Relational Aggression and Externalizing: A Common Etiology?

A Thesis SUBMITTED TO THE FACULTY OF

UNIVERSITY OF MINNESOTA BY

Bridget Carey

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF ARTS

Matt McGue

December 2016

© Bridget Carey 2016

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Acknowledgements

Many individuals deserve recognition for their direct and indirect contributions to

this project. Special appreciation must go to my mentor, Matt McGue. Beyond providing

me with guidance and direction, he has shown me great generosity, kindness, and

patience. Words alone cannot express my gratitude for the time and energy he has

invested in me during this journey.

I would like to acknowledge the indirect contributions of the late Irving

Gottesman and of my father, Gregory Carey. Jointly they have instilled in me the

importance of scientific inquiry. Their commitment to sound and honest research will

forever inspire and motivate me.

Last, I would like to thank Conor and my family who showered me with

unconditional support and encouragement. I would not be where I am today without

them.

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Abstract

Previous research suggests that a highly heritable general externalizing factor contributes

to individual differences in a range of behaviors marked by impulsivity and disinhibition,

such as rule-breaking and aggression. Relational aggression has been found to be

moderately heritable and to share common genetic and environmental influences with

physical aggression, though no prior studies have examined the etiological commonality

between relational aggression and a more broadly construed externalizing domain. Using

a sample of 499 like-sex twin pairs, the present study confirmed that six measures of

externalizing-related behaviors formed two distinct subfactors of rule-breaking and

aggression. A confirmatory factor analysis revealed that relational aggression correlated

nearly equally with both factors. Factors of aggression, rule-breaking, and relational

aggression were fit in an independent pathway model which revealed that relational

aggression was influenced by additive genetics and non-shared environmental effects (a2

= .31 and e2 = .69). A majority of the heritability of relational aggression (72%) was

shared with the aggression and rule breaking factors, whereas the majority of the non-

shared environmental influence (88%) was specific to relational aggression. Findings

suggest that relational aggression should be included in the broader externalizing domain,

and that it may be its own distinct subfactor of externalizing, rather than simply being an

alternate form of aggression.

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Table of Contents

List of Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

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List of Tables

Table 1: Descriptive Statistics for Included Measures . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Table 2: Pearson r Correlations of all Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Table 3: Fit Statistics for CFA Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Table 4: Intraclass Correlations for Monozygotic and Dizygotic Twin Pairs . . . . . . . . 25

Table 5: Biometric Model Fit Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Table 6: Standardized Path Coefficients (with 95% Confidence Intervals) and

Total Variance Estimates (with 95% Confidence Intervals) for

Best-Fitting Independent Pathway Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Table 7: Genetic and Environmental Correlations

(with 95% Confidence Intervals) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

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List of Figures

Figure 1: Hierarchical Cluster Analysis of Aggression and

Rule-Breaking Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Figure 2: Visualization and Standardized Loadings for CFA of Aggression

and Rule-Breaking Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Figure 3: Visualization and Standardized Loadings for CFA of Aggression,

Rule-Breaking, and Relational Aggression Factors . . . . . . . . . . . . . . . . . . . . . . . 31

Figure 4 (a) Visual Representation of a Full Independent Pathway Model

and (b) Visual Representation of Best-Fitting Independent Pathway

Model for Current Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

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Introduction

The conceptualization of the externalizing spectrum emerged with the observation

that disorders marked by impulsivity, disruptiveness, and aggression frequently co-occur

(Achenbach, 1966; Krueger, 1999; Krueger et al., 2002). While current diagnostic tools

favor a discrete categorical approach to psychopathology, a large body of research

supports the existence of a dimensional organization of externalizing in both adolescents

and adults (Krueger, 2002; Krueger et al., 2007; Walton, Ormel, & Krueger, 2011). This

approach indicates a highly heritable general externalizing factor (heritability around .80;

Krueger, 2002) that contributes to the risk of a heterogeneous cluster of personality

factors and behaviors, such as impulsivity, disinhibition, substance use and abuse,

delinquency, and hostility. These facets of externalizing can generally be broken into two

subdomains: rule-breaking and aggression. Rule-breaking is typically characterized by

more “covert” forms of antisocial behavior, such as lying, cheating, or stealing.

Aggression, on the other hand, consists of acts that aim to harm others and that are

viewed as hurtful to the victims. Historically, the construct of aggression has been

limited to physical or verbal actions; however, in recent decades, there has been strong

support for the inclusion of other forms of aggression, such as relational aggression.

Rather than seeking to intimidate or harm a target victim, relational aggression is

characterized by manipulative behaviors that aim to harm relationships, reputations, or

social standings. The victimization may come in the form of gossiping, spreading rumors,

selective social inclusion or exclusion, or placing conditions on friendships (Crick &

Grotpeter, 1995). Early studies of relational aggression reported that it is a tactic

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predominantly employed by females, and that once this non-physical form of aggression

is taken into consideration, the gap in levels of aggression between males and females

diminishes significantly (Crick & Grotpeter, 1995) However, since the time of these early

reports, there have been inconsistent findings regarding which gender demonstrates

higher levels of relational aggression, with some studies reporting no differences in

relational aggression across genders, and even in some instances, reporting higher levels

among males. In a more recent meta-analytic review, Card et al. (2008) reported that

females are only slightly more relationally aggressive than males, and that this difference

remains stable across all ages, but the authors note that the magnitude of the sex

differences are essentially negligible. (For other reviews of gender differences in

relational aggression, see Archer & Coyne, 2005 or Merrell, Buchanan, & Tran, 2006).

One finding that does appear to be consistent within the literature across all age ranges is

that females generally rate higher on relationally aggressive measures than physical

aggression, while males exhibit the opposite pattern (Archer & Coyne, 2005).

Almost all studies examining both physical and relational aggression report a

significant positive correlation between the two; however, there is a tremendous amount

of variation in correlation strength across studies. In the aforementioned meta-analysis,

Card et al. reported that across 97 studies the range of correlations spanned from .07 to

1.0. They calculated an average correlation of .76, but found that the method in which the

aggressive measures were assessed as well as the sex of the participants both significantly

moderated the magnitude of reported correlations, with lower correlations among studies

employing observer reports and female samples. While there seems to be sufficient

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evidence of a significantly relationship between relational aggression and physical

aggression, factor analytic studies maintain that they should be considered distinct

constructs (Crick & Grotpeter, 1995; Vaillancourt et al., 2003, Burt & Donnellan, 2009,

Tackett et al., 2013). Evidence of their association and their distinctiveness can be

observed in their relationships to other constructs. Like physical aggression, relational

aggression has been linked to peer rejection, negative friendship quality, callous-

unemotional personality traits, conduct problems, and delinquency (Crick et al., 1997;

Kokkinos, Voulgaridou, & Markos, 2016; Crick, Ostrov, & Werner, 2006; Card et al.,

2008). However, unlike physical aggression, relational aggression has a moderately

strong relationship with internalizing, and perhaps surprisingly, a positive relationship

with prosocial behavior (Card et al., 2008; Werner & Crick, 1999).

Several studies have sought to identify etiological bases for relational aggression,

many of which focus on social factors, such as family, peer, and school environmental

influences (e.g., Ostrov, Crick, & Stauffacher, 2006; Casas et al., 2006; Nelson & Crick,

2002). Another approach is use genetically informative samples to perform biometric

analyses which are able to estimate the extent to which variation phenotypes are

influenced by additive and dominant genetics (A or D, respectively), shared

environmental influences (C), and non-shared environmental influences (E). Only three

studies have used this approach to examine the extent to which these factors contribute to

individual differences in relational aggression, and their results are somewhat

inconsistent. In a 2005 study of 234 6-year-old twin pairs, Brendgen and colleagues

reported only modest heritability and shared environmental influences on relational

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aggression (.20-.23 each for both teacher reports and peer nominations), with the majority

of phenotypic variance being attributed to the non-shared environment. A follow-up

study by Brendgen et al. (2008) using a larger sample of 406 pairs of like-sex 7-year-old

twins involved in the same longitudinal study from their 2005 report, found no significant

shared environmental influences for relational aggression, and reported an increased

heritability estimate of 42.9%. In the 2005 study, the AE and CE models for relational

aggression provided equal fits, but an improved fit was obtained when A and C were

constrained to be equal in an ACE model. Despite containing an overlap of participants

between the two studies, it is likely that the larger sample employed in the 2008 study

allowed a more precise differentiation between the AE and CE models, showing a

preference for a solution that only contained additive genetic and non-shared

environmental effects. A separate research group also examined the genetic and

environmental influences on relational aggression using a sample of 1981 twin pairs who

ranged in age from 6 to 19 years old (Tackett et al., 2009). In this study, Tackett and

colleagues reported that the best fitting model did not include shared environmental

influences, and that additive genetics accounted for roughly half of the phenotypic

variation in relational aggression. (There is also a 2009 study by Lighart et al. that reports

a heritability of .66 for relational aggression, however through the description of the

items used to measure ‘relational aggression’ it is apparent that the construct at hand is

actually a ‘rule-breaking’ factor rather than aggressive acts aimed at harming reputations

and relationships.) The Brendgen and Tackett studies suggest that relational aggression is

modestly to moderately heritable, though there is no complete consensus as to whether

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the shared environment contributes to similarity in relational aggression. The

discrepancies in variance estimates are likely due, at least in part, to the differences in

sample sizes across studies. Only the 2005 study by Brendgen and colleagues reported

significant shared environmental influences, and that study employed a significantly

smaller sample than the same research group’s 2008 study or than the Tackett et al. study

(234 twin pairs, compared to 406 and 1981, respectively). However, it is also possible

that these discrepancies are a reflection of other variations in the research designs, such

as the ages of the participants or the method in which the data were collected. For

example, both of the Brendgen et al. studies examined relational aggression via peer

nominations and teacher reports among elementary school aged children, while Tackett

and colleagues used structured interviews with the twins, whose ages spanned from

childhood through late adolescence.

There is support in the literature for the inclusion of relational aggression within

the externalizing spectrum (Tackett et al., 2013; Burt et al., 2012; Prinstein, Boergers, &

Vernberg, 2001), and indeed, several studies are beginning to include relational

aggression in their attempts to explore the externalizing spectrum (e.g., Lahey et al.,

2004; Krueger et al., 2007), including genetically informative designs (Baker et al.,

2007). However, no published studies to date have attempted to specifically examine the

etiological commonalities between relational aggression and a broader externalizing

domain. The two previously mentioned studies of 6- and then 7-year-old twins by

Brendgen and colleagues did examine the common genetic and environmental

contributions between physical and relational aggression. For their analyses of 6 years-

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olds, the authors report that 62% of genetic influences and 9% of the non-shared

environmental influences are shared between the two forms of aggression when using

teacher ratings. Among peer nominations, the shared genetic influences climb to 100%,

while non-shared environmental influences drop to zero. When they reexamined the

twins at age 7, a combined teacher rating and peer nomination score suggested 90%

genetic overlap between latent genetic factors contributing to physical aggression and

relational aggression, whereas the latent non-shared environmental factors shared around

16%.

In addition to the indication that physical and relational aggression share common

etiological factors, there is also strong evidence that there is a non-trivial genetic overlap

between the Aggression and Rule-Breaking factors of antisocial behavior and

externalizing (Niv et al., 2013; Bartels et al., 2003; Burt, 2013). This suggests the

potential for a shared etiology between relational aggression and rule-breaking behaviors.

To further support this possibility, in a study of 1,087 6 to18-year-olds, Tackett et al.

(2013) found that the best-fitting bifactor model of antisocial behavior was one that

included Rule-Breaking, Aggression, and Relational Aggression as separate factors

loading on a general Antisocial Behavior factor. They reported moderately strong

correlations between relational aggression and both aggression and rule-breaking, and

suggested that relational aggression may not be just a component of aggression, but rather

a unique subfactor of antisocial behavior. Taken in conjunction, these findings highlight

the importance of expanding the focus of studies of relational aggression to examine how

it fits into the broad domain of externalizing.

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The present study is an attempt to do exactly that. To the authors’ knowledge, this

is the first study that seeks to measure the extent to which relational aggression shares

genetic and environmental influences with other externalizing-related behaviors.

Additionally, it is the first genetically informative study to specifically examine relational

aggression during mid-adolescence, which will provide insight into how genetic and

environmental influences may shift from childhood into adolescence.

Method

Sample

The sample was drawn from 499 like-sex twin pairs involved in the Enrichment

Study with the Minnesota Center for Twin and Family Research (MCTFR). A subset of

the participants for this sample (roughly 48%) were screened and selected for inclusion

on the basis of being at an elevated risk for externalizing psychopathology at a young

age. (For a full discussion of the recruitment of this sample, see Keyes et al., 2009.) 52%

of the 499 twin pairs are female; 303 pairs are monozygotic (MZ) while the remaining

196 are dizygotic (DZ). Measures for this study were taken at the sample’s first follow-up

assessment when participants were an average age of 15.1 years old (standard deviation =

.55). Actual ages ranged from 13.6 to 17.0 years old. Means and standard deviations of

ages did not significantly differ between male and female participants: Males = 15.0

years old (sd = .51 years); Females = 15.1 years old (sd = .59 years).

Measures

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In addition to relational aggression, the measures included in analyses were

specifically selected to reflect the aggression and rule-breaking components of

externalizing.

Children’s Social Behavioral Scale – Self Report (CSBS-S). Adapted from

Crick & Grotpeter’s (1995) original teacher and peer rating scales, the CSBS-S is a self-

report measure of prosocial behavior, relational aggression, and physical aggression. Five

items were used to measure each of the constructs, though only the relational aggression

and physical aggression measures were included in the current analyses. The CSBS-S

asks participants to indicate how often they engage in certain behaviors on a five point

Likert scale, with response options ranging from 1 (“Never”) to 5 (“All the time”). All

items specifically are geared towards participants’ interactions with other students in their

schools. Relational aggression questions address participants engagement in exclusionary

or gossiping behavior, such as “How often did you try to get even with another student by

excluding him/her from your group of friends?” or “How often did you spread rumors or

gossip about another student to make others not like him/her anymore?” Physical

aggression questions addressed aspects of intimidation, threats of violence, and violent

actions, such as “How often did you hit another student?” or “How often did you threaten

to beat up another student if he/she didn’t do what you wanted him/her to do?” Scores for

both measures were calculating by totaling responses to each item, and each measure had

acceptable internal consistency (Cronbach’s alphas of .76 and .79, respectively).

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Delinquent Behavior Inventory (DBI). A 21-item abbreviated form of the DBI

(Gibson, 1967) measured the extent to which participants had engaged in various

delinquent acts, such as stealing, trespassing, or destroying property. Participants were

asked to indicate whether they had or had not engaged in each behavior, and a total score

was calculated by counting the number of acts the participant endorsed. Thus, a score of

21 indicates that the participant had engaged in every delinquent act listed at least once,

whereas a score of 0 indicates that the participant had not engaged in any of the

delinquent acts ever. The abbreviated DBI had a good internal consistency reliability of

.85.

Multidimensional Personality Questionnaire (MPQ) Aggression Scale.

Aggression was also measured as a personality trait using the MPQ Aggression scale,

which asks questions about retaliatory behavior and physical aggression. As described by

Tellegen and Waller (2008), it represents “the tendency to be involved in adversarial

interpersonal transactions as victimizer,” though the questions focus on verbal and

physical aggression, and none of the items address relational aggression. This scale of the

MPQ showed a good internal consistency measure of .78.

Opinions and Attitudes Questionnaire (OAQ). While the previous measures

attempted to measure the extent to which participants engaged in delinquent or aggressive

acts, the Opinions and Attitudes Questionnaire is aimed at measuring participants’ views

about how acceptable it is to engage in these types of acts. This 40-item inventory

includes scales on Antisocial Attitudes, Aggressive Attitudes, Prosocial Attitudes,

Popularity, and Family, though only the first two were included in the present analyses.

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The questions on the inventory offer hypothetical situations or statements regarding

attitudes about an action or interaction and ask participants to indicate whether they agree

a lot, agree a little, disagree a little, or disagree a lot with each statement. For example,

two of the eight items on the Antisocial Attitudes scale read, “I’d rather tell my parents a

lie than admit I had done something that would make them angry,” or “It’s okay for

someone my age to try a cigarette now and then.” The Aggression Attitudes scale is also

composed of eight questions including, “If a person challenges you, you have to be ready

to fight back,” and “If another kid cut in front of me in line, I’d probably push him or her

out of the way.” Again, rather than having to report on actual behavior, the participant is

asked to endorse how acceptable they view it, even if they have never engaged in such a

behavior. The item responses were coded 1 to 4, with 4 corresponding with the Agree a

lot response options. Item scores for each measure were summed to create a total score.

Both measures taken from the Opinions and Attitudes Questionnaire had good internal

consistencies, each equaling .85.

Substance Use. Substance use and abuse is another status violation element

associated with the rule-breaking component of externalizing (Krueger et al., 2002).

Because the participants are at such a young age, the number who have reached a clinical

level of substance use dependence is extremely low, thus a measure of how many

substances had ever been tried by the time of the assessment was used for analyses.

Participants were asked to indicate whether or not they had ever used any substances

from a list of ten categories of illicit substances, such as marijuana, cocaine, barbiturates,

or tranquilizers. While non-illicit substances, such as tobacco and alcohol also have

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strong relations to externalizing, they were not included in the present analyses. The

number of drugs endorsed was summed to create a total score. As expected, the internal

consistency of the number of substances used was particularly low (∝ = .35). This is

likely due to two factors: first, due to the young age of the sample and the sensitivity of

the subject matter, very few participants endorsed the use of any substance. In fact, fewer

than 10% reported that they had ever tried any of the illicit substances from the list.

Second, alpha is interpretable if all items are measures of the same latent factor. While all

items on this measure are illicit drugs, there is likely a strong differentiation in the eyes of

the participants between a substance that may be considered “softer,” such as marijuana

and another “harder” substance, such as methamphetamine. This is supported by the fact

that 82% of the participants who reported using any substance had only tried marijuana,

while only the remaining 18% of participants who reported use had tried substances other

than marijuana. Despite this shortcoming, we still view this as a beneficial measure of

externalizing, as it identifies the subset of participants who would be willing to

participate in such a risky behavior at a young age.

Results

Table 1 presents descriptive statistics for each measure. Males scored

significantly higher than females on all physical aggression scales (CSBS-S Physical

Aggression, OAQ Aggression Attitudes, and MPQ Aggression) as well as on the DBI.

There were no significant gender differences observed for CSBS-S Relational

Aggression, OAQ Antisocial Attitudes, or for number of drugs ever tried.

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Due to the nature of the topic of study, all of the collected measures were

positively skewed, with the exception of the MPQ Aggression scale. To account for this,

all skewed measures were log transformed prior to all other analyses reported here.

Additionally, to account for linear and non-linear gender differences in mean scores, male

and female scores were standardized separately for each measure. Correlations of the

seven gender-corrected measures can be found in Table 2. The magnitude of correlations

range from .26 to .67, with the strongest correlations found between measures of similar

constructs (i.e., alternative measures of aggression or rule-breaking). Elevated

correlations were also observed among measures that were collected within the same

inventory, such as the Aggression Attitudes and Antisocial Attitude scales from the

Opinions and Attitudes Questionnaire, as well as between the Relational Aggression and

Physical Aggression scales of the CSBS-S.

A hierarchical cluster analysis was performed using the ICLUST package in R to

evaluate whether the aggression and rule-breaking measures followed their anticipated

associations. This method uses alpha (α), a measure of the mean of all split-half

reliabilities, and coefficient beta (β), an estimate of the worst split-half reliability, to join

clusters together. Clusters will join together stepwise until the measures of internal

consistency cease to improve with clustering (Revelle, 1978). The measure of relational

aggression was omitted from the cluster analysis so that its relationship with factors

derived from the cluster solution could be analyzed separately. When no number of

clusters was specified in the model, the six included measures converged on one cluster

(Figure 1), with the next level of clustering producing the two expected factors of

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externalizing: Aggression (AGG) and Rule-Breaking (RB). The AGG cluster consisted of

CSBS-S Physcial Aggression, the MPQ Aggression scale, and the OAQ Aggression

Attitudes scale. The RB cluster consisted of the DBI, OAQ Antisocial Attitudes scale,

and the number of drugs ever tried. When a two cluster model was specified in ICLUST,

the cluster fit measure, which is a measure of the how well the model reproduces the

correlation matrix, is equal to that of the one cluster solution (cluster fit = .89). This

suggests that the AGG and RB clusters likely belong to a common externalizing factor,

but that they could also be considered two distinct clusters of that externalizing factor.

Confirmatory factor analyses (CFA) of the six aggression and rule-breaking

measures were carried out using the lavaan package in R to confirm the fit of the

hierarchical structure observed from the cluster analysis. Because the hierarchical

clustering model converged on one cluster when no number of clusters was specified,

both one- and two-factor CFAs were tested. In the one-factor models, all six measures

loaded on a single factor. In accordance with findings from the hierarchical cluster

analysis, in the two-factor models, the AGG factor consisted of CSBS-S, MPQ, and OAQ

measures of aggression, and the RB factor consisted of the DBI, the OAQ Antisocial

attitude scale, and the number of drugs ever used. The best fitting model was a two-factor

model that allowed residual correlations for the two measures taken from a common

inventory (OAQ Aggression and OAQ Antisocial). This model provided a better fit than

a one-factor model in which no residuals were allowed to correlate (chi-squared

difference test: χ2 difference = 210.17, degrees of freedom difference = 2, p < .001), a

one-factor model in which residuals from the two OAQ measures were allowed to

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correlate (χ2 difference = 209.22, degrees of freedom difference = 1, p < .001), and a two-

factor model in which no residuals were allowed to correlate (χ2 difference = 22.17,

degrees of freedom difference = 1, p < .001). Fit statistics for all models can be found in

Table 2. Within the best-fitting model, all measures held moderately high loadings on

their respective factors, with standardized loadings ranging from .65 to .84 (see Figure 2

for all standardized loadings). Additionally, a two-factor model provided a better fit than

a one-factor model, but within the two-factor model, the two factors (RB and AGG) were

highly correlated (.74). Taken together, this lends support to previous findings that RB

and AGG should be considered distinct factors, though they are likely both part of a

broader externalizing factor.

In order to determine the relationship between relational aggression and the AGG

and RB factors confirmed above, a three-factor CFA was conducted in which relational

aggression was set as its own factor (RAgg). Like the results from the previous CFA, the

best fitting model necessitated the allowance of residuals to correlate between the two

OAQ measures. Additionally, it allowed the CSBS-S Physical Aggression measure to

cross load on the RAgg factor to account for the common CSBS-S inventory used to

collect both measure. (It should be noted that with the relational aggression measure as

the only measure loading on the RAgg factor, there would be no residual variance with

which the CSBS-S Physical Aggression could correlate. Thus, rather than have residuals

correlate between the two CSBS-S measures, the best alternative was to allow the cross-

loading of the Physical Aggression measure on both AGG and RAgg.) The model that

accounted for common inventories was a significant improvement over a three-factor

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model in which no residuals were allowed to correlate (χ2 difference = 133.2, degrees of

freedom difference = 3, P < .001) and a three-factor model in which only the residuals

between the two OAQ measures were allowed to correlate (χ2 difference = 100.7, degrees

of freedom difference = 2 P < .001). As seen in Figure 3, in this model, we again see

moderate to high loadings of measures on their specified factors, with standardized

loadings ranging from .50 to .84 (with the exception of the relational aggression measure

on its own factor, which only slightly deviated from 1.00, due to the cross-loading of the

Physical Aggression measure). Additionally, RAgg moderately correlated with both

AGG and RB (.47 and .44, respectively), and it showed no obvious preference in its

relation to AGG and RB.

Biometric Analyses

Because not all participants had completed every measure, creating a number of

missing data points in the data set, composite scores for RB and AGG were computed by

taking the average of the standardized measures for each factor. Standardized relational

aggression scores remained alone to create the RAgg factor.

The genetically informative design of twin studies allows for the parsing out of

genetic and environmental influences on measured phenotypes. In these studies,

phenotypic similarity can be attributed to additive genetics (A), and/or shared

environmental influences(C), and phenotypic dissimilarity can be attributed to non-shared

environmental influences (E). Monozygotic (MZ) twins share all of their genetic

material, while dizygotic (DZ) twins only share half of their genes on average. Thus, if

MZ twin pairs are systematically more similar on a trait than DZ twin pairs, it provides

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evidence that the increased similarity is, at least in part, a function of increased genetic

similarity. Conversely, if DZ twin correlations approach the magnitude of MZ twins, it

provides evidence of shared environmental influences. By extending this logic, it is also

possible to model the extent to which genetic and environmental influences are shared

between multiple traits, such is the case with an independent pathway model. When

multiple phenotypes are fit in an independent pathway model, the phenotypic variance

and covariance can be partition into common genetic and environmental components that

are shared among the phenotypes, as well as residual genetic and environmental

components that are specific to each individual phenotype.

MZ and DZ twin pair intraclass correlations for AGG, RB, and RAgg can be

found in Table 4. For all three factors, MZ twin pairs are more similar to each other than

DZ twin pairs, suggesting genetic influences on each of them. However, for RB, DZ twin

correlations are significantly more than half MZ twin correlations suggesting the shared

environment likely influences individual differences in rule-breaking behavior.

All biometric models were fit in R using OpenMx (Neale et al., 2015). An

independent pathway model was fit to the AGG, RB, and RAgg factors. When a genetic

model is comprised of three variables, such as in the present analyses, the number of

genetic and environmental correlations from which estimates are derived is equal to the

number of variables in the model. Because of this, a full Cholesky decomposition and

independent pathway model provided equivalent fits and variance estimates for this data.

However, one of the benefits to using an independent pathway model is that it presumes

no order to the variables within the model, whereas a Cholesky decomposition will

17

prioritize variables based on their order. For the purposes of the present study, the

independent pathway model allows more easily interpretable information about the

genetic and environmental influences that are shared among AGG, RB, and RAgg, as

well as the genetic and environmental influences that are specific to each of them.

An alternative to the independent pathway model is the common pathway model.

Rather than assuming that genetic and environmental influences affect the included

phenotypes directly, the common pathway model assumes that genetic and environmental

effects influence a latent liability that contributes to individual differences in the included

phenotypes. The independent pathway model provided a better fit than a common

pathway model, so further sub-models were derived from a full independent pathway

model. (For fit statistics for all models, see Table 5. Model fits were compared using

likelihood ratio chi-square tests as well as Akaike’s information criterion; AIC.)

In the full independent pathway model, there were several path estimates that

were very small or equal to zero, so all such pathways were tested. RB was the only

factor showing any influence from the shared environment, so in turn, the common C

factor, and then the specific C paths for AGG and RAgg were constrained to zero. Each

of these sub-models showed significant improvement of fit with each constraint. The sub-

model with all C pathways constrained to zero except for the specific pathway to RB was

also a better fit than an AE independent pathway model in which all C pathways were

constrained to 0. An additional sub-model was run that constrained the specific genetic

effects on RB to zero. This sub-model also improved the fit. Last, due to small parameter

estimates for the common non-shared environmental influences on RB and AGG, two

18

sub-models were run in turn that constrained each pathway to zero; however, both had a

worse fit than when the pathways were not constrained to zero. Thus, the best fitting

model was one in which all factors were influenced by common additive genetic effects

and non-shared environmental effects, and in which AGG and RAgg were also influence

by specific additive genetic and non-shared environmental effects, and RB was also

influenced by specific shared and non-shared environmental effects (see Figure 4 for a

visual of a full independent pathway model as well as a visual of the best-fitting model

for the current analyses). Standardized path coefficients and variance estimates from this

model can be found in Table 6.

The additive genetic correlations for each pair of phenotypes were .80 (95% CI =

.69-.89) between AGG and RB, .66 (95% CI = .52-.82) between AGG and RAgg, and .83

(95% CI = .69-1.00) between RB and RAgg. The non-shared environmental correlations

for each pair of phenotypes were .28 (95% CI = .18-.39) between AGG and RB, .31 (95%

CI = .21-.41) between AGG and RAgg, and .10 (95% CI = .05-.22) between RB and

RAgg.

Discussion

In the present sample, there was no significant difference in mean-level relational

aggression scores between males and females, though males consistently scored

significantly higher than females on measures of physical aggression. A hierarchical

cluster analysis and subsequent confirmatory factor analysis confirmed that measures of

aggression and rule-breaking split into two related, yet distinct, subfactors of a broader

19

externalizing domain. Within the confirmatory factor analysis, the correlations between

the relational aggression factor and aggression and rule-breaking factors were nearly

equal, suggesting that relational aggression is likely not a subcomponent of aggression,

but rather its own distinct factor within externalizing.

The primary goal of this study was to identify the etiological commonalities

between relational aggression and other externalizing behaviors during adolescence. In

congruence with the literature, factors of aggression, rule-breaking, and relational

aggression were all moderately heritable (a2 = .49, .61, and .31, respectively). There were

significant genetic correlations between all three factors, and the majority of the

heritability of each factor could be attributed to additive genetic effects that were

common to the three phenotypes (64% for aggression, 100% for rule-breaking, and 71%

for relational aggression). However, aggression and relational aggression had additional

additive genetic influences that were specific to each of them. The remaining variance of

aggression and relational aggression (e2 = .51 and .69, respectively), and a significant

amount of the variance in rule-breaking (e2 = .24), was accounted for by non-shared

environmental influences. Most of the non-shared environmental influence on aggression

(86%) came from the factor common to all three phenotypes. Conversely, a majority of

the non-shared environmental influences on rule-breaking and relational aggression (92%

and 88%, respectively) were specific to each of them. Rule-breaking was the only factor

in the present study that was significantly influenced by the shared environment (c2 =

.15), a finding that is consistent with other studies of rule-breaking and aggression (e.g.,

Bartels et al., 2003; Tackett et al., 2005). The lack of significant shared environmental

20

effects on relational aggression provide further evidence that it is unlikely that

environments shared by family members contribute to their similarity in relationally

aggressive behaviors.

Taken together, these findings provide etiological support for Tackett et al.’s

(2013) notion that relational aggression not only belongs within the externalizing

spectrum, but that it is likely a distinct subfactor of externalizing, separate from, but also

related to, both aggression and rule-breaking. The current results suggest that, during

adolescence, the same genetic liability that contributes to individual differences in

physically aggressive and rule-breaking behaviors also influences individual differences

in relational aggression, but that the extent to which these relationally aggressive

behaviors are expressed also is in part due to a distinct genetic susceptibility as well as

idiosyncratic environmental circumstances that are unique to each individual. In other

words, certain individuals may inherit a stronger genetic propensity to act out, but this

acting out behavior may only come in the form of relational aggression with the addition

of specific genetic factors and under circumstances that make this type of behavior more

adaptive or ideal for the given individual.

The current study relied solely on self-report measures. Due to the nature of

inquiry, participants may be hesitant to admit the full extent to which they participated in

illegal or socially undesirable behaviors, such as substance use or gossiping.

Additionally, they may be naive to the extent to which they engage in the behaviors. In

younger samples, it is common to see externalizing behaviors and relationally aggressive

behaviors measured through parent, teacher, and/or peer-reports, and it has been shown

21

that the informant method used can significantly affect the strength of correlations across

traits (e.g., Card et al., 2008) or twin pair correlations and heritability estimates (e.g.,

Bartels et al., 2003). Thus, it would be ideal for future studies on the present topic to

employ multiple informants to determine whether there are consistencies in findings.

Relational aggression, aggression, and rule-breaking behaviors have their own

unique developmental trajectories (Burt, 2009; Crick, Ostrov, & Werner, 2006). Thus, it

is unknown whether the current findings would be replicated in significantly older or

younger samples, or whether the etiological relationship between these factors would

change across development. While the current study may portray a snapshot of the

etiological relationship between relational aggression, aggression, and rule-breaking

during adolescents, it is possible that this may not be accurate for significantly younger or

older samples.

Additionally, externalizing literature suggests a significant link between alcohol

and nicotine use with illicit drug use and with externalizing psychopathology. The current

study only included one measure illicit drug use, though this facet of externalizing may

be improved by coming up with a composite score including alcohol, tobacco, and illicit

drug use, including the frequency at which they are used.

22

Table 1 Descriptive Statistics for Included Measures

N N items

Range of scores

Alpha

Raw mean (sd) Males

Raw mean (sd) Females

Standardized mean gender differences (males -females)

CSBS-S Relational Aggression

820 5 5-

25 0.76 6.9 (2.1)

6.6 (2.0) .16

CSBS-S Physical Aggression

822 5 5-

25 0.79 7.1 (2.3)

6.0 (1.8) .50

Delinquent Behavior Inventory

917 21 0-

21 0.85 3.0 (3.3)

2.4 (3.0) .20

Opinions and Attitudes Antisocial Scale

917 8 8-

32 0.85 13.6 (4.6)

13.5 (5.1) .02

Opinions and Attitudes Aggression Scale

918 8 8-

32 0.85 16.2 (4.6)

13.2 (4.3) .70

MPQ Aggression Scale

909 18 18-

72 .78 43.2 (9.1)

35.5 (9.7) .80

Number of Drugs Ever Tried

790 10 0-

10 .35 .73 (1.0)

.82 (1.3) -.08

From left to right: N = number of individuals who completed the measure; N items = number of items included in the measure; Range of scores = range of possible scores an individual could receive on the measure; Alpha = Cronbach’s Alpha; raw scores for males and females (and standard deviations); standardized mean differences between genders, calculated by subtracting female average standardized scores from male average standardized scores, thus a positive value indicates a higher male average and a negative value indicates a higher female average.

23

Table 2 Pearson r Correlations of all measures

1 2 3 4 5 6 1. CSBS-S Relational Aggression 2. CSBS-S Physical Aggression .57 3. DBI .37 .46 4. OAQ Antisocial Scale .36 .39 .67 5. OAQ Aggression Scale .37 .53 .55 .60 6. MPQ Aggression Scale .37 .50 .42 .47 .64 7. Number of drugs ever tried .26 .34 .59 .61 .37 .33

All measures corrected for gender. All correlations are significant (p < .001)

24

Table 3 Fit Statistics for CFA Models

Model AIC BIC RMSEA (90% CI) Models including only the six measures of RB and AGG One-factor model (EXT) with no

residual correlations -6595.98 -6540.75 .19 (.17-.21)

One-factor model (EXT) allowing residuals to correlate between common inventories

-6954.93 -6535.09 .20 (.18-.23)

Two-factor model (AGG & RB) with no residual correlations

-6781.99 -6722.15 .10 (.08-.12)

Two-factor model (AGG & RB) allowing residuals to correlate between OAQ measures

-6802.15 -6737.15 .07 (.04-.09)

Models including six measures of RB and AGG as well as RAgg Three-factor model (AGG, RB, &

RAgg) with no residual correlations -8353.65 -8280.03 .14(.12-.16)

Three-factor model (AGG, RB, & RAgg) allowing residuals to correlate between OAQ measures

-8384.78 -8306.56 .13 (.11-.15)

Three-factor model (AGG, RB, & RAgg) allowing residuals to correlate between OAQ measures and the cross-loading of CSBS-S Physical Aggression on the RAgg factor

-8480.85 -8393.43 .07 (.05-.09)

AIC = Akaike information criterion; BIC = Bayesian information criterion; RMSEA = Root Mean Square Error of Approximation EXT = Externalizing Factor; AGG = Aggression Factor; RB = Rule-Breaking Factor; RAgg = Relational Aggression Factor; OAQ = Opinions and Attitudes Questionnaire

25

Table 4 Intraclass Correlations for Monozygotic and Dizygotic Twin Pairs

Total MZ Pairs rMZ Total DZ Pairs rDZ AGG 279

.47

178 .23

RB 279 .72

178 .52

RAgg 245 .27

155 .14

Total MZ/DZ Pairs = total number of complete monozygotic/dizygotic twin pairs. rMZ = intraclass correlation between monozygotic twin pairs; rDZ = intraclass correlations between dizygotic twin pairs. AGG = Composite scores for Aggression; RB = Composite scores for Rule-Breaking; RAgg = Relational Aggression scores. All correlations are statistically significant (p < 001).

26

Table 5 Biometric Model Fit Statistics

Likelihood ratio chi-squared test*

Model -2LL df Δ -2LL Δ df p AIC Independent (IP) ACE Model

8793.94 2641 36.89 33 .294 3511.61

Common Pathway ACE model

8811.14 2645 54.43 37 .032 3521.14

IP ACE model with Cc constrained to 0

8794.92 2644 38.20 36 .370 3506.92

IP ACE model with all Cc constrained to 0 and with CS pathways for AGG and RAgg constrained to 0

8794.92 2646 38.20 38 .460 3502.92

IP AE model (no C) 8797.95 2647 41.23 39 .373 3503.95 IP ACE model with CC, CS pathways to AGG and RAgg, and As pathway to RB constrained to 0

8794.92 2647 38.29 39 .506 3500.92

IP ACE model with CC, CS pathways to AGG and RAgg, As pathway to RB, and Ec path to RB constrained to

8821.90 2648 65.18 40 .007 3525.90

IP ACE model with CC, CS pathways to AGG and RAgg, As pathway to RB, and Ec path to AGG constrained to

8845.71 2648 88.99 40 .00 3549.71

* All models compared against fully saturated model. -2LL = -2 Log Likelihood of model; df = degrees of freedom for model; Δ -2LL difference in -2 Log Likelihood between model and a fully unsaturated model; Δ df = difference in degrees of freedom between model and a fully unsaturated model; p = p-value for likelihood ratio chi-squared test; AIC = Akaike information criterion; A = additive genetics; C = shared environmental influences; E = non-shared environmental influences; Cc = shared environmental influences common to all factors; Ec = non-shared environmental influences common to all factors; AS = additive genetic influences specific to each factor Cs = shared environmental influences specific to each factor. Bold indicates the best fitting model according to Akaike’s information criterion.

27

Table 6 Standardized path coefficients (with 95% confidence intervals) and total variance estimates (with 95% confidence intervals) for best-fitting independent pathway model

Standardized path coefficients (and 95% confidence intervals) for common additive genetic effects (aC), additive genetic effects specific to each phenotype (aS), shared environmental effects specific to each phenotype (cS), common non-shared environmental effects (eC), and non-shared environmental effects specific to each phenotype (eS). a2 = proportion of phenotypic variance attributed to variance in additive genetics. c2 = proportion of phenotypic variance attributed to variance in shared environment. e2 = proportion of phenotypic variance attributed to variance in non-shared environment.

Factor aC aS Total a2 cS Total c2 eC eS Total e2

AGG .56 (.47-.64)

.42 (.37-.51)

.49 (.40-.57)

- - .66 (.43-.77)

.27 (.00-.56)

.51 (.43-.60)

RB .78 (.70-.86)

- .61 (.49-.74)

.38 (.17-.50)

.15 (.03-.25)

.15 (.09-.23)

.47 (.42-.52)

.24 (.20-.29)

RAgg .47 (.37-.55)

.31 (.05-.43)

.31 (.20-.41)

- - .28 (.17-.45)

.78 (.70-.85)

.69 (.59-.80)

28

Table 7 Genetic and Environmental Correlations (with 95% Confidence Intervals)

Additive Genetic (A) Correlations

Non-Shared Environmental (E) Correlations

AGG RB AGG RB RB .80 (.69-.89) .28 (.18-.39) RAgg .66 (.52-.82) .83 (.69-1.0) .31 (.21-.41) .10 (.05-.22)

Estimated additive genetic and non-shared environmental effects shared between each pair of traits.

29

Figure 1 Hierarchical Cluster Analysis of Aggression and Rule-Breaking Measures

In the ICLUST package combines clusters until measures of internal consistency cease to improve. Alpha (α) is a measure of the mean of all split-half reliabilities. Coefficient beta (β) is an estimate of the worst split-half reliability, to join clusters together. Cluster loadings for each cluster are also indicated in the figure.

30

Figure 2 Visualization and Standardized Loadings for CFA of Aggression and Rule-Breaking Factors

The best fitting model allowed residuals from both OAQ measures to correlate.

31

Figure 3 Visualization and Standardized Loadings for CFA of Aggression, Rule-Breaking, and Relational Aggression Factors.

The best fitting model allowed residuals from OAQ measures to correlate, as well as a cross loading of the Physical Aggression measure to cross load on the RAgg factor to account for the common CSBS-S inventory used for both measures.

32

Figure 4: (a) Visual Representation of a Full Independent Pathway Model

(b) Visual Representation of Best-Fitting Independent Pathway Model for Current Analyses

Ac = additive genetic influences common to all factors; Cc = shared environmental influences common to all factors; Ec = non-shared environmental influences common to all factors; AS = additive genetic influences specific to each factor Cs = shared environmental influences specific to each factor; Es = non-shared environmental influences specific to each factor.

33

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