome, and combining this with PEERS survey data on individual characteristics facilitated the study of situational interaction.

Aggression-relevant propensity
Aggression-relevant propensity is a composite measure which comprises standardized and summed subscales of aggression-relevant morality (moral rules and emotions) and the ability to exercise selfcontrol.These constructs were measured with adapted versions of the PADS+ scales (see Wikström,13 For example, the original PADS+ STB instrument recorded situational data on the number of peers present and linked this with individual-level measures of peer delinquency.This is problematic as it assumes that the peers referred to in the survey are the same peers who were present in the setting in the STB.14 These 15-minute intervals better capture the shape of the school day as lessons and break times are typically measured in these denominations.Moreover, the current study focuses on the presence of peers who may be present in (or absent from) settings for relatively brief periods.As the PEERS STB only collected data on time spent at school (cf.24-hour periods in the PADS+ study), this adaptation was possible without unduly increasing the research burden.15 This peer nomination technique resembles Warr's (2002) proposed micro-life course approach to the study of peer influence.Warr recommended the development of a time diary method that integrates data on social interactions with information about each peer to track peer influence over weeks or hours rather than months or years.By combining the methodological innovations of Warr (2002) and the PADS+ STB, the PEERS STB is more powerful than either method in isolation for studying the situational role of peer influence in the explanation of aggressive behavior.
16 Previous studies using STB data have also aggregated situational measures to individuals to create a more sophisticated measure of environmental exposure.However, this was not done in the current study as the STB interviews were not conducted with the full sample.Oberwittler et al., 2012;Wikström & Svensson, 2010) and the scale items are reported in Appendix A. First, aggression-relevant moral rules were measured with a 12-item scale that captures how wrong participants think it is for someone their age to engage in acts of physical, verbal, and relational aggression at school (alpha = .89).Second, aggression-relevant moral emotions were measured with modified versions of the PADS+ shame and guilt subscales.The nine-item ability to anticipate shame scale asked whether participants would feel ashamed if their best friends, teachers, or parents found out they had engaged in three types of aggressive behavior at school (alpha = .89).The six-item ability to anticipate guilt scale asked participants whether they would feel guilty if they engaged in various forms of aggression at school (alpha = .86).Finally, the ability to exercise self-control was measured with the PADS+ eight-item generalized scale which captures impulsivity, risk-taking, and future orientation (alpha = .79).These relatively stable traits are assumed to be related to the situational ability to exercise self-control (i.e., the ability to act in line with personal morality when there is external pressure to do otherwise) (Wikström & Treiber, 2007). 17 To construct the aggression-relevant propensity index, the moral rules and moral emotions scales were standardized and summed to create a morality index.The morality index and ability to exercise self-control scale were standardized and summed to create a propensity index which was standardized to create a final z-score with higher scores reflecting high aggression-relevant propensity (approximately normally distributed).An additive propensity index is traditionally constructed in tests of SAT (e.g., Hirtenlehner & Treiber, 2017;Svensson & Pauwels, 2010;Wikström, Oberwittler et al., 2012) and the construction of the PEERS propensity index also includes the moral emotions subscales to more comprehensively capture the morality construct. 18 Aggression-relevant propensity is measured at the individual-level and this measure is also applied to situational data units (see also Beier 2018;Hardie, 2017Hardie, , 2021;;Wikström, Oberwittler et al., 2012;Wikström et al., 2010Wikström et al., , 2018)).As individual characteristics are relatively stable, it is assumed that this generalized propensity measure is strongly associated with the situational application of morality and the ability to exercise self-control (Wikström, Oberwittler et al., 2012: 132).The situational analyses presented in this study categorize participants into high and low propensity groups using the overall PEERS sample mean.Whilst this threshold is sample-dependent and inevitably arbitrary, this dichotomization illustrates key differences between groups (Hardie, 2020, 2017, 2021; Wikström,  Oberwittler et al., 2012; Wikström et al., 2018). 19  Association with aggressive peers Association with aggressive peers was measured with standardized and summed peer attitudinal and behavioral subscales (see Appendix A).Perceptual measures of peer characteristics are necessary for tests of SAT as it is the individual's subjective perception of the moral context that is causally implicated in the explanation of rule-breaking behavior (Hardie, 2021;Hirtenlehner, 2018;Wikström, 2006).Perceptions of peer attitudes toward aggression were measured with a 12-item scale that was inspired by Paluck and Shepherd's (2012) measure of prescriptive social norms.Participants were asked how many of their school friends thought it was okay to engage in different types of aggression (alpha = .93).Perceptions of peer involvement in aggression were measured with a 12-item scale which was based on the PADS+ peer crime involvement scale (Wikström, Oberwittler et al., 2012: 152-3).Participants were asked how often their school friends engaged in different types of 17 Whilst this is the most commonly used measure of SAT's ability to exercise self-control construct, this scale has been criticized due to the "discrepancy between the conceptualization and operationalization" (Hirtenlehner & Reinecke, 2018: 6; see also Kroneberg & Schulz, 2018). 18 Given the potential interplay between morality and the ability to exercise self-control, some researchers have challenged the suitability of an additive propensity index (e.g., Hirtenlehner & Reinecke, 2018;Hirtenlehner et al., 2021).Future research should improve upon the operationalization of the ability to exercise self-control and identify the most appropriate procedure for constructing the propensity index.
19 Trichotomisation (± one standard deviation from the mean) is usually preferable to dichotomization when categorizing variables (Hardie, 2017).However, trichotomisation was not used in this study as it resulted in multiple small or non-existent groups and it was not possible to reliably compare the group means.
aggression at school (alpha = .93).The aggressive peer index was created by standardizing and summing the perceived peer attitudes and peer behaviors scales.This index was standardized to create a final z-score where higher values corresponded with greater levels of affiliation with aggressive peers.Scores were positively skewed which shows that most adolescents believed their school friends disapproved of aggression and rarely engaged in aggressive behavior.

Aggression frequency
Individual-level aggression frequency was measured with a 12-item self-report scale (alpha = .89;Appendix A) that was inspired by Björkqvist, Lagerspetz, and Kaukiainen's (1992) Direct and Indirect Aggression Scale (see also Österman et al. 1994, 1998).Participants were asked how many times they had engaged in different types of aggression at school over the last month.Responses were given on a sevenpoint scale inspired by Straus' (1979) Conflict Tactics Scale and numeric scores were assigned to each response category (never = 0, once = 1, twice = 2, 3-5 times = 4, 6-10 times = 8, 11-20 times = 16, 20+ times = 25).Whilst individual-level aggression frequency is not a genuine count variable, these frequency scores retain the order of magnitude between participants and indicate the general level of involvement in aggression (see Barton-Crosby 2017: 125).The selection and development of this individual-level aggression frequency measure is discussed further in Kennedy (2022: 143-6).
Aggression was highly prevalent in the PEERS sample and at least one act of aggression was reported by 84.3% of participants (n = 332).The individual-level aggression frequency variable displayed a negative binomial distribution and there was a notable group of high-frequency perpetrators who were responsible for a large proportion of aggressive behavior.Whilst many participants (n = 103; 26.1%) reported four or fewer aggressive acts over the previous month, 51 participants (12.9%) reported engaging in aggression more than twice a day.The heavily skewed distribution of aggression violates the assumptions of linear regression models and various safeguards were employed in the individual-level analyses. 20Outliers were retained for analytical purposes as they provide critical data for testing complex or subtle relationships.Moreover, these high-frequency perpetrators are particularly important to study as effectively intervening with this group should result in the greatest reductions in aggressive behavior.

Presence of aggressive peers
The situational analyses presented in this study are restricted to STB data units in which close friends were physically present (n = 7702, 78.1%).These data units were dichotomized depending on whether (i) one or more aggressive friends were present, and (ii) only non-aggressive friends were present.First, each participant nominated up to 10 of their closest friends at school.They were told that their close friends were the peers who they liked the most and spent the most time with at school.Second, the perceived aggression-relevant attitudes of each nominated friend was measured with a three-item scale.Participants were asked whether each friend thought it was okay to engage in physical, verbal or relational aggression at school.Responses for each item were dichotomized and summed to create an overall score for each friend.An a priori conservative threshold was adopted and each friend was classified as aggressive if they approved of all three types of aggression (i.e., reported an overall score of three). 21Finally, the participant reported which close friends they were with for each 15-minute unit during the previous four school days.Each friend was recorded as present if they were physically in the same action setting as the participant for the majority of the 15-minute period.By linking this presence data with data on the perceived aggression-relevant attitudes of each nominated friend, the PEERS 20 Log transformation failed to normalize the individual-level aggression frequency variable and this technique was not adopted in this study.Log transformation complicates the interpretation of statistical interactions and may weaken subtle interaction effects (Hardie, 2020) whilst sacrificing important data (Cohen, 1990).

21
The use of a conservative threshold means that the number and influence of aggressive peers is likely to be underestimated compared to a more liberal approach.Future studies can use the PEERS dataset to investigate the effects of alternative thresholds.
STB method was able to capture unique situational data on (and generate complex constructions of) the types of peers present in the setting.

Aggressive incidents
The second measure of aggression was a binary situational measure that captured whether an aggressive incident occurred during each temporal unit.The end-of-day summary method (Phipps & Vernon, 2009) was employed and participants were asked whether they had engaged in 12 forms of aggressive behavior at school.Each aggressive act was coded in the temporal unit during which it occurred (up to a maximum of 12 acts per unit).A total of 143 aggressive acts were reported across 9860 temporal units (equivalent to 360 school days across 90 participants) and 41 STB participants (45.6%) reported at least one aggressive act over the previous four days.There was a significant and moderate correlation between aggression frequency in the STB and the PEERS survey (r s = .45,p < .001,n = 90).
Aggressive incidents were measured as a binary outcome for each temporal unit.Participants reported multiple aggressive acts in 18 temporal units and there were 117 distinct temporal units in which aggression occurred.This study assumes that multiple aggressive acts that occurred within a single temporal unit were part of a sequence of aggressive behavior and these are treated as single incidents for the situational analyses.The STB analyses presented in this paper focus on the 109 aggressive incidents that occurred when close friends were present.

Analytical approach
This study employs a combination of additive and interactive approaches to demonstrate both statistical dependence and situational convergence.The distinction between statistical interaction (dependence) and situational interaction (convergence) is often overlooked (Hardie, 2020) yet it is crucial for appreciating the unique contributions of this study.First, this study applies traditional additive methods to individual-level survey data to assess statistical dependence between independent measures of individual characteristics and environmental features in the prediction of individual-level aggression frequency. 22These analyses can complement situational approaches by providing evidence that is consistent with the situational mechanism and generating policy-relevant conclusions about differential vulnerability to particular types of environmental exposure (Hardie, 2017(Hardie, , 2020(Hardie, , 2021)).However, these analyses require "an assumption of cooccurrence of the exposure and action" (Hardie, 2020: 54; see also Wikström et al., 2018;Wikström & Kroneberg, 2022) as there is no spatio-temporal link between individual-level exposure and aggression frequency data.Conclusions drawn from these analyses therefore require the auxiliary assumption that aggression occurred when adolescents were in the company of these aggressive peers (see Hirtenlehner & Schulz, 2020).Consequently, these analyses are unable to establish whether acts of aggression are most likely to occur when high propensity adolescents are with aggressive peers.
To mitigate these limitations, this study also applies interactive methods to PEERS STB data to assess situational interaction between explanatory variables.This approach captures the spatio-temporal convergence of individual characteristics and environmental features to identify the convergent conditions under which aggressive behavior is more or less likely to occur (Hardie, 2020).Situational analyses are rarely presented in empirical research (for exceptions, see Hardie, 2017Hardie, , 2021;;Wikström et al., 2010Wikström et al., , 2018;;Wikström, Oberwittler et al., 2012) but they are essential for forming conclusions about situational models and action decision-making processes (Hardie, 2020). 23One limitation of these analyses is that the findings only apply at 22 This approach has been adopted in the majority of studies testing person-environment interactions within an SAT framework to evidence situational interaction in the absence of situational data (e.g., Hirtenlehner & Hardie, 2016;Hirtenlehner & Treiber, 2017;Hirtenlehner et al., 2015;Svensson, 2015;Svensson & Pauwels, 2010;Wikström & Svensson, 2008;Wikström et al., 2011).

23
There are four criminological publications to date that have presented situational analyses of situational data (e.g., Hardie, 2021;Wikström et al., 2010Wikström et al., , 2018;;Wikström, Oberwittler et al., 2012).These publications all used PADS+ data and "appropriate replication studies using other situational data are much needed" (Hardie, 2020: 90).The current study has responded to this challenge by applying situational analytical methods to the novel and independent PEERS dataset.
the level of situations and they cannot generate conclusions about individuals, environments, or the differential vulnerability of certain types of individuals to certain types of environments (Hardie, 2020).Consequently, this study employs a combination of additive and interactive analytical approaches to evidence both statistical dependence and situational convergence as "each mitigates the limitations of the other" (Hardie, 2021: 6).Together, these methods can build an overall picture that is consistent with the situational model of peer influence.

Individual-level analytical approach
This study first applies traditional regression-based methods to individual-level survey data to study statistical interaction (dependence) between individual characteristics and environmental features in the explanation of aggression.As it is methodologically challenging to demonstrate and interpret statistical interactions, this study adopts Hardie's (2020) multimethod approach to replicate the findings.This approach mitigates the limitations of traditional methods which are imperfect for assessing statistical interaction when the individual-level aggression frequency variable is highly skewed and violates the assumptions of linear regression models (Hardie, 2017(Hardie, , 2020(Hardie, , 2021)).Many issues can undermine the search for significant interaction effects including inadequate measurement of theoretical constructs and recruitment of non-representative samples which lack variation across key measures (Hardie, 2020).Moreover, it is challenging to ensure sufficient statistical power to adequately test complex statistical interaction effects (Wikström & Kroneberg, 2022).Consequently, Hardie (2020: 64) has warned that "[r]esearchers should be wary of concluding 'no interaction' from a single method or model of multiplicative interaction" (see also Wikström & Kroneberg, 2022).Statistical controls will not be included in these analyses due to the lack of theoretical rationale (Pauwels et al., 2009; see also Becker 2005;Spector & Brannick, 2011) and the risk of underestimating the efficacy of the causally relevant variables (Hardie, 2020: 92). 24 The first analyses estimate OLS linear regression models of individual-level aggression frequency to assess statistical dependence between explanatory variables (see Hardie, 2020).The OLS regression model includes a two-way interaction term and all predictor variables (Braumoeller 2004).All independent variables are z-standardized and model outputs report unstandardized coefficients (Aiken and West 1991;Friedrich, 1982).Quadratic terms of predictor variables are computed to correct for the skewed distribution of the aggression frequency variable and absorb the non-linear aspects of the association with explanatory variables (Lubinski & Humphreys, 1990).Any significant quadratic terms are included in the model.The models are also estimated using clustered robust standard errors (Hannon & Knapp, 2003) which correct for heteroscedasticity of residuals and the nesting of participants in schools.The presence of a significant interaction term in a regression model constitutes evidence of statistical interaction (Cohen et al., 2013;Gerstner & Oberwittler, 2018;Jaccard et al., 1990).
This study also presents a visual representation and comparisons of group averages to aid the interpretation of statistical interaction.The interaction graph plots the mean aggression frequency for dichotomized and intersected peer and propensity groups.Statistical interaction is illustrated by "a gradient of association between one independent variable and the dependent outcome (or predicted outcome) that increases or decreases according to an increase or decrease in the other independent variable" (Hardie, 2020: 71).Although the dichotomization of explanatory variables is inevitably arbitrary and subjective (Hardie, 2017(Hardie, , 2020(Hardie, , 2021;;Wikström, Oberwittler et al., 2012), these powerful graphs are useful for illustrating the nature of statistical interactions.
This study also conducts robust regression analyses (Andersen 2008) to assess the robustness of these findings (see e.g., Hirtenlehner, 2020;Hirtenlehner et al., 2021).Robust regression techniques generate parameter estimates and standard errors which are resistant to the influence of outliers and 24 For example, Wikström et al. (2018) found that the inclusion of day and time as control variables in statistical models led to significant decreases in predictive power.This was evidence of overfitting and suggested that these control variables lacked predictive efficacy once the key explanatory variables were accounted for.
the skewed distribution of the dependent variable.Given the extreme negative distribution of the individual-level aggression frequency variable, these analyses employ Huber's (2004) M-estimator to ensure the results are robust to heavy-tailed error distributions.These robust regression analyses minimize the influence of extreme values on regression slopes and mitigate contamination through a "second data-generating process" (Hirtenlehner et al., 2021: 19).Consequently, these analyses can confirm that any statistical interactions observed in the OLS models are not spurious when assumptions of normality are violated.
Finally, this study employs comparisons of marginal effects observed in negative binomial regression models (Hilbe, 2011) to test the statistical interaction in a non-linear framework.Whilst negative binomial regression models are appropriate for modeling skewed and overdispersed count variables (Hilbe, 2011(Hilbe, , 2014)), it is notoriously challenging to interpret statistical interaction effects in non-linear models (Hirtenlehner & Schulz, 2020).Consequently, this study relies on comparisons of marginal effects (Karaca-Mandic et al., 2012;Mood, 2010;Williams, 2012) obtained from negative binomial regression models to test statistical interaction between explanatory variables.Marginal effects express "how the expected value of the count response changes with a one-unit increase in the predictor variable, with other variables held at fixed values" (Hirtenlehner et al., 2021: 181).Whilst this is arguably the most suitable approach for studying statistical interaction within a non-linear framework (Hardie, 2020), it involves a loss of information on the continuous moderator variable (Barton-Crosby and Hirtenlehner 2020).Consequently, this procedure is employed primarily as a robustness check of findings from linear regression models.
This study estimates negative binomial regression models and includes the corresponding multiplicative term.Predictor variables are z-standardized (Aiken and West 1991) and analyses employ clustered robust standard errors as participants are nested in schools.The conditional marginal effects of affiliation with aggressive peers are computed at representative values of aggression-relevant propensity (the moderator variable).Following previous research (e.g., Barton-Crosby and Hirtenlehner 2020; Hirtenlehner et al., 2021;Hirtenlehner & Schulz, 2020), this study sets these values at the mean and one standard deviation above and below the mean.These analyses employ Paternoster et al.'s (1998) z-test for equality of regression coefficients to examine whether these conditional effects are significantly different.

Situational analytical approach
This study also applies situational methods to novel PEERS STB data to evidence situational interaction (convergence) between individual and environmental factors.Unlike individual-level data, situational STB data is structured so that each observation refers to a situation (person-environment interaction) and the associated behavioral outcome.Situational analyses must demonstrate that the likelihood of aggressive outcomes is dependent on the convergence of certain theoretical conditions irrespective of group size (Hardie, 2020).This means that situational analyses must investigate whether the rate of aggression differs significantly between different groups of situations.By identifying the convergent conditions under which aggressive behavior is more or less likely to occur, situational analyses afford more precise conclusions about the operation of the action decisionmaking process.Although the situational process cannot be tested directly, evidence of situational interaction constitutes indirect support for the theoretical model (Hardie, 2017(Hardie, , 2020(Hardie, , 2021;;Wikström, Oberwittler et al., 2012;Wikström et al., 2018; see also Murray et al., 2009).
This study uses the group comparison approach (Wikström, Oberwittler et al., 2012) which was further developed by Hardie (2017Hardie ( , 2020Hardie ( , 2021) ) to examine situational interaction.First, all situational data units in which peers are present are categorized by dichotomizing and intersecting the independent variables of theoretical interest.The number of observations in each group varies due to intervariable relationships resulting from processes of selection and emergence (Hardie, 2020).However, this is unproblematic as the same causal process should apply regardless of the "causes of the causes" (Hardie, 2020: 91).Second, the rate of aggression is calculated for each of the four groups of situations.The number of aggressive outcomes reported in each group is divided by the total number of data units recorded for that group (aggressive outcomes + non-aggressive outcomes).Rate calculations ensure that conditions under which participants spend a large proportion of their time but engage in proportionately fewer aggressive incidents do not overshadow conditions under which relatively little time is spent but proportionately more aggressive episodes occur (Hardie, 2020).Rates of aggressive incidents are expressed per 25 hours (100 × 15-minute units) to account for variations in the number of data units for each group.Finally, the rates for each group of situations are compared using a visual graph, risk ratios, and significance tests.Risk ratios (exposed rate/unexposed rate) are calculated to quantify the magnitude of the difference in aggression rates under various conditions and a visual graph is presented to illustrate the nature of situational interaction between explanatory variables.Two-proportion z-tests (Agresti 2002;Fleiss et al., 2003) are also conducted to assess the significance of group differences in rates of aggression (see Hardie, 2017Hardie, , 2020Hardie, , 2021)).

Causal ordering
The temporal ordering of data collection in the PEERS study was driven by theoretical and methodological considerations (see Kennedy, 2022: 180-2).The PEERS study employed a mechanistic approach to causality which emphasizes the importance of causal mechanisms linking cause and effect (Matsueda, 2017;Opp, 2020;Proctor & Niemeyer, 2019;Wikström, 2004Wikström, , 2006Wikström, , 2008Wikström, , 2011;;Wikström et al., 2012Wikström et al., , 2018;;Wikström & Kroneberg, 2022).Whilst longitudinal designs are valuable for studying long-term developmental processes (Little et al., 2009), they are inappropriate for testing situational mechanisms (Pauwels, 2018;Wikström, 2008;Wikström et al. 2018) as the relevant causal process occurs over minutes or seconds rather than months or years (Bruinsma et al., 2015;Pauwels, 2018;Wikström, 2008;Wikström et al., 2018).Consequently, measurements of independent and dependent variables should be taken simultaneously or as close in time as possible (Hardie, 2017;Wikström et al., 2018) and it should be assumed that "the 'interaction' produces the 'action' rather than the other way round" (Wikström et al., 2018: 16).By combining measurement proximity with well-reasoned theoretical assumptions, it is possible to draw causal conclusions in the absence of strict causal ordering.
The PEERS study applied current individual-level data on aggression-relevant propensity and association with aggressive peers to predict prior involvement in aggression over the previous month.Although this violates strict cause-and-effect temporal ordering, the explanatory variables are relatively stable and unlikely to change significantly over the course of one month.Moreover, this approach is generally used in analyses of PADS+ data and it does not have a significant impact on the magnitude of the correlations (see Hardie, 2017;Wikström, Oberwittler et al., 2012). 25Causal ordering was retained for situational analyses of PEERS STB data as the STB interviews were conducted approximately one week following survey administration.Individual-level data on aggressionrelevant propensity was captured by the PEERS survey prior to the STB reference period and applied to STB data units.

Dependence
Table 1 reports the results from OLS linear regression models predicting individual-level aggression frequency.As the quadratic term of the propensity variable was significant in an initial model (not shown), this term is included in both models.Model 1 estimates the independent effects of propensity and affiliation with aggressive peers on aggression frequency.The results show that both propensity and affiliation with aggressive peers have significant and comparable independent effects on 25 The approach is particularly defensible in the current study as the reference period for the dependent variable (aggression frequency) was one month.In contrast, the PADS+ study collected crime frequency data spanning the previous year.
aggression.Adolescents with weak aggression-relevant propensity and adolescents who affiliate with aggressive peers are significantly more likely to engage in school-based aggression.
Model 2 introduces a multiplicative interaction term between propensity and affiliation with aggressive peers.This model shows that there is a significant statistical dependency effect between these explanatory variables in the explanation of aggressive behavior.The interaction term was significant (b = 5.02, p = 0.022) and the inclusion of this interaction term increased the amount of variance explained by the model by 1.6 percentage points.The positive sign of the interaction term suggests that association with aggressive peers is more important for adolescents with higher levels of aggression-relevant propensity.Moreover, the inclusion of the interaction term almost halves the quadratic propensity term coefficient thus decreasing the curvilinearity of the propensity-aggression relationship.This conservative test suggests that the interaction effect is not spurious and enhances the reliability of these findings.
A series of robust linear regression analyses (Andersen 2008) was conducted to assess the robustness of these findings.Table 2 shows the results from these robust regression models predicting individuallevel aggression frequency.Model 1 reports the main effects of propensity and affiliation with aggressive peers on aggressive behavior.Both explanatory variables had significant and comparable independent effects on aggression replicating the OLS findings above.Model 2 introduces an interaction term between these explanatory variables.The significant interaction term (b = 6.71, p = .004)shows that the effect of affiliation with aggressive peers is dependent on propensity and the inclusion of this interaction term substantially increases the amount of variance explained by the model.Quadratic terms of predictor variables were not significant in Model 2 and are not presented.These results fully corroborate the OLS linear regression findings presented above.
Figure 2 illustrates the nature of this two-way interaction in the explanation of aggressive behavior.This graph plots the mean self-reported aggression frequency for dichotomized propensity and peer groups (see Table 3 for participant distribution).Despite the significant correlation between propensity and peer variables (r s = .37,p < .001), the smallest group captures 15.5% of participants (n = 61).Figure 2 shows that aggression-relevant propensity moderates the relationship between affiliation with aggressive peers and aggression frequency at the individual level.Affiliation with aggressive peers is associated with increases in aggression for both high and low propensity groups; however, high propensity adolescents are more vulnerable to the aggressive peer effect.These differential vulnerability findings are consistent with the situational model of peer influence.
Marginal effects observed in negative binomial regression models (Hilbe, 2011) were compared as a final test of the statistical interaction.Table 4 shows that the marginal effects of affiliation with aggressive peers significantly increase as the propensity for aggression increases.Affiliation with aggressive peers has the strongest effect on aggression for adolescents with high propensity and the weakest effect for adolescents with low propensity (albeit there is still a sizable influence).The effect of affiliation with aggressive peers in the high propensity condition (ME = 14.88, p < .001) is more than double the effect in the low propensity condition (ME = 6.76, p < .001)(z = 6.72, p < .001).A series of pairwise comparison tests confirmed that all three effect differences were significant.These sensitivity analyses reproduce the findings from the linear regression models in a non-linear framework.Taken together, these findings provide compelling evidence that low propensity (i.e., strong aggressionrelevant morality and a well-developed ability to exercise self-control) protects adolescents from the negative influence of aggressive peers.

Convergence
Table 5 categorizes data units into four (2 × 2) groups using dichotomized and intersected propensity and peer variables.Whilst both low and high propensity adolescents spent a significant amount of time  with aggressive peers, the proportion of time spent with aggressive peers was greater for high propensity adolescents.High propensity adolescents spent almost one-third of their school time with aggressive peers (31.4%) compared to around one-fifth (21.2%) for low propensity adolescents.
Although the group sizes varied due to social processes of development and selection (Hardie, 2020), they captured sufficient variation to analyze situational interaction between explanatory variables.As a preliminary note, Table 5 reports the rates of STB aggression by aggressive and non-aggressive peer conditions.Aggression was 3.81 times more likely when aggressive peers were present (3.09incidents per 25 hours spent under these conditions) than when adolescents were with non-aggressive peers (0.81 incidents per 25 hours) (z = 7.47, p < .001).Whilst adolescents spent around one-quarter of their time (26.4%) with aggressive friends, more than half of the aggressive incidents reported (57.8%, n = 63) occurred during this time.Table 5 also reports the rates of aggression for the high and low propensity conditions.Aggression was 3.88 times more likely under conditions characterized by high propensity (2.21 incidents per 25 hours) than conditions characterized by low propensity (0.57 incidents per 25 hours) (z = 6.10, p < .001).These findings support the preliminary hypotheses and demonstrate the main effects of propensity and the presence of aggressive peers at the situational level.
More importantly, Table 5 compares rates of aggression for the four dichotomized and intersected peer and propensity groups.Aggression was most likely in situations characterized by the convergence of high propensity and the presence of aggressive peers.The rate of aggression was 10.00 times higher when high propensity adolescents were with aggressive peers (4.40 incidents per 25 hours) than when low propensity adolescents were with nonaggressive peers (0.44 incidents per 25 hours) (z = 9.26, p < .001).Crucially, the effect of aggressive peers on aggression was greater in the high propensity condition than in the low propensity condition (Figure 3).The rate of aggression in the high propensity condition was 3.64 times higher when adolescents were with aggressive peers than when they were with nonaggressive peers (z = 6.37, p < .001).However, there were no significant differences in the rate of aggression in the non-aggressive and aggressive peer conditions for situations characterized by low propensity (rr = 2.32, z = 1.90, p = .571).These findings demonstrate the situational interaction between propensity and the presence of aggressive peers in the explanation of aggression.

Dependence
Both linear and non-linear models revealed a robust statistical dependency effect which was illustrated with a graphical representation.These results showed that there was a significant statistical interaction between aggression-relevant propensity and affiliation with aggressive peers.The effect of association with aggressive peers on aggression was greater for high propensity adolescents than low propensity adolescents.This suggests that whilst high propensity adolescents are situationally vulnerable to the influence of aggressive peers, low propensity adolescents are situationally resistant to criminogenic peer effects.This two-way statistical interaction is consistent with SAT's situational model and highlights the importance of theorizing and testing person-environment interactions when studying peer influence.This study found that association with aggressive peers and high aggression-relevant propensity each independently increased the likelihood of aggressive behavior.These preliminary findings are consistent with a large body of criminological and psychological research that has linked various measures of peer norms (e.g., Espelage et al., 2003;Henry et al., 2000Henry et al., , 2011;;Mercer et al., 2009;Salmivalli & Voeten, 2004;Sentse et al., 2007Sentse et al., , 2015;;Scholte et al., 2010;Werner & Hill, 2010), aggression-relevant attitudes (e.g., Boulton, Bucci, and Hawker 1999;Boulton, Trueman, and Flemington 2002;Gendron et al., 2011;Guerra et al., 2011;Henry et al., 2000;Huesmann & Guerra, 1997;Huesmann et al., 1992;Li et al., 2015;McConville & Cornell, 2003;Rigby and Slee, 1991;Salmivalli & Voeten, 2004;Slaby & Guerra, 1988), and selfcontrol (e.g., Farrington & Baldry, 2010) to aggressive behavior.However, the presence of statistical interaction in the data suggests that research on the role of peer influence must shift beyond traditional analyses of unconditional main effects and account for individual differences in order to fully understand situational peer effects.
The two-way interaction finding shows that aggression-relevant propensity moderates the effect of association with aggressive peers on aggressive behavior.Yet whilst high propensity adolescents were particularly vulnerable, low propensity adolescents were not fully immune to the influence of aggressive peers: association with aggressive peers increased aggression amongst the low propensity group albeit to a lesser degree (for a similar finding in the context of crime, see Hirtenlehner et al., 2021).This is unsurprising as the dichotomized propensity groups are relatively arbitrary and adolescents with a genuinely low propensity for aggressive behavior are likely to be rare in non-delinquent samples.As the propensity variable is normally distributed, many adolescents in the low and high propensity groups had similar aggression-relevant propensity scores and the differences between them may be minimal.
These statistical dependence findings extend existing research on peer influence and aggressive behavior.First, they reinforce the enhancement or social interaction model which emphasizes the conditional nature of peer influence on the development (or expression) of aggression, violence, and antisocial behavior (Vitaro et al., 2012(Vitaro et al., , 2018)).The findings build on a growing body of research which has highlighted the moderating effects of individual characteristics such as attitudes (Molano et al., 2013;Vitaro et al., 2000), low self-regulation (Goodnight et al., 2006;Dishion & Connell, 2006;Gardner et al., 2008), and susceptibility to peer influence (Monahan et al., 2009).Second, these results complement Ernst and Lenkewitz's (2020) finding that adolescents who have not internalized the "code of the street" are not violent regardless of context.The findings are also consistent with Wright et al.'s (2001) social amplification hypothesis which claims that antisocial bonds to delinquent peers promote offending primarily amongst individuals with a strong criminal disposition.Finally, these findings build on the social ecological approach to bullying and aggression (Hong & Espelage, 2012;Swearer & Doll, 2001;Swearer and Espelege, 2004;Swearer & Hymel, 2015) which highlights the central role of the interaction between personal characteristics and features of the social context. 26 Moreover, these individual-level findings extend the empirical foundation of SAT by demonstrating the peer-propensity interaction in the context of school-based aggression.Many studies have shown that the effect of association with delinquent peers on offending is greater for people with low self-control (e.g., Hirtenlehner & Baier, 2019;Hirtenlehner & Hardie, 2016;Hirtenlehner et al., 2015;Hirtenlehner et al., 2021;Mobarake et al., 2014;Morselli & Tremblay, 2004;Ousey & Wilcox, 2007;Wright et al., 2001)  27 and weak morality (e.g., Mears et al., 1998;Hirtenlehner et al., 2021). 28The current study establishes support for the differential vulnerability hypothesis in a new domain of moral rule-breaking and bolsters SAT's claim to be a general theory of moral action.
However, the conclusions that can be drawn from these individual-level analyses are limited.Analyses conducted at the individual level cannot distinguish between social processes (i.e., processes of development and selection) and the situational decision-making process (Hardie, 2021).It is possible that association with aggressive peers influences the development of individual aggressionrelevant propensity (Wikström & Treiber, 2019) rather than the action decision-making process.Although these individual-level findings are consistent with the situational model, they require "an assumption of co-occurrence" (Hardie, 2020: 54; see also Wikström et al., 2018;Wikström & Kroneberg, 2022) and do not afford the specific conclusion that acts of aggression are most likely to

26
The social ecological approach applies Bronfenbrenner's (1977Bronfenbrenner's ( , 1979) ) ecological systems perspective to the study of aggression and school bullying.This perspective proposes that individual development results from complex and reciprocal interactions between people and their social environments.27 However, it should be noted that this effect is not universal across all studies (see e.g., Bruinsma et al., 2015;De Buck & Pauwels, 2019;McGloin & Shermer, 2009;Meldrum et al., 2009).

28
In the context of crime, Hirtenlehner et al. (2021) found evidence of a significant three-way interaction between morality, selfcontrol, and association with delinquent peers.The ability to exercise self-control moderated the effect of association with delinquent peers most for adolescents with weak morality.When adolescents had strong morality, the size of the peer effect did not vary significantly depending on the ability to exercise self-control.
occur when aggression-prone adolescents are in the company of aggressive peers.Situational analyses of situational data (discussed below) are required to form more precise conclusions about the situational model and action decision-making process.

Convergence
The current study is the first to use STB data to evidence the situational interaction (convergence) between aggression-relevant propensity and the presence of aggressive peers in explaining school-based aggression.Previous studies on peer influence conducted within the SAT framework have lacked the situational data required to demonstrate this convergence and this was only possible in the current study due to the methodological development of the PEERS STB.These novel findings confirm the assumption in the individual-level analyses presented above that aggression is most likely to occur when high propensity adolescents are in the company of aggressive peers.Moreover, these findings fully support the situational model of peer influence and are consistent with what researchers would expect to observe if the action decision-making process was operating as theorized.
Preliminary analyses showed that school-based aggression was more likely to occur in situations characterized by the presence of aggressive peers.This novel finding provides initial support for the situational model by demonstrating the spatio-temporal convergence between aggressive outcomes and the presence of aggressive peers using PEERS STB data.This finding is consistent with the claim that the presence of aggressive peers increases the likelihood of experiencing aggression-relevant motivations, weakens the perceived aggression-relevant moral norms of the setting and personal morality, and weakens deterrence perceptions and the ability to exercise self-control.In addition, analyses showed that aggression was more likely to occur in situations characterized by high aggression-relevant propensity.This finding aligns with previous STB research on the situational role of action-relevant propensity in the explanation of crime (e.g., Hardie, 2017Hardie, , 2021;;Wikström, Oberwittler et al., 2012;Wikström et al., 2010Wikström et al., , 2018)).Applying SAT, high propensity adolescents are more likely to see and choose aggression as a viable action alternative in response to a relevant motivation.
However, these preliminary findings are superseded by the presence of situational interaction which showed that the effect of aggressive peers was greatest in situations characterized by high propensity.This study found that whilst the presence of aggressive peers increased aggression fourfold in situations characterized by high propensity, there was no significant difference in aggression in situations characterized by low propensity.This suggests that although the presence of aggressive peers is generally conducive to aggressive behavior, aggressive peers are largely irrelevant in the action contexts of low propensity adolescents. 29 These situational findings extend prior research which has shown statistical dependence between association with aggressive peers and individual characteristics in the explanation of aggressive behavior.Similarly, many studies testing SAT's situational model at the individual level have found that the effect of association with delinquent peers on offending is greater for adolescents with high propensity (e.g., Gerstner & Oberwittler, 2018;Wikström, Oberwittler et al., 2012), or low self-control (e.g., Hirtenlehner & Baier, 2019;Hirtenlehner & Hardie, 2016;Hirtenlehner et al., 2015).However, the situational findings presented in the current study provide empirical clarification that aggression is most likely to take place when high propensity adolescents are in the presence of aggressive peers.These findings suggest that intervention policies and programs which prevent the spatio-temporal convergence of high propensity adolescents and aggressive peers may be particularly effective for reducing school-based aggression.

29
However, the presence of aggressive peers may influence aggression indirectly for low propensity adolescents through developmental processes of personal emergence (Wikström, 2019a;Wikström & Treiber, 2019).Investigation of this hypothesis requires longitudinal data and was beyond the scope of this study.

Practical implications
The primary recommendation to emerge from this study is that strengthening aggression-relevant propensity (morality and the ability to exercise self-control) may be more fundamental for preventing aggression than reducing exposure to aggressive peers (for a similar conclusion in the context of crime, see Wikström et al., 2018).Whilst it is unrealistic for adolescents to avoid affiliation with aggressive peers entirely (Vitaro et al., 2018), educators and parents can protect adolescents from the influence of aggressive peers by strengthening their morality and ability to exercise self-control (see also Hirtenlehner et al., 2021).This would also have an indirect effect on aggression by reducing the number of aggressive peers available to interact with and befriend in the population.Strengthening aggression-relevant propensity can be achieved through the provision of moral education and cognitive nurturing which are psychosocial processes in which social institutions (e.g., schools and families) play important roles (Wikström, 2019b;Wikström & Treiber, 2017, 2019).This recommendation challenges the philosophy behind the new generation of peer-oriented interventions which focus (either primarily or exclusively) on strengthening the social context (e.g., Kärnä et al., 2011;Paluck et al., 2016;Polanin et al., 2012;Salmivalli et al., 2010).Although these peer-oriented interventions are likely to influence the development of aggression-relevant propensity, this is neither their primary aim nor the assumed mechanism of change.
The second practical implication is the need to limit association with aggressive peers and this is particularly the case for aggression-prone adolescents. 30This strategy would directly reduce aggression by strengthening the moral contexts of settings in which adolescents participate by (i) decreasing aggression-relevant motivation, (ii) strengthening anti-aggression moral norms, (iii) increasing levels of perceived deterrence associated with aggressive behavior, and (iv) reducing social sanctions for not engaging in aggression.As the peer context is critical for shaping adolescent development (Brechwald and Prinstein 2011;Gifford-Smith et al., 2005;Hartup, 1993), this strategy would also indirectly reduce aggression by preventing the development of the propensity to engage in aggressive behavior.Schools and families can reduce exposure to aggressive peers by implementing peer-oriented interventions (e.g., Kärnä et al., 2011;Paluck et al., 2016) that aim to change the aggression-relevant attitudes and behaviors of the broader peer group.They can also manipulate processes of social and self-selection to avoid or minimize the aggregation of aggressive youth (e.g., by rethinking instructional and disciplinary school policies).However, one potential problem with this suggestion is the risk of iatrogenic developmental effects on conventional peers (see Dodge et al., 2006;Vitaro et al., 2012).This policy issue cannot be resolved without future research and underscores the need to build on the findings in this study by elaborating and testing the social model of SAT.

Next steps
This study has generated broad theoretical and methodological implications for future research.First, these findings show that future research on the role of peer influence in the explanation of schoolbased aggression must account for individual differences.It is misleading to draw conclusions and develop policy recommendations from the study of main effects alone when there is compelling evidence that peer variables interact with individual characteristics.Second, future research on situational models should prioritize the collection and analysis of real-world situational data.The PEERS study has showcased the unique benefits that STB data can provide (see also Hardie, 2017Hardie, , 2020Hardie, , 2021;;Wikström et al., 2012;Wikström et al., 2010Wikström et al., , 2018) ) and future research should capitalize on these methods.Future studies could also explore the value and feasibility of novel inferential methods of analysis that can evidence situational interaction (see e.g., Wikström et al., 2018; for a discussion, see Hardie, 2020: 94-5).Although these advanced methods are not necessary for 30 Relatedly, a large body of intervention research has found that the aggregation of deviant youth may result in iatrogenic effects (e.g., Dishion & Andrews, 1995;Dishion et al., 1999; see also Dishion & Tipsord, 2011;Dodge et al., 2006;Gifford-Smith et al., 2005).
demonstrating situational interaction, replication of situational findings with different methodological approaches would bolster confidence in the conclusions (Hardie, 2020: 94).
There are also several specific recommendations for future research.First, future research should use appropriate data and analyses to test additional propositions derived from this application of SAT's situational model to the study of peer influence.For example, future studies should collect and analyze situational data to investigate the role of motivation and the interplay between deterrence perceptions and aggressive peers.A second avenue for future research involves the theoretical expansion of this situational model to include the role of non-aggressive peers such as bystanders and defenders.Research could also combine this model with Hardie's (2021) application to advance knowledge about the complementary and competing influences of peers and guardians on aggressive behavior.The final recommendation is to apply the social model of SAT (Treiber, 2017;Wikström, 2017;Wikström, Oberwittler et al., 2012) to the study of peer influence and aggression.Future research should employ and expand this social model to explore novel research questions such as (i) how (and under what conditions) does association with aggressive peers affect the development of aggression-relevant propensity?, and (ii) how (and in what circumstances) does association with aggressive peers influence selection processes that determine the convergence of certain types of people and settings?This research would facilitate refinement of the practical implications that have emerged from this study.

Conclusion
This study has addressed the theoretical, methodological, and empirical challenges that have limited the study of peer influence and school-based aggression.The recent shift away from individualistic approaches to focus on the role of the broader peer group in the explanation of aggression has resulted in the popularity of peer-oriented interventions (see e.g., Kärnä et al., 2011;Paluck et al., 2016;Polanin et al., 2012;Salmivalli et al., 2010).However, this paper has argued that advancing the study of peer influence and aggression requires a situational approach that centers the person-environment interaction and specifies the (situational) causal mechanisms that produce aggressive behavior.This study has also argued that testing situational models with appropriate data and analyses requires methodological innovations which capture the micro-dynamics of peer influence and aggression in real-world contexts.
This paper presented a novel application of SAT's situational model to the study of peer influence and school-based aggression.It specified how and why the presence of aggressive peers influences the action decision-making process and identified the individual characteristics that amplify or diminish the effects of aggressive peers.This study also pioneered an innovative adaptation of the PADS+ STB method to collect unique situational data on the types of peers present in the setting for the first time.This was the major methodological contribution of the PEERS study and it can be applied to support future research on SAT and the situational dynamics of peer influence.Finally, this study presented situational analyses of novel PEERS STB data and additive analyses of survey data to test the situational model of peer influence.
This study is one of very few to demonstrate both statistical dependence and situational convergence to test situational models of action within an SAT framework.The convergence findings from the situational analyses are consistent with what we would expect to observe if the decision-making process was functioning as hypothesized.The dependence findings from the individual-level analyses complement these situational findings and provide policy-relevant clarification regarding the differential effects of aggressive peers at the individual level (see also Hardie, 2020Hardie, , 2021)).The most significant finding to emerge from this study is that high propensity adolescents are situationally vulnerable to the influence of aggressive peers and low propensity adolescents are situationally resistant.This finding has major practical implications as it suggests that strengthening aggression-relevant propensity (morality and the ability to exercise self-control) may be more fundamental for reducing school-based aggression than minimizing association with aggressive peers.

Figure 1 .
Figure 1.The input to the perception-choice process in the causation of aggression.

Figure 2 .
Figure 2. The nature of the interaction between propensity and peer norms.

Figure 3 .
Figure 3. Situational interaction between propensity and type of peers.

Table 1 .
OLS clustered robust standard error linear regression predicting (unlogged) aggression frequency from propensity and peer norms (N = 394).

Table 2 .
Robust linear regression models for the interaction between propensity and peer norms (N = 394).

Table 4 .
Marginal effects of peer norms at representative values of propensity (clustered robust standard errors (N = 394).

Table 5 .
STB aggressive incident rate per 25 hours by propensity and type of peers.