School bullying and social ne wo ks
Mas e hesis
Mónica Vasco Ruiz
Supe iso : Ja omí Ko ářík
Mas e in Economics: Empi ical Applica ions and Policies
2021/22
Uni e si y o he Basque Coun y UPV/EHU
School Bullying and Social Ne wo ks.
M´onica Vasco Ruiz
July 29, 2022
Abs ac
Al hough school bullying has eno mous heal h, social, and economic
consequences ha las h oughou he en i e human li e, mos bullying-
p e en ion p og ams a e ine ec i e pa ially because de ec ing bullies and
hei ic ims is challenging. This s udy p oposes o employ social ne wo ks
o iden i y he ic ims o bullying. To ha aim, we elici iendship and
enmi y ne wo ks and documen who su e s bullying in se e al seconda y
schools in sou he n Spain. We show ha bo h iendship- and enmi y-
ne wo k measu es a e ele an and complemen a y p edic o s o ic imiza-
ion, independen o classic non-ne wo k cha ac e is ics employed in he
li e a u e. Howe e , how indi idual posi ioning and global ea u es o he
social o ganiza ion de e mine who su e s bullying di e s ac oss male and
emale adolescen s. We discuss ou esul s in ela ion o exis ing heo ies
o bullying ic imiza ion in psychology and sociology.
Keywo ds: Agg ession, social ne wo ks, school bullying, ic imiza ion, iendship,
enmi y, gende .
1 In oduc ion
Human beha io mus be unde s ood in e ms o social con ex s and g oups o
which people belong (Mo eno, 1934). No su p isingly, social condi ions in child-
hood and adolescence shape human de elopmen . Indeed, he e is la ge e idence
ha child en wi h posi i e ela ionships wi h hei pee s ha e highe le els o emo-
ional well-being, pa icipa ion, and academic achie emen (Wen zel, 2017). In
con as , nega i e ela ionships in childhood ha e ad e se e ec s on many ace s o
one’s li e (Fa ing on, 1989; Pee s e al., 2007; Po i niche and Enache, 2014). Fu -
he mo e, such impac on childhood and adolescence pee ela ionships inc eases
o e ime (Kaess, 2018).
One o he mos se ious socializa ion p oblems in schools is bullying (Olweus,
2013; Ju onen and G aham, 2014). School bullying is de ined as epea ed and dis-
up i e beha io whe e one o se e al classma es in en ionally annoy o hu o he
1
classma es, bo h physically and emo ionally. I can ake a ious o ms, includ-
ing physical assaul , sho es, easing, making h ea s, name-calling, o humilia ion
(C¸alı¸skan e al., 2019).
School bullying is a pe sis en wo ldwide phenomenon (UNICEF, 2018; WHO,
2013) and i s consequences ex end o all domains o bullies’ and ic ims’ li e and
span h oughou he whole li e. Mo e di ec ly, bullying co ela es o dep ession,
suicidal and c iminal endencies, d ug abuse and iolence in bo h childhood and
adul hood (Be ns ein and Wa son, 1997). Howe e , bullying also has less di ec
consequences. Indi iduals in ol ed in bullying ha e lowe educa ion and inancial
skills (Zych e al., 2015) and highe unemploymen a es, lowe weal h and income
la e in li e (e.g. Hong and Espelage (2012); Takizawa e al. (2014); Wolke and
Le eya (2015); B imblecombe e al. (2018); Ca ell e al. (2018); Sa zosa and
U z´ua (2021)).
Al hough bullying is an unde s udied opic in economics,1 his phenomenon
and i s consequences ha e s imula ed la ge li e a u e in o he ields. They a e
o g ea conce n among policymake s (O ega Ruiz e al., 2013; Bald y and Fa -
ing on, 2007; Huang e al., 2019; Olweus and Limbe , 2010; Menesini and Salmi-
alli, 2017; Rigby, 2002).2Mo i a ed by he li e a u e, a conside able numbe o
bullying-p e en ion p og ams a ge ing g oup-le el beha io ha e been designed
and implemen ed all a ound he Wo ld (see Salmi alli (2010) o a e iew). How-
e e , he me a-analy ic s udies has concluded ha hese p og ams a e ine ec i e
(Smi h e al., 2004; Me ell e al., 2008; T o i and Fa ing on, 2011; Ga ney e al.,
2019; Fe guson e al., 2007). The disappoin ing esul s o he exis ing bullying
p e en ion p og ams gene a e se e al ques ions.
In his s udy, we answe some o hese ques ions. In pa icula , we i s
ask whe he ic imiza ion is ela ed mo e o posi i e o nega i e ela ionships
o whe he posi i e and nega i e ela ionships a e wo independen p edic o s o
bullying. Second, is bullying a g oup-wide phenomenon indeed, as sugges ed by
he li e a u e in sociology, o is i only ela ed o local ne wo ks, wi hou any e-
la ion o mo e dis an ne wo k neighbo hoods? Las ly, since bullying is a gende -
speci ic phenomenon (Maccoby and Jacklin, 1980; Olweus, 1991; Ca bone-Lopez
e al., 2010; Sil a e al., 2013; Sen se e al., 2015), we pay pa icula a en ion o
whe he how social o ganiza ion ela es o ic imiza ion di e s ac oss gende s.
To answe hese ques ions, we exploi he ools o ne wo k heo y, linking
bullying ic imiza ion and he pa e ns o social in e ac ions. To hese aims, we
i s elici a la ge da ase on 3,035 s uden s in 11 high schools in Andalusia, he
mos popula ed egion in Spain. No ably, he da a con ain an eno mous amoun
o in o ma ion abou all he s uden s, hei classes, and schools, including he
iendship and enmi y ne wo ks and sel - and o he - epo ed bullying ic imiza ion
(see Sec ion 3 o de ails). In ou analysis, we explo e o wha ex en he iendship
1See e.g. B own and Taylo (2008) o Sa zosa and U z´ua (2021) o excep ions.
2S op bullying (www.s opbullying.go ) and Bea Bullying (www.coe.in /en/web/edc/bea -
bullying) a e examples o public p og ams documen ing and a ge ing bullying in he US and
Eu opean Union, espec i ely.
2
and/o enmi y ne wo k in o ma ion a di e en le els p edic he likelihood o
becoming a ic im o bullying.
Ou esul s indica e ha ic ims occupy pe iphe al posi ions in he class iend-
ship ne wo ks. Howe e , hey a e mo e cen al in he enmi y ne wo ks bo h lo-
cally using local measu es o cen ali y and globally using global measu es o one’s
cen ali y.3Mo eo e , bo h ypes o ela ionships a e independen p edic o s o
ic imiza ion. Ne wo k-wide cha ac e is ics o he class ne wo ks also play a ole
while explaining ic imiza ion, bu hei impac is quan i a i ely weake han ha
o indi idual posi ioning, con adic ing he classic app oaches o bullying p e en-
ion ha exclusi ely a ge g oups a he han indi iduals. Howe e , since bo h
le els ma e di e en ly, he exis ing p og ams should a ge bo h g oups and indi-
iduals. Mo eo e , he posi ioning o male and emale ic ims di e conside ably,
sugges ing ha he easons why each gende is ic imized a e di e en .
To he bes o ou knowledge, he only pape ha ela es bullying ne wo ks is
Mou apa e al. (2004). They analyze a sample o p edominan ly La ino and Asian
schools in he U.S. and co ela e bullying wi h ce ain ea u es o s uden s’ local
ne wo ks, such as he numbe o iends and he likelihood o people ha ing iends
engaged in bullying. They ind ha ic ims ecei e ewe iendship nomina ions
om o he s, bu his e ec only holds o women. As opposed o Mou apa e al.
(2004), ou sample is mo e ex ensi e and d ama ically mo e ep esen a i e o he
gene al school popula ion. In addi ion, we combine bo h iendship and enmi y
ne wo ks, and ou da a–pa icula ly he high numbe o independen ne wo ks
in ou sample–allow us o analyze he ole o (no only s uden s’ di ec ne wo k
neighbo hoods bu also) he en i e ne wo k a chi ec u e in he school. The e o e,
ou esul s la gely ex end hei wo k, p o ide a mo e gene al pic u e o he ole
o social o ganiza ion in bullying, and p o ide di e en policy ecommenda ions.
The emainde o he pape is s uc u ed as ollows. Sec ion 2 e iews he
li e a u e and p esen s ou esea ch hypo heses. In Sec ion 3, we desc ibe ou
me hodology and he da a. Sec ion 4 p esen s he esul s. Finally, he las sec ion
concludes.
2 Rela ed li e a u e and esea ch hypo heses
Ou s a ing hypo hesis is ha , since bullying is by de ini ion a social phe-
nomenon, he s uc u e o he social o ganiza ion in schools can s imula e o
mi iga e bullying. Howe e , he open ques ion is which pa icula ea u es o so-
cial o ganiza ion ma e and how. In his sec ion, we gene a e se e al esea ch
hypo heses based on he exis ing heo ies o bullying ic imiza ion in psychol-
ogy and sociology. To achie e hese aims, we ocus on analyzing he in e ac ion
pa e ns among pee s a school using ne wo k da a. Social ne wo k analysis is a
sui able app oach o s udying links be ween nodes, how hey a e connec ed by ex-
is ing iendship o enmi y, o hey a e isola ed due o lack o hese links (Bo ga i
3See Sec ion 3 o he di e en measu es employed in his s udy.
3
e al., 2018; Wasse man e al., 1994).
We i s discuss whe he bullying is a local o g oup-le el phenomenon. Al-
hough he li e a u e conside s di e en le els wi hin he socio-cul u al s uc u e
(Hinde and S e enson-Hinde, 1987), cu en ly, he dominan heo y in he li e -
a u e ha mo i a es mos o he in e en ions is ha bullying is a g oup-le el
phenomenon (O’connell e al., 1999; Oldenbu g e al., 2018; Lage spe z e al.,
1982; Su on and Smi h, 1999).
The e o e, i he g oup-le el no ms and o ganiza ion ma e , hen ne wo k he-
o y p edic s ha ne wo k-wide cha ac e is ics ( a he han indi idual posi ioning)
p edic he ex en o ic imiza ion. Hence, we hypo hesize he ollowing:
H1Global-wide ne wo k cha ac e is ics p edic he ex en o bullying
ic imiza ion.
Howe e , he li e a u e does no p o ide any speci ic heo y ega ding which
cha ac e is ics de e mine bullying and in which di ec ion. Hence, a he han
gene a ing ou speci ic hypo heses, we le he da a speak and explo e he na -
u al candida es pos ula ed by ne wo k heo y, such as measu es o in eg a ion,
connec i i y, and hie a chy (see Sec ion 3).
In con as o he cu en heo ies, he ea lie li e a u e has mos ly ocused
on iden i ying indi idual isk ac o s (Ju onen and G aham, 2001, 2014) and he
de e minan s o ic imiza ion (G aham, 2016; Olweus, 1997). Hence, we also co -
ela e ic imiza ion wi h indi idual posi ioning in iendship and enmi y ne wo ks.
As o iendship ne wo ks, Haynie e al. (2001) s a e ha ic ims exhibi lowe
sel -es eem, eel lonelie , and a e less happy a school han hei pee s. A he
same ime, i has also been shown ha con lic can be educed wi h he social
in luence o e e ing s uden s and ha iendships can p o ide p o ec ion agains
ic imiza ion (Paluck e al., 2016; Paluck and Shephe d, 2012). These claims
sugges ha ic ims should ha e ewe iends o , in ne wo k e minology, should
ha e lowe connec i i y and deg ee in he iendship ne wo ks. In con as o
hese claims, Mou apa e al. (2004) do no ind co ela ions be ween he numbe
o iends and ic imiza ion hough.
Ou second hypo hesis is:
H2Connec i i y/deg ee in he iendship ne wo ks is nega i ely ela ed o
ic imiza ion.
The ole o connec i i y (i.e. local cen ali y) no wi hs anding, he e a e nei-
he heo ies no empi ical e idence ega ding he ole o whe he he ic ims
would be less cen al globally. Since ou ne wo k app oach allows us o compu e
global cen ali y measu es (see Sec ion 3), we es whe he being globally cen al–
on op o ha ing many iends–plays a ole in ic imiza ion bu we p o ide no
esea ch hypo hesis in his espec .
4
As discussed abo e, nega i e in e ac ions migh also ma e . Mo eo e , since
bullying is a nega i e social phenomenon by de ini ion, enmi y in e ac ions migh ,
in ac , be mo e impo an p edic o s han iendships. I has been documen ed
ha nega i e pee a i udes and hos ile school en i onmen al ac o s can inc ease
he equency o bullying (Meye -Adams and Conne , 2008; Pelleg ini and Ba ini,
2000; To u a e al., 2009; Hong and Espelage, 2012; Rigby, 2005). The e o e, we
es whe he ha ing many enemies ( ha is, high local cen ali y in he enmi y
ne wo k) p edic bullying ic imiza ion, using he ollowing hypo hesis:
H3High connec i i y in enmi y ne wo ks p edic s bullying ic imiza ion.
Once again, we ha e no hypo hesis ega ding whe he less local measu es o
posi ioning in he enmi y ne wo ks ma e and how.
Finally, he e is ex ensi e e idence ha bullying is a gende -speci ic phe-
nomenon in de e minan s and o ms. Gi ls end o engage in mo e indi ec bul-
lying (such as gossiping) while boys a e mo e di ec (e.g., agg ession) (Fa ing on
and Bald y, 2010; Olweus, 1991; Schei haue e al., 2006; Bo g, 1999). Boys a e
mo e likely o be in ol ed in bullying han gi ls, al hough his e ec is less o-
bus ac oss s udies (Ma kkanen e al., 2021). In addi ion, almos all esul s in
Mou apa e al. (2004) a e gende -speci ic. The e o e, we hypo hesize ha :
H4Social ne wo k posi ioning and global s uc u e o he class iendship and
enmi y ne wo ks de e mine bullying ic imiza ion di e en ly ac oss
gende s.
Apa om he hypo heses s a ed abo e, we es o he issues ha a e no
suppo ed o discussed in he li e a u e bu which we ind o p ac ical ele ance.
Fo example, will he local posi ioning be mo e, equally, o less impo an han
he ne wo k-wide pa e ns? Is he ole o posi i e and nega i e ela ionships
complemen a y p edic o s o bullying, o do hey p o ide he same in o ma ion
abou bullying? These ques ions a e ele an because p ac ical applica ions o ou
esul s should po en ially elici he whole ne wo k a chi ec u es and bo h nega i e
and posi i e ela ionships. Tha would equi e da a collec ion and wo k ha is
mo e complex han elici ing and employing simple indi idual cha ac e is ics.
3 Da a and me hodology
The da a o his p ojec ha e been collec ed by he au ho s as a pa o he COM-
PHAS p ojec .4We collec ed a sample o schools in sou he n Spain, in which we
conduc ed an ex ensi e in-class su ey wi h 1s - 4 h g ade s uden s. The su ey
4The p ojec called Mapeo de Compe encias y Habilidades del Alumnado de Ense˜nanza Se-
cunda ia is managed by he Loyola Beha io al LAB (a beha io al economics esea ch cen e )
and he ETEA Founda ion a he Uni e sidad Loyola Andaluc´ıa. The p ojec was posi i ely
e alua ed by he E hics Commi ee o he Uni e sidad Loyola Andaluc´ıa.
5
was compu e ized using an online pla o m Sand (h ps://sand.kampal.com), de-
signed o he elici a ion o ne wo k (and o he ) da a. The su ey was conduc ed
be ween 2021 and 2022 in 11 seconda y schools in Andalusia, Spain. All s uden s
in he sampled schools we e con ac ed and in i ed o ca y ou he su ey. Ou
o he 3,035 s uden s o icially en olled in he schools, 2,521 ag eed o s a he
expe imen . We ound absen eeism cases, and some s uden s did no inish he
online su ey. A o al o 2,401 s uden s comple ed he en i e su ey. In his inal
sample, 1,210 we e men, 1,157 women, 21 epo ed non-bina y gende , and he
es did no answe he gende ques ion. A ac ion o 7.4% o s uden s a e o
mig an o igin; his igu e is sligh ly lowe han he a e age o 9.9% in he Spanish
non-Uni e si y educa ion sys em.
The scope o he su ey was b oad and no only o ien ed owa d he goal o he
p esen s udy. We elici ed a la ge ba e y o s uden s’ skills, abili ies, beha io s,
and a i udes. The su ey was designed o p o ide da a on a ious aspec s ha
play a cen al ole in an adolescen ’s daily li e. The i s pa ocuses on he
sociodemog aphic cha ac e is ics o he school. Addi ionally, we elici s uden s’
school achie emen , pe o med isk, and ime decision-making asks, inancial
li e acy, and cogni i e e lec ion es s, e c. Mo eo e , we elici ed s uden s’ sel -
es eem and pe sonal sa is ac ion.
Impo an ly, he su ey also included ques ions ega ding subjec s’ ela ion-
ships wi h o he s uden s in hei school. This included iends and, ou o he
iends, he bes iends, as well as enemies and, ou o he enemies, he wo s
enemies. Fo ha pu pose, he appica ion p o ided all s uden s wi h lis o all
he o he s uden s om he same school and yea . Hence, each ne wo k in ou
da a co esponds o all s uden s om di e en classes bu he same yea in one
school.
Las , pa icipan s indica ed in he lis o o he s uden s hose who su e ed
bullying. They we e explici ly s a ed ha i hey su e ed i hemsel es, hey
should ma k hei own name, and i hey knew abou any o he s uden s who
su e ed bullying, hey should ma k hem. Below, we e m sel - epo ed bullying
he case when a s uden included he sel in he lis o bullied people in he school
and o he - epo ed bullying when o he s indica ed someone as a ic im.
F om he iendship and enmi y lis s, we cons uc ed he ne wo ks using he
R so wa e and analyzed hem. The ne wo k da a will se e as ou p ima y
explana o y a iables in Sec ion 4.
We pe o med a nonlinea eg ession analysis wi h he s a is ical package
S a a. Ou models co ela e iendship and enmi y ne wo k measu es wi h di e -
en a iables on bullying ic imiza ion (see below).
3.1 Dependen a iables
Ou dependen a iable e lec s whe he an indi idual su e s bullying o no .
Du ing he elici a ion s age, he su ey explici ly included a de ini ion o bullying,
6
complying wi h he guidelines o he E hics commi ee and he Spanish laws. Mo e
p ecisely, he s uden s ha e been p o ided wi h he ollowing in o ma ion:
”Bullying exis s when, epea edly, se e al s uden s in en ionally annoy a
classma e who is unable o s op i . The annoyance can be one o mo e o
he ollowing ac s:
•Teasing, insul s, badmou hing, ejec ion, nega i e commen s and hu-
milia ion (which can also be cybe bullying h ough Facebook, Wha -
sapp, Twi e , e c.)
•Th ea s, hi s, sho es and he like.
I he e is bullying in you class g oup, ma k hose who a e bullied (max.
3). I hey do i o you, ma k you sel . I he e is no bullying, don’ ma k
anyone.”
As men ioned abo e, apa om his in o ma ion, he p og am SAND has p o-
ided all s uden s wi h a lis o all he people in he same yea in hei school,
including hemsel es. They we e simply asked o ma k hose who su e ed bully-
ing, including hemsel es i ha was he case acco ding o hei opinion.
F om he epo ed da a, we can dis inguish wo bina y a iables indica ing
whe he a s uden is a ic im o no . Fi s ly, sel - epo ed bullying is he case when
a s uden names himsel as a ic im, while o he - epo ed bullying e e s o cases
when a s uden is named by ano he as a ic im. Bo h a iables ake he alue o
1 (0) i he pa icipan is (no ) a ic im. Table 1 summa izes hese a iables on
agg ega e and by gende . Al hough emales a e mo e likely o sel - epo , males
a e mo e likely o be named by hei pee s. In addi ion, we employ a ca ego ical
a iable measu ing he numbe o imes o he classma es ha e men ioned a s uden
as a ic im (labeled No. men ions below). This a iable anges 0 o 8 in ou da a.
Table 1: F ac ions o sel - epo ed and o he - epo ed bullying, disagg ega ed by
gende
To al Males Females O he s
N M N M N M N M
Sel ic im-bullying 2,518 0.029 1209 0.026 1157 0.035 152 0.013
O he s ic im-bullying 3,029 0.094 1210 0.125 1157 0.067 662 0.083
In addi ion o hese a iables, we also analyze wo o he measu es, which we
label as “in e sec ion” and “union” o sel - and o he - epo ed bullying. Mo e
p ecisely, a s uden is conside ed bullied using he in e sec ion a iable i she sel -
epo he sel as a ic im and a leas one o he indi idual co obo a es i . A
s uden is conside ed a ic im unde he union a iable i she sel - epo s he sel
as a ic im o a leas one o he indi idual epo s ha she su e s bullying. Table
2 p o ides he numbe o cases in each o he ou si ua ions gene a ed by such
7
classi ica ion.
Table 2: Numbe o cases o bullying ic imiza ion in unc ion o who epo s ha
a s uden s su e bullying.
No o he s- epo ed Yes o he s- epo ed To al
No sel - epo ed 2,237 207 2,244
Yes sel - epo ed 38 36 74
To al 2,269 241 2,518
In o al, 2,518 pa icipan s answe ed he ques ion abou bullying, among whom
315 indi iduals a e ma ked ei he by hemsel es o by o he s as bullying ic ims,
ep esen ing oughly 12% o he sample. Only 74 (2.9%) s uden s sel - epo ed
as ic ims o bullying, while 241 (9,4%) we e epo ed as ic ims by o he class-
ma es. Thei pee s co obo a e almos 50% o he sel - epo ed cases. These
cases co espond o ou in e sec ion a iable. In con as , 14% o o he epo s
a e co obo a ed by he ic im.
In o de o analyze he ole o he en i e ne wo k a chi ec u e, we conside de-
penden a iables ha add up o he ic ims o bullying in each ne wo k. Again we
can conside he a iables “in e sec ion” and “union” o sel - and o he - epo ed
bullying. Howe e , o he 30 ne wo ks ob ained5only 1 does no con ain any ype
o bullying case, as Table 3 shows. The e o e, we ocus on he in e sec ion a i-
able o g ea e eliabili y. This dependen a iable is used in he Sec ion 4.2.2. I
coun s he cases o bullying epo ed by he ic ims and con i med by hei pee s
in each ne wo k.
Table 3: Numbe o ne wo ks by classi ica ion based on who epo s he ic im o
bullying
No o he s- epo ed Yes o he s- epo ed To al
No sel - epo ed 1 2 3
Yes sel - epo ed 0 27 27
To al 1 29 30
3.2 Ne wo k a iables
3.2.1 Indi idual posi ioning
The ne wo ks we e elici ed sepa a ely o each school-yea uni . Tha is, each ne -
wo k con ains people om classes co esponding o he same yea in ou school.
We cons uc ed ou di e en ne wo ks om ou da a: iendship, bes - iendship,
enmi y, and wo s -enmi y ne wo ks (see Sec ion 4.1 o hei cha ac e is ics).
The e o e, each pa icipan has ou alues o each indi idual ne wo k measu e.
5See Sec ion 3.2.2 o ne wo ks ob ained
8
Table 8: Gene al cha ac e is ics o posi i e and nega i e ne wo ks: Global mea-
su emen s
F iends Bes F iends Enemies Wo s enemies
Numbe o nodes 3,035 3,035 3,035 3,035
Numbe o edges 35,784 12,007 13,333 3,122
Densi y (possible edges) 0.00388 0.00130 0.00144 0.00034
Recip oci y 0.45025 0.38144 0.12360 0.09865
Deg ee: a e age 23.58089 7.91235 8.78616 2.05733
(S d. De .) (15.88297) (6.74629) (10.75836) (3.78667)
Gian componen 179 176 180 151
Isola ed nodes 30 166 121 1003
Clus e ing coe icien : o al 0.41263 0.31937 0.17001 0.07154
Clus e ing coe icien : a e age 0.50461 0.45046 0.30659 0.15787
Deg ee co ela ion: 0.17172 0.08361 -0.06212 -0.11370
Diame e 3 6 4 9
Mean dis ance 2.10301 3.15178 2.40451 3.60126
Asso a i i y 0.09335 0.04157 -0.15590 -0.16327
Homophily (Gende ) 0.29484 0.46091 0.03706 0.08926
Homophily (Class) 0.49239 0.51912 0.23593 0.32718
In con as , we obse e in e es ing simila i ies ac oss he iendship and nega-
i e s uc u es. Bo h ne wo ks con ain gian componen s o simila sizes and bo h
exhibi ypical ne wo k hie a chies o social ne wo ks. The la e is co obo a ed
by he compa ison o he deg ee dis ibu ion in ou ne wo ks wi h compa able
andom g aphs in Figu es 3 and 4.11 The compa ison o he deg ee dis ibu ion o
he obse ed ( ed) and andom (g een) ne wo ks in Figu es 3 and 4 clea ly illus-
a e he ypical “ a - ails” o socially gene a ed social ne wo ks: oo many people
a e ei he e y pe iphe al ( he le ail o he ed deg ee dis ibu ions in Figu es
3 and 4) o e y connec ed ( he igh ail) as compa ed o he andom ne wo ks.
Hence, impo an social p ocesses a e behind o ming iendship and enmi y ne -
wo ks. The aim o his s udy is o es whe he such hie a chy is connec ed wi h
who is bullied in he schools and, he e o e, whe he he same p ocesses behind
he ne wo k o ma ion may be d i ing bullying ic imiza ion.
11Compa able andom ne wo ks a e ne wo ks wi h he same numbe o nodes and connec ions
in which he links a e dis ibu ed andomly in he popula ion.
15
Figu e 3: Compa ison o he de-
g ee dis ibu ion o he iend-
ship ne wo k. Red=T ue ne wo k;
g een= andom ne wo k
Figu e 4: Compa ison o he deg ee
dis ibu ion o he enmi y ne wo k.
Red=T ue ne wo k; g een= andom
ne wo k
4.2 Ne wo ks and Bullying
In his sec ion, we analyze o wha ex en we can iden i y indi iduals who a e
being bullied using he in o ma ion abou he social ne wo ks summa ized in he
p e ious sec ion.
We illus a e he idea using Figu es 5 - 8 ha plo he iendship, bes -
iendship, enmi y, and wo s -enmi y ne wo ks, espec i ely. This ime, we colo
he ne wo k membe s acco ding o hei ic imiza ion s a us. The majo i y o
he nodes a e whi e because mos people do no su e bullying. Blue nodes ep-
esen adolescen s who sel - epo being bullied a school bu a e no named as
ic ims by o he s. Yellow nodes co espond o s uden s whom hei classma es
name as ic ims, bu hey do no sel - epo ha .12 Las , g een nodes a e cases
o people who bo h sel - epo hemsel es and a e epo ed by o he s as ic ims
(co esponding o ou a iable in e sec ion).
A close look a he ou ne wo ks e eals a clea pa e n: he ic ims end o
occupy pe iphe al posi ions in he iendship ne wo ks, while hey ind hemsel es
in he cen e o he g aphs in he enmi y ne wo ks. In he case o nega i e and
posi i e ne wo ks, hese ea u es a e mo e e iden when he links a e s onge (i.e.
in he bes - iendship and wo s -enmi y ne wo ks).
12The e a e no such cases in Figu es 5 - 8.
16
Figu e 5: F iendship ne wo k in one
school colo ed by bullying ic imiza-
ion. Whi e = no bullying; blue = Sel -
epo ed; g een = In e sec ion
Figu e 6: Bes - iendship ne wo k in
one school colo ed by bullying ic im-
iza ion. Colo s de ined as in Figu e 5.
Figu e 7: Enmi y ne wo k in one
school colo ed by bullying ic imiza-
ion. Colo s de ined as in Figu e 5.
Figu e 8: Wo s -enmi y ne wo k in
one school colo ed by bullying ic-
imiza ion. Colo s de ined as in Fig-
u e 5.
In he ollowing sec ion, we o mally es he obse a ions using eg ession analy-
sis. We mos ly employ logis ic eg essions o p edic whe he a s uden is a ic im
o bullying, using he di e en ne wo k measu es as p edic o s and o he socioe-
conomic cha ac e is ics as con ol a iables.
17
4.2.1 Bullying and indi idual posi ioning
In his sec ion, we illus a e s ep by s ep he p edic ion abili y o he posi i e
ne wo ks only, ollowed by he nega i e ne wo ks only and inally, we inco po a e
bo h ypes in o he s a is ical models. In he main pa o he analysis, we ocus
on ou bullying in e sec ion as he dependen a iable o sa e on space. The
esul s o he o he a iables a e quali a i ely simila and we only epo ou
esul s o he o he dependen a iables in Sec ion 4.2.4, whe e we p esen ou
selec ed model.
As a s a ing poin , we eplica e he analysis p esen ed by Mou apa e al.
(2004) who only use local a iables and iendship ne wo ks. In his exe cise,
we ob ain simila es ima es bu ou s end o be mo e signi ican , p obably due
o he g ea e s a is ical powe o ou sample size. We con i m ha ic ims o
bullying ecei e ewe iendship nomina ions and hei iends a e also mo e likely
o be ic ims o bullying, bu , as opposed o Mou apa e al. (2004), ou esul s
a e s a is ically s ong. Using he enmi y ne wo ks ins ead o combining bo h
shows ha he nega i e ne wo ks in a model Mou apa e al. (2004) o Mou apa
e al. (2004) e eals ha nega i e ela ionships deli e impo an and independen
in o ma ion om iendship ne wo ks while de ec ing he ic ims o bullying (see
Appendix A.1 o de ails). Since ou main models epo ed below ex end he
analysis o Mou apa e al. (2004) conside ably, we elega e he esul s o his
eplica ion analysis o Appendix A.1.
Table 9 epo s he esul s o a mo e gene al model using he bullying in e sec-
ion a iable de ined in Sec ion 3, in which one is labeled as a ic im i bo h she
and o he s epo he as such. We employ he logis ic eg essions and he di e en
models di e as ollows: model (1) only includes he iendship ne wo ks bu , in
con as o Mou apa e al. (2004), we in oduce he densi y o s uden s’ ne wo k
neighbou hoods ( o analyze he e ec o social cohesion) and global-cen ali y
measu es o each indi idual ( o es whe he he e ec o cen ali y goes beyond
one’s immedia e ne wo k neighbo hood). Model (2) epea s his analysis eplac-
ing he iendship ne wo k wi h he enmi y one; he emaining models combine
bo h ne wo k ypes, bu model (4) adds con ols o he ne wo k a iables and
model (5) clus e s he e o s a he le el o he ne wo k o accoun o possible
co ela ions in he da a. Table 9 also epo McFadden’s pseudo R2as measu e
o goodness o i (McFadden, 1973); McFadden (1977) claims ha a model has
a good i i he pseudo R2>0.2 (see also Lee (2013)). Table 9 e eals ha he
iendship and enmi y ne wo ks each sepa a ely explain 4-7% o he a iabili y o
he dependen a iables. Since his numbe inc eases o o e 10% in model (3),
he in o ma ion p o ided by each ne wo k ype does no o e lap much. I we in-
clude he adi ional de e minan s conside ed in he li e a u e, he p edic abili y
o ou model ises o almos 30%.13 The likelihood a io chi-squa e es s illus a e
ha all ou models clea ly ou pe o m a model wi hou eg esso s. Fu he mo e,
no model su e s om collinea i y as he Va iance In la ion Fac o (VIF) is always
13All con ol a iables a e in oduced in Sec ion 3.3. Gende dummy ne e esul s signi ican ,
bu , in line wi h he li e a u e, he mig an dummy is a obus p edic o o ic imiza ion.
18
well below 10.
As o he ne wo k a iables, se e al cen ali y measu es a e signi ican p e-
dic o s o bullying in he iendship ne wo k. In con as , only he in-deg ee and
he ac ion o ecip oca ed enmi ies a e signi ican in he model. In Sec ion 4.2.4,
we discuss he ole o he indi idual a iables in mo e de ail.
Table 9: Resul s o eg ession o bullying and indi idual posi ioning. Logis ic
eg ession and indi idual-le el analysis.
(1) (2) (3) (4) (5)
VARIABLES In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion
Ou deg ee (+) 0.042** 0.039** 0.035 0.035
In deg ee (+) -0.141*** -0.141*** -0.208*** -0.208***
Be weenness (+) 0.000 0.000 0.002 0.002*
Eigen ec o (+) -3.870 -3.962 -4.712 -4.712**
Closeness (+) -1.007 -0.765 -1.495 -1.495
Clus e ing (+) 0.768 0.588 0.860 0.860
Recip ocal deg ee (+) -0.360 -0.273 0.744 0.744
F iend ic ims 2.549*** 2.097*** 0.848 0.848
Ou deg ee (-) 0.013 0.008 0.006 0.006
In deg ee (-) 0.099*** 0.079*** 0.076** 0.076**
Be weenness (-) 0.000 0.000 -0.000 -0.000
Eigen ec o (-) 0.167 0.408 -2.331 -2.331
Closeness (-) -1.088 -1.259 -0.709 -0.709
Clus e ing (-) -0.743 -0.663 -0.849 -0.849
Recip ocal deg ee (-) -0.065 -0.028 0.675 0.675*
Enemy ic ims 0.485 0.301 -0.530 -0.530
Cons an -3.952*** -4.870*** -4.199*** -0.219 -0.219
Obse a ions 3,035 3,035 3,035 2,241 2,241
Pseudo R20.0750 0.0404 0.107 0.298 0.298
P ob< χ20.0000 0.0000 0.0000 0.0000
VIF 3.58 1.61 2.91 4.91 4.91
Con ols No No No Yes Yes
Clus e -Robus S.E. No No No No Yes
*** p<0.01, ** p<0.05, * p<0.1
F iendship ne wo k (+), enmi y ne wo k (-)
P obabili y o ob aining he χ2s a is ic, es ing he o e all model
Va iance In la ion Fac o , VIF<10 i no mul icollinea i y
Con ol a iables desc ibed in Sec ion 3.3
Robus s anda d e o s clus e ed a ne wo k le el (30 clus e s)
Table 10 epea s he analysis om o models (4-5) in Table 9 o each gende
sepa a ely. The analysis clea ly e eals ha who is bullied is clea ly gende -
speci ic. Fi s o all, di e en ne wo k cha ac e is ics p edic bullying ic imiza-
ion among men and women. Mos impo an ly hough, he abili y o p edic
bullying (as illus a ed by pseudo R2) inc eases conside ably wi h espec o he
pooled eg essions in Table 9. I p edic ed by gende sepa a ely, we can explain
oughly 41% and 36% o he a iabili y o he dependen a iable in he case o
men and women, espec i ely. Hence, p edic ing bullying ic imiza ion using ne -
wo ks should conside men and women sepa a ely.
19
Table 10: Resul s o eg ession o bullying and indi idual posi ioning by gende .
Logis ic eg ession and indi idual-le el analysis.
Males Females
(1) (2) (3) (4)
VARIABLES In e sec ion In e sec ion In e sec ion In e sec ion
Ou deg ee (+) -0.005 -0.005 0.088** 0.088**
In-deg ee (+) -0.029 -0.029 -0.381*** -0.381***
Be weenness (+) 0.003* 0.003** 0.000 0.000
Eigen ec o (+) -3.203 -3.203 -158.432*** -158.432***
Closeness (+) 1.655 1.655 -1.894 -1.894
Clus e ing (+) -1.316 -1.316 0.101 0.101
Recip ocal deg ee (+) -3.012* -3.012* 3.162*** 3.162***
F iend ic ims 0.618 0.618 0.457 0.457
Ou deg ee (-) 0.014 0.014 -0.002 -0.002
In deg ee (-) 0.070 0.070 0.110** 0.110**
Be weenness (-) 0.001 0.001 -0.000 -0.000
Eigen ec o (-) -948.680** -948.680** -0.309 -0.309
Closeness (-) 0.898 0.898 -10.701 -10.701
Clus e ing (-) 2.103* 2.103** -1.374 -1.374
Recip ocal deg ee (-) 0.552 0.552 0.725 0.725
Enemy ic ims -0.992 -0.992 -0.908 -0.908
Cons an 5.877* 5.877* -1.863 -1.863
Obse a ions 840 840 1,072 1,072
Pseudo R20.415 0.415 0.358 0.358
P ob< χ20 0
VIF 5.46 5.46 5.07 5.07
Con ols Yes Yes Yes Yes
Clus e -Robus S.E. No Yes No Yes
*** p<0.01, ** p<0.05, * p<0.1
F iendship ne wo k (+), enmi y ne wo k (-)
P obabili y o ob aining he χ2s a is ic, es ing he o e all model
Con ol a iables desc ibed in Sec ion 3.3
Clus e ed S anda d E o s by ne wo k (30 clus e s)
4.2.2 Bullying and ne wo k-wide cha ac e is ics
In his sec ion, we e i y whe he global ne wo k measu es can p edic bullying ic-
imiza ion a he ne wo k le el. Ou dependen a iable is he numbe o bullying
ic ims in each ne wo k ( ha is, yea -school uni ) and he explana o y a iables
a e ne wo k-wide cha ac e is ics. Hence, each eg ession is conduc ed wi h 30
obse a ions. Since he global measu es a e highly co ela ed (see Appendix A.3
o co ela ion ma ices), Table 11 p esen s nume ous simple linea eg essions,
in which each model conside s one unique global ne wo k cha ac e is ic bu he
same o bo h he iendship and enmi y ne wo k (as well as con ols). The e o e,
models (1 - 9) in Table 11 only di e in he eg esso s lis ed in he i s column
o he able.
We es ima e ha he densi y o he enmi y ne wo k is co ela ed wi h he in-
20
s ances o bullying in he ne wo k (model (1)), bu his is no he case o iendship
ne wo ks. Simila ly, highe ecip oci y o enmi ies and hei highe homophily in-
c eases bullying (models (2) and (7)). Model (3) e eals a nega i e ela ionship
be ween he a e age in-deg ee and bullying in he iendship ne wo k: mo e iend-
ships dec ease bullying. In con as , in model (6), he ela ionship obse ed wi h
he iendship ne wo k in he s anda d de ia ion o clus e ing is posi i e. The
emaining global measu es a e ne e signi ican . All in all, ce ain ne wo k a chi-
ec u es migh s imula e o mi iga e bullying. We in es iga e his claim in he
ollowing sec ion combining indi idual posi ioning and global ne wo k measu es.
Table 11: Resul s o linea eg ession o bullying and ne wo k-wide cha ac e is ics
(1) (2) (3) (4) (5) (6) (7) (8) (9)
VARIABLES In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion
Densi y (+) -1.030
Densi y (-) 13.057*
Global ecip oci y (+) -3.199
Global ecip oci y (-) 8.802***
A e age in deg ee (+) -0.136**
A e age in deg ee (-) -0.033
SD in deg ee (+) -0.258
SD in deg ee (-) -0.221
Global clus e ing (+) -1.120
Global clus e ing (-) -1.675
SD clus e ing (+) 12.600*
SD clus e ing (-) 2.762
G oup homophily (+) -0.009
G oup homophily (-) 1.500*
Modula i y (+) -0.450
Modula i y (-) -0.857
No. communi ies (+) 0.021
No. communi ies (-) -0.019
Cons an -0.706 0.022 2.477** 2.299** 1.868 -1.490 -0.088 0.933 0.730
Obse a ions 30 30 30 30 30 30 30 30 30
R20.360 0.471 0.359 0.354 0.285 0.366 0.418 0.282 0.284
Con ols Yes Yes Yes Yes Yes Yes Yes Yes Yes
Clus e -Robus S.E. Yes Yes Yes Yes Yes Yes Yes Yes Yes
*** p<0.01, ** p<0.05, * p<0.1
F iendship ne wo k (+), enmi y ne wo k (-)
Con ol a iables desc ibed in Sec ion 3.3
Clus e ed S anda d E o s by ne wo k (30 clus e s)
4.2.3 Bo h indi idual posi ioning and global cha ac e is ics as p edic-
o s o bullying
In his sec ion, we es whe he indi idual posi ioning combined wi h global ne -
wo k measu es can p edic indi idual-le el ic imiza ion. Table 12 p esen s nine
logis ic eg essions. The benchma k model is a eg ession (5) om Table 9; we
complemen his model wi h he global ne wo k-wide measu es one by one (as in
Table 12 abo e).
We obse e ha in-deg ee is a obus p edic o o ic imiza ion bo h in he
iendship and enmi y ne wo ks. In addi ion, global cen ali y measu es, namely
eigen ec o o be weenness, in he iendship ne wo k also emain signi ican , sug-
ges ing he cen ali y p o ec s om bullying beyond he e ec o local in-deg ee.
Vic ims end o be less cen al in posi i e ne wo ks locally and globally. Cen al-
i y beyond he local neighbo hood in enmi y ne wo ks does no seem o con ibu e
o bullying.
Rega ding he global measu es, he esul s mimic hose in Table 11. Vic ims o
21
bullying end o belong o ne wo ks wi h ewe enmi ies whe e hei ecip oci y is
highe . Low hie a chy (low s anda d de ia ion o deg ees) in he enmi y ne wo k
p e en s bullying. Mo eo e , a highe numbe o ne wo k subcommuni ies ( e-
lec ed in bo h modula i y and numbe o communi ies) s imula es ic imiza ion.
O e all, hese esul s con i m ha ne wo ks ma e , bu iendship and enmi y
ne wo ks on he one hand and di e en ne wo k ea u es a he indi idual and
global le el, on he o he , a ec bullying di e en ly.
Table 12: Resul s o eg essions o bullying and indi idual posi ioning and global
cha ac e is ics. Logis ic eg ession and indi idual-le el analysis.
(1) (2) (3) (4) (5) (6) (7) (8) (9)
VARIABLES In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion
Ou deg ee (+) 0.028 0.031 0.040 0.033 0.027 0.037 0.040 0.029 0.034
In deg ee (+) -0.206*** -0.193*** -0.178*** -0.189*** -0.203*** -0.206*** -0.166*** -0.209*** -0.215***
Be weenness (+) 0.002* 0.002* 0.001 0.002 0.002* 0.002 0.001 0.002** 0.002*
Eigen ec o (+) -5.083** -5.265*** -3.356 -2.982 -4.336** -4.998*** -4.719** -6.846*** -4.401**
Clus e ing (+) 0.292 0.214 0.919 0.410 0.427 0.842 0.718 0.550 0.713
Closeness (+) -3.971 -6.683 -1.514 -2.403 -2.141 -1.447 -4.225 -2.883* -1.055
Recip ocal deg ee (+) 0.598 0.552 0.621 0.615 0.650 0.811 0.469 0.673 0.791
F iend ic ims 0.189 0.262 0.673 0.771 0.888 0.924 0.015 0.408 0.730
Ou deg ee (-) 0.002 0.004 0.014 0.011 0.012 0.006 0.007 0.010 0.002
In deg ee (-) 0.071** 0.081** 0.121*** 0.120*** 0.097** 0.081** 0.099** 0.089** 0.078**
Be weenness (-) 0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 0.000
Eigen ec o (-) -1.786 -1.382 -1.981 -1.617 -1.322 -2.615 -0.088 -2.386 -2.220
Clus e ing (-) -1.086 -0.881 -0.011 -0.146 0.098 -0.910 -0.238 -0.449 -0.782
Closeness (-) -0.626 -0.752 -1.124 -1.143 -0.975 -0.814 -0.960 -0.889 -0.631
Recip ocal deg ee (-) 0.579 0.555 0.425 0.377 0.515 0.648 0.462 0.534 0.644
Enemy ic ims -1.362 -1.467 -0.799 -0.875 -0.664 -0.494 -1.598* -0.959 -0.445
Densi y (+) 0.434
Densi y (-) 15.287
Global ecip oci y (+) -0.201
Global ecip oci y (-) 7.883**
A e age in deg ee (+) -0.141
A e age in deg ee (-) -0.360***
SD in deg ee (+) -0.131
SD in deg ee (-) -0.722***
Global clus e ing (+) 5.327**
Global clus e ing (-) -12.461*
SD clus e ing (+) 1.764
SD clus e ing (-) 3.438
G oup homophily (+) 1.920
G oup homophily (-) 2.356*
Modula i y (+) -5.957*
Modula i y (-) 0.669
No. communi ies (+) -0.190**
No. communi ies (-) 0.040
Cons an -1.451 -1.691 2.632 2.813 -0.533 -1.134 -3.231 1.279 0.076
Obse a ions 2,241 2,241 2,241 2,241 2,241 2,241 2,241 2,241 2,241
Pseudo R20.313 0.322 0.318 0.325 0.314 0.299 0.329 0.311 0.307
VIF 5.62 6.90 6.59 7.39 7.26 8.26 5.61 6.31 5.24
Con ols Yes Yes Yes Yes Yes Yes Yes Yes Yes
Clus e -Robus S.E. Yes Yes Yes Yes Yes Yes Yes Yes Yes
*** p<0.01, ** p<0.05, * p<0.1
F iendship ne wo k (+), enmi y ne wo k (-)
Con ol a iables desc ibed in Sec ion 3.3
Clus e ed S anda d E o s by ne wo k (30 clus e s)
4.2.4 Selec ing inal models
Since many a iables in Table 12 a e ne e signi ican , his sec ion p esen s models
in which we only es ic a en ion o dependen ne wo k a iables ha esul
signi ican in a leas one eg ession. Since his leads o one unique model, Table
13 includes he selec ed model o each o he dependen a iables in oduced
in Sec ion 3: bullying in e sec ion (model (1)), bullying union (2), sel - epo ed
bullying (3), o he - epo ed bullying (4), and he numbe o imes one is men ioned
as a ic im by o he s (5).
22
Being bullied is obus ly ela ed o he numbe o imes one is named as a
iend (popula i y) posi i ely and he numbe o imes one is named as an en-
emy nega i ely. Mo eo e , global cen ali y in he iendship ne wo k consis en ly
p edic s bullying. Mo eo e , he highe he ac ion o ic ims’ enemies, he less
likely she is a ic im he sel . A he ne wo k-wide le el, seg ega ion–measu ed by
he numbe o communi ies and homophily on class oom–s imula es bullying.
The bes i ing model is (1), whe e he dependen a iable is he in e sec ion;
i explains 34%. Ou models p edic much less o he o he dependen a iables.
Howe e , i we selec ou models sepa a ely o each gende , he i inc eases
subs an ially. Fo example, Table 14 epo s he in e sec ion a iable’s case and
shows ha ou model’s p edic i e abili y inc eases by 44.1% and 10.6% o males
and emales, espec i ely. Hence, once again, he gende -speci ic analysis is mo e
sui able p edic ing ic imiza ion han he pooled analysis.
Table 13: Resul o inal logis ic eg ession and indi idual-le el analysis.
(1) (2) (3) (4) (5)
VARIABLES In e sec ion Union Sel -R O he s-R No. o he s-R
Ou deg ee (+) 0.052* 0.008 0.021 0.009 0.003**
In deg ee (+) -0.136*** -0.088*** -0.062** -0.099*** -0.016***
Eigen ec o (+) -7.271*** -0.546 -5.630*** -0.095 0.062
In deg ee (-) 0.111*** 0.125*** 0.054** 0.140*** 0.030***
Enemy ic ims -1.686* -0.416 -0.717 -0.456* -0.090**
N. isola es (+) -0.952*** 0.096 -0.149 0.061 0.024
N. communi ies (+) 0.542* -0.120* 0.053 -0.098 -0.024
G oup homophily (-) 3.776*** 1.200*** 1.501*** 1.407*** 0.353***
Cons an -3.971** 0.637 -0.009 -0.234 0.653***
Obse a ions 2,241 2,241 2,241 2,241 2,241
VIF 7.34 7.34 7.34 7.34
(Pseudo) R20.340 0.141 0.174 0.165 0.0972
Con ols Yes Yes Yes Yes Yes
Clus e -Robus S.E. Yes Yes Yes Yes Yes
*** p<0.01, ** p<0.05, * p<0.1
F iendship ne wo k (+), enmi y ne wo k (-)
Con ol a iables desc ibed in Sec ion 3.3
Clus e ed S anda d E o s by ne wo k (30 clus e s)
23
Table 14: Resul o inal logis ic eg ession and indi idual-le el analysis by gende .
Males Females
(1) (2)
VARIABLES In e sec ion In e sec ion
Ou deg ee (+) 0.072**
In deg ee (+) -0.317***
Eigen ec o (+) -5.169*** -151.192***
Be weenness (+) 0.003***
Recip oci y (+) -4.235*** 2.567*
In deg ee (-) 0.148** 0.141**
Gende homophily (+) -4.926***
G oup homophily (+) 3.103***
N. impo an communi ies (+) 0.587***
Densi y (-) 60.246***
Asso a i i y (-) 9.411**
SD in deg ee (-) -1.225***
G oup homophily (-) 4.464***
Cons an -9.209** -0.744
Obse a ions 858 1,077
Pseudo R20.490 0.376
Con ols Yes Yes
Clus e -Robus S.E. Yes Yes
*** p<0.01, ** p<0.05, * p<0.1
F iendship ne wo k (+), enmi y ne wo k (-)
Con ol a iables desc ibed in Sec ion 3.3
Clus e ed S anda d E o s by ne wo k (30 clus e s)
5 Conclusions and Discussion
Since school bullying is by de ini ion a social phenomenon, we ask o wha ex en
iendship and enmi y ne wo ks a school se e o iden i y he ic ims o bully-
ing. Ou esul s show ha social o ganiza ion as desc ibed by hese ne wo ks
p o ides a piece o quan i a i ely impo an and independen in o ma ion abou
who su e s bullying in ou da a. We pa icula ly obse e ha (i) bo h indi idual
ne wo k posi ioning and ne wo k-wide o ganiza ion play a ole while p edic ing
ic imiza ion, bu di e en cha ac e is ics play a ole a he indi idual s. global
le el, and indi idual posi ioning seems o be somewha mo e ele an han he
global a chi ec u e; (ii) iendship and enmi y ne wo ks play an o hogonal ole
in p edic ing ic imiza ion; and (iii) he way he ne wo k p edic ic imiza ion
di e s conside ably ac oss bo h sexes.
Be o e we discuss he implica ions o ou esul s o di e en heo ies o bul-
lying in psychology and sociology, we would like o emphasize ha ou analysis
is pu ely co ela ional. We do no claim ha - no does ou da a allow us o
p o e whe he - speci ic ne wo k posi ioning leads o bullying o whe he being a
ic im o bullying leads o speci ic ne wo k posi ions. In ac , we belie e ha bo h
phenomena e ol e hand in hand and none o hem “causes” he o he . We insis
ha ou analysis is a simple i ing exe cise which es s whe he we use ne wo k
da a in o de o p edic who can su e om bullying because obse ing who is
bullied di ec ly is o many easons challenging.
24
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32
A Appendices
A.1 Fi s appendix
We eplica ed he Mou apa e al. (2004) analysis. In his analysis, we only ocus
on iendship ne wo ks. Fou logis ic eg ession models a e es ima ed o explain
he bina y a iables o bullying and jus one linea eg ession in he las place.
Table 15 con ains he coe icien s.
Table 15: Resul s o logis ic eg ession o ic ims a iables: posi i e ne wo k
(1) (2) (3) (4) (5)
VARIABLES In e sec ion Union Sel -R O he s-R No. o he s-R
Ou deg ee 0.035** 0.008 0.008 0.012 0.003*
(0.017) (0.009) (0.015) (0.009) (0.002)
In deg ee -0.185*** -0.088*** -0.085*** -0.101*** -0.016***
(0.045) (0.017) (0.028) (0.018) (0.003)
Recip ocal deg ee 1.167 0.224 0.347 0.316 0.039
(0.769) (0.314) (0.509) (0.343) (0.062)
F iend ic ims 1.413* 2.792*** 1.643*** 2.770*** 0.685***
(0.741) (0.422) (0.611) (0.437) (0.140)
Mig an 0.038** 0.024*** 0.026** 0.026*** 0.004
(0.015) (0.009) (0.013) (0.009) (0.002)
Cons an -3.601*** -1.563*** -2.982*** -1.719*** 0.247***
(0.473) (0.202) (0.340) (0.217) (0.040)
Obse a ions 2,368 2,368 2,363 2,368 2,368
(Pseudo) R20.0836 0.0644 0.0356 0.0701 0.046
P ob >F (χ2) 0.0000 0.0000 0.0001 0.0000 0.0000
Robus s anda d e o s in pa en heses
*** p<0.01, ** p<0.05, * p<0.1
Hence, i is con i med ha ic ims o bullying ecei e ewe nomina ions, e-
ga dless o whe he hey ha e sel - epo ed o ha e been epo ed by o he pee s.
Fu he mo e, he coun o iends who a e bullied is also signi ican . Vic ims ha e
mo e iends who a e also ic ims o bullying.
Mo eo e , conside ing model (1)14, which e lec s he in e sec ion, he measu e
ou deg ee is also signi ican .
This same model is es ima ed by gende , p esen ing he esul s in Table 16.
In deg ee is signi ican in all ou models, while he a ibu es o iends a e only
signi ican in he union. Howe e , i is no ewo hy ha he e a e di e ences
ega ding gende . Model (3) indica es ha women included in he in e sec ion
cases, who su e bullying, end o men ion mo e iends and no iceably ha e
mo e ecip ocal iends.
14I is e i ied ha he model does no p esen mul icollinea i y p oblems, i has an a e age
VIF o 3.18
33
Table 16: Resul s o logis ic eg ession o ic ims a iables by gende
Males Females
(1) (2) (3) (4)
VARIABLES In e sec ion Union In e sec ion Union
Ou deg ee 0.020 0.004 0.064** 0.011
(0.022) (0.012) (0.027) (0.014)
In deg ee -0.107* -0.099*** -0.289*** -0.085***
(0.060) (0.020) (0.074) (0.030)
Recip oci y -0.807 0.182 2.688*** 0.480
(1.515) (0.418) (0.941) (0.507)
F iend ic ims 2.020 2.949*** 0.797 2.521***
(1.501) (0.639) (0.936) (0.589)
Mig an -0.010 0.020* 0.052*** 0.028**
(0.017) (0.011) (0.018) (0.014)
Cons an -3.465*** -1.117*** -3.668*** -2.052***
(0.730) (0.298) (0.634) (0.296)
Obse a ions 1,137 1,137 1,089 1,089
Pseudo R20.0552 0.0808 0.145 0.0545
P ob< χ20.0110 0.0000 0.0003 0.0000
Robus s anda d e o s in pa en heses
*** p<0.01, ** p<0.05, * p<0.1
Simila ly, an analysis o nega i e ne wo ks is pe o med. In his case, ins ead
o including he coun o iends who a e bullied, we ake in o accoun he enemies
who a e bullied.
Table 17: Resul s o logis ic eg ession o ic ims a iables: nega i e ne wo k
(1) (2) (3) (4) (5)
VARIABLES In e sec ion Union Sel -R O he s-R No. o he s-R
Ou deg ee 0.017** 0.005 0.019*** -0.002 0.002
(0.008) (0.007) (0.006) (0.009) (0.002)
In deg ee 0.092*** 0.111*** 0.063*** 0.120*** 0.026***
(0.019) (0.013) (0.017) (0.013) (0.005)
Recip oci y 0.555 -0.089 -0.230 0.036 0.047*
(0.398) (0.177) (0.277) (0.193) (0.029)
Vic im enemies 0.315 0.289 0.043 0.350 0.049
(0.560) (0.242) (0.396) (0.259) (0.041)
Mig an 0.032*** 0.022** 0.025** 0.024** 0.003
(0.010) (0.010) (0.011) (0.010) (0.002)
Cons an -5.178*** -2.697*** -3.868*** -2.945*** 0.007
(0.334) (0.137) (0.213) (0.151) (0.026)
Obse a ions 2,368 2,368 2,368 2,368 2,368
(Pseudo) R20.0477 0.0487 0.0272 0.0567 0.035
P ob >F (χ2) 0.0000 0.0000 0.0000 0.0000 0.0000
Robus s anda d e o s in pa en heses
*** p<0.01, ** p<0.05, * p<0.1
The esul s ob ained wi h he nega i e ne wo k a e simila o hose wi h he
posi i e ne wo k. Men ions ecei ed as enemies a e signi ican in all models. How-
e e , excep o in deg ee, no o he a iable is signi ican in all models. In models
(1) and (3), men ions made s and ou . The mo e enemies men ioned, he mo e
34
likely i is o be bullied and sel - epo i .
Table 18 shows he model by gende . In he case o men, he men ions ecei ed
as enemies a e signi ican as in he p e ious model. On he con a y, in he emale
model (3), he deg ee o ecip oci y also s ands ou , he ic ims end o ha e mo e
bad ecip ocal ela ionships.
Table 18: Resul s o eg ession: nega i e ne wo k by gende
Males Females
(1) (2) (3) (4)
VARIABLES In e sec ion Union In e sec ion Union
Ou deg ee 0.017 -0.002 0.016* 0.016*
(0.012) (0.010) (0.009) (0.008)
In deg ee 0.120*** 0.150*** 0.075*** 0.095***
(0.034) (0.019) (0.026) (0.018)
Recip oci y -0.178 -0.261 0.957** -0.045
(0.799) (0.233) (0.440) (0.288)
Vic im enemies 0.478 -0.014 0.201 0.855**
(0.904) (0.312) (0.748) (0.407)
Mig an -0.006 0.021 0.040*** 0.023*
(0.015) (0.014) (0.012) (0.014)
Cons an -5.254*** -2.441*** -5.031*** -3.152***
(0.537) (0.184) (0.423) (0.222)
Obse a ions 1,137 1,137 1,089 1,089
Pseudo R20.0477 0.0680 0.0628 0.0557
P ob > χ20.0002 0.0000 0.0410 0.0000
Robus s anda d e o s in pa en heses
*** p<0.01, ** p<0.05, * p<0.1
Table 19: Resul s o eg ession: posi i e ne wo k (Bes iends)
(1) (2) (3) (4) (5)
VARIABLES bullying in e sec ion bullying union sel bullying o he s bullying n o he s bullying
Ou deg ee 0.016 0.023** -0.003 0.030*** 0.008***
(0.013) (0.009) (0.021) (0.010) (0.003)
In deg ee -0.269*** -0.198*** -0.172*** -0.209*** -0.031***
(0.099) (0.033) (0.066) (0.036) (0.005)
Recip oci y 0.063 0.275 -0.499 0.484** 0.108***
(0.523) (0.202) (0.395) (0.213) (0.039)
Bes iend ic ims 1.440*** 2.369*** 1.551*** 2.328*** 0.519***
(0.536) (0.297) (0.439) (0.299) (0.106)
Mig an -0.005 0.028*** -0.151 0.030*** 0.004*
(0.012) (0.010) (0.486) (0.010) (0.002)
Cons an -3.624*** -1.819*** -2.822*** -2.079*** 0.166***
(0.364) (0.153) (0.284) (0.162) (0.027)
Obse a ions 2,368 2,368 2,363 2,368 2,368
R20.041
Pseudo R20.0470 0.0717 0.0428 0.0734
P ob > χ20.0005 0.0000 0.0000 0.0000
Robus s anda d e o s in pa en heses
*** p<0.01, ** p<0.05, * p<0.1
35
A.2 Second appendix
Table 20: Posi i e and Nega i e Ne wo k Reg ession Resul s: Ou deg ee
(1) (2) (3) (4) (5) (6) (7) (8)
VARIABLES In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion
Ou deg ee (+) 0.012 0.003 0.007 0.019 0.019 0.018 0.019 0.001
Ou deg eee (-) 0.018*** 0.020*** 0.021*** 0.012 0.011 0.010 0.010 0.012
Recip oci y (+) -1.203** -1.161** -1.137* -1.167** -1.220** -1.125* -0.714
Recip oci y (-) 0.285 0.313 0.330 0.233 0.246 0.416 1.223***
Eigen ec o (+) -5.561 -6.021 -6.065 -5.980 -5.613 -6.465
Eigen ec o (-) 0.521 0.586 0.557 0.610 0.258 -2.507
Be weenness (+) -0.001 -0.001 -0.001 -0.001 0.001
Be weenness (-) 0.000*** 0.000*** 0.000*** 0.000*** 0.000
Closeness (+) -1.053 -1.067 -0.924 -2.077
Closeness (-) -1.205 -1.184 -1.007 -0.167
Clus e ing (+) 0.275 0.210 0.306
Clus e ing (-) -0.208 -0.324 -0.763
F iend ic ims 2.715*** 1.223
Enemy ic ims 0.399 -0.120
Cons an -4.675*** -4.054*** -4.102*** -4.182*** -4.055*** -4.121*** -4.553*** -0.116
Obse a ions 3,035 3,035 3,035 3,035 3,035 3,035 3,035 2,241
Pseudo R20.00877 0.0185 0.0263 0.0338 0.0362 0.0366 0.0557 0.235
P ob< χ20.0010 0.0003 0.0004 0.0011 0.0042 0.0025 0.0000 0.0000
Con ols No No No No No No No Yes
*** p<0.01, ** p<0.05, * p<0.1
F iendship ne wo k (+), enmi y ne wo k (-)
Con ol a iables desc ibed in Sec ion 3.3
Table 21: Posi i e and Nega i e Ne wo k Reg ession Resul s: In deg ee
(1) (2) (3) (4) (5) (6) (7) (8)
VARIABLES In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion In e sec ion
In deg ee (+) -0.102*** -0.104*** -0.096*** -0.115*** -0.117*** -0.123*** -0.120*** -0.195***
In deg ee (-) 0.102*** 0.101*** 0.102*** 0.094*** 0.094*** 0.094*** 0.084*** 0.072**
Recip oci y (+) -0.781 -0.837 -0.658 -0.681 -0.752 -0.758 0.337
Recip oci y (-) -0.264 -0.246 -0.198 -0.309 -0.266 -0.094 0.648
Eigen ec o (+) -4.607 -4.140 -4.287 -3.917 -3.521 -3.754
Eigen ec o (-) 0.546 0.781 0.683 0.883 0.763 -2.320
Be weenness (+) 0.001 0.001 0.001 0.001 0.003***
Be weenness (-) 0.000 0.000 0.000 0.000 0.000
Closeness (+) -1.226** -1.164* -1.109* -1.783
Closeness (-) -1.473 -1.429 -1.295 -0.715
Clus e ing (+) 0.580 0.477 0.789
Clus e ing (-) -0.791 -0.814 -0.974
F iend ic ims 2.054*** 0.815
Enemy ic ims 0.316 -0.525
Cons an -3.975*** -3.401*** -3.427*** -3.519*** -3.369*** -3.399*** -3.660*** 0.363
Obse a ions 3,035 3,035 3,035 3,035 3,035 3,035 3,035 2,241
Pseudo R20.0607 0.0701 0.0732 0.0783 0.0821 0.0855 0.0977 0.294
P ob< χ20.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Con ols No No No No No No No Yes
*** p<0.01, ** p<0.05, * p<0.1
F iendship ne wo k (+), enmi y ne wo k (-)
Con ol a iables desc ibed in Sec ion 3.3
36
Table 22: co ela ion coe icien s local measu es
Va iables (1) (2) (3) (4)
(1) Ou deg ee (+) 1.000
(2) Ou deg ee (-) 0.095 1.000
(0.000)
(3) In deg ee (+) 0.410 0.045 1.000
(0.000) (0.013)
(4) In deg ee (-) -0.009 0.107 -0.013 1.000
(0.635) (0.000) (0.487)
A.3 Thi d appendix
Table 23: Co ela ion coe icien s global measu es (posi i e ne wo k)
Va iables (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21)
(1) Num nodes (+) 1.000
(2) Num edges (+) 0.847 1.000
(0.000)
(3) Densi y (+) -0.826 -0.547 1.000
(0.000) (0.000)
(4) Global ecip oci y (+) -0.751 -0.560 0.774 1.000
(0.000) (0.000) (0.000)
(5) Asso a i i y (+) 0.237 0.011 -0.389 -0.151 1.000
(0.000) (0.528) (0.000) (0.000)
(6) A e age in deg ee (+) -0.017 0.475 0.383 0.184 -0.391 1.000
(0.337) (0.000) (0.000) (0.000) (0.000)
(7) A e age deg ee (+) -0.017 0.475 0.383 0.184 -0.391 1.000 1.000
(0.337) (0.000) (0.000) (0.000) (0.000) (0.000)
(8) SD deg ee (+) 0.698 0.913 -0.372 -0.434 -0.053 0.589 0.589 1.000
(0.000) (0.000) (0.000) (0.000) (0.003) (0.000) (0.000)
(9) SD in deg ee (+) 0.588 0.793 -0.258 -0.268 -0.075 0.588 0.588 0.867 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(10) Global clus e ing (+) -0.874 -0.655 0.941 0.848 -0.219 0.270 0.270 -0.475 -0.323 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(11) A e age clus e ing (+) -0.853 -0.603 0.930 0.805 -0.369 0.313 0.313 -0.403 -0.346 0.958 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(12) SD clus e ing (+) 0.399 -0.035 -0.572 -0.266 0.525 -0.744 -0.744 -0.074 -0.120 -0.446 -0.468 1.000
(0.000) (0.053) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(13) G. componen (+) 0.997 0.860 -0.829 -0.763 0.222 0.003 0.003 0.709 0.585 -0.880 -0.847 0.372 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.851) (0.851) (0.000) (0.000) (0.000) (0.000) (0.000)
(14) No. isola es (+) 0.456 0.194 -0.319 -0.178 0.278 -0.272 -0.272 0.153 0.286 -0.291 -0.430 0.512 0.391 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(15) Mean dis ance (+) 0.637 0.249 -0.858 -0.618 0.406 -0.599 -0.599 0.048 0.082 -0.749 -0.804 0.647 0.629 0.360 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.008) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(16) Diame e (+) 0.503 0.173 -0.721 -0.562 0.270 -0.537 -0.537 0.030 0.049 -0.660 -0.726 0.493 0.497 0.285 0.864 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.100) (0.007) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(17) Gende homophily (+) 0.309 0.041 -0.516 -0.354 0.308 -0.445 -0.445 0.033 0.026 -0.457 -0.445 0.534 0.306 0.195 0.428 0.326 1.000
(0.000) (0.023) (0.000) (0.000) (0.000) (0.000) (0.000) (0.066) (0.152) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(18) G oup homophily (+) -0.382 -0.361 0.210 0.495 0.157 -0.211 -0.211 -0.468 -0.516 0.290 0.261 0.042 -0.386 -0.115 -0.184 -0.222 -0.279 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.021) (0.000) (0.000) (0.000) (0.000) (0.000)
(19) Modula i y (+) 0.361 0.004 -0.699 -0.306 0.333 -0.568 -0.568 -0.204 -0.227 -0.492 -0.510 0.560 0.358 0.185 0.759 0.578 0.387 0.179 1.000
(0.000) (0.820) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(20) No. communi ies (+) 0.642 0.373 -0.476 -0.344 0.328 -0.257 -0.257 0.318 0.398 -0.467 -0.581 0.566 0.587 0.958 0.466 0.377 0.259 -0.230 0.212 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(21) No. impo an comm. (+) 0.833 0.670 -0.686 -0.721 0.266 -0.085 -0.085 0.586 0.453 -0.778 -0.735 0.369 0.841 0.267 0.497 0.434 0.299 -0.495 0.150 0.505 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
37
Table 24: Co ela ion coe icien s global measu es (nega i e ne wo k)
Va iables (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21)
(1) No. nodes (-) 1.000
(2) No. edges (-) 0.610 1.000
(0.000)
(3) Densi y (-) -0.778 -0.183 1.000
(0.000) (0.000)
(4) Global ecip oci y (-) -0.541 -0.207 0.783 1.000
(0.000) (0.000) (0.000)
(5) Asso a i i y (-) -0.003 -0.259 -0.172 -0.153 1.000
(0.863) (0.000) (0.000) (0.000)
(6) A e age in deg ee (-) -0.096 0.700 0.490 0.216 -0.284 1.000
(0.000) (0.000) (0.000) (0.000) (0.000)
(7) A e age deg ee (-) -0.096 0.700 0.490 0.216 -0.284 1.000 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(8) SD deg ee (-) 0.234 0.837 0.095 -0.158 -0.409 0.830 0.830 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(9) SD in deg ee (-) 0.026 0.714 0.384 0.187 -0.242 0.903 0.903 0.732 1.000
(0.155) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(10) Global clus e ing (-) -0.622 0.113 0.791 0.533 -0.079 0.699 0.699 0.349 0.670 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(11) A e age clus e ing (-) -0.121 0.537 0.367 0.054 -0.463 0.772 0.772 0.858 0.662 0.588 1.000
(0.000) (0.000) (0.000) (0.003) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(12) SD clus e ing (-) 0.326 0.263 -0.309 -0.315 -0.259 -0.022 -0.022 0.426 -0.032 -0.147 0.506 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.235) (0.235) (0.000) (0.082) (0.000) (0.000)
(13) G. componen (-) 0.990 0.687 -0.728 -0.509 -0.043 0.005 0.005 0.337 0.105 -0.563 -0.016 0.364 1.000
(0.000) (0.000) (0.000) (0.000) (0.019) (0.789) (0.789) (0.000) (0.000) (0.000) (0.370) (0.000)
(14) No. isola es (-) 0.316 -0.358 -0.528 -0.364 0.253 -0.692 -0.692 -0.620 -0.531 -0.549 -0.724 -0.156 0.177 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(15) Mean dis ance (-) 0.578 -0.007 -0.615 -0.473 0.257 -0.461 -0.461 -0.352 -0.303 -0.563 -0.545 -0.157 0.501 0.640 1.000
(0.000) (0.700) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(16) Diame e (-) 0.476 -0.052 -0.531 -0.440 0.355 -0.433 -0.433 -0.383 -0.273 -0.517 -0.570 -0.303 0.399 0.605 0.917 1.000
(0.000) (0.004) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(17) Gende homophily (-) 0.461 0.243 -0.413 -0.351 -0.046 -0.134 -0.134 0.122 -0.001 -0.293 0.064 0.440 0.434 0.281 0.357 0.302 1.000
(0.000) (0.000) (0.000) (0.000) (0.011) (0.000) (0.000) (0.000) (0.963) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(18) G oup homophily (-) -0.105 -0.324 0.280 0.478 0.264 -0.238 -0.238 -0.485 -0.156 0.036 -0.354 -0.350 -0.136 0.168 0.125 0.225 -0.088 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.049) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(19) Modula i y (-) 0.446 -0.301 -0.673 -0.342 0.342 -0.708 -0.708 -0.648 -0.544 -0.649 -0.749 -0.172 0.339 0.803 0.675 0.652 0.228 0.265 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(20) No. communi ies (-) 0.442 -0.278 -0.623 -0.405 0.254 -0.710 -0.710 -0.583 -0.522 -0.635 -0.712 -0.075 0.310 0.976 0.701 0.663 0.376 0.150 0.826 1.000
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
(21) No. impo an comm (-) 0.599 0.004 -0.765 -0.597 0.091 -0.533 -0.533 -0.210 -0.454 -0.774 -0.375 0.207 0.552 0.447 0.550 0.574 0.473 -0.078 0.589 0.572 1.000
(0.000) (0.826) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
38
