Bidirectional association between normative adjustment and bullying perpetration in adolescence: A prospective longitudinal study

Abstract

Normative adjustment stimulates the development of attitudes and behaviours that promote school climate. Previous research has shown that it is a relevant factor in preventing involvement in risk behaviours that affect the quality of peer relationships in classrooms and schools. Previous the development of behaviour adjusted to the norms which promotes interaction processes fostering a positive atmosphere in the classroom and in the school. The aim of this study is to analyse the prospective influence of norma-tive adjustment on bullying perpetration over four time periods spaced six months apart (18 months). A total of 3017 adolescents between 11 and 16 years (49.5% girls; M ageT1 = 13.15, SD = 1.09) are involved in the present study. The Random Intercept Cross-Lagged Model results indicate an influential bidirectional association between normative adjustment and bullying perpetration over time. When the adolescents' normative adjustment increases, their involvement in bullying perpetration decreases six months later. On the other hand, when the adolescents' bullying perpetration increases over time, a decrease in nor-mative adjustment is evident later. The unconditional univariate growth results report that normative adjustment increases, while bullying perpetration decreases. These findings are discussed in terms of the need to consider contextual factors and how they interact in our understanding and prevention of bullying in schools.
El ajuste normativo estimula el desarrollo de actitudes y comportamientos que promueven la convivencia escolar. Estudios previos subrayan su relevancia para prevenir la implicación en comportamientos de riesgo que afectan a la calidad de las relaciones entre iguales en el aula y en el centro escolar. El objetivo del estudio es analizar la influencia prospectiva entre el ajuste normativo y la perpetración de acoso durante cuatro períodos de tiempo con un intervalo de seis meses (18 meses). Han participado un total de 3.017 adolescentes entre 11 y 16 años (49.5% niñas; M edad T1 = 13.15, DT = 1.09). Los resultados del Modelo Random Intercept Cross-Lagged indican una asociación bidireccional entre el ajuste normativo y la perpetración del acoso a lo largo del tiempo. Cuando los adolescentes aumentan su ajuste normativo, disminuye su participación en la perpetración del acoso seis meses después. A su vez, cuando aumenta la implicación en agresión, se registra una disminución en su ajuste normativo a lo largo del tiempo. Los resultados de crecimiento univariado incondicional informan que el ajuste normativo aumenta mientras que la agresión en acoso escolar disminuye. Los hallazgos se discuten en términos de la necesidad de considerar la interacción longitudinal con factores contextuales para comprender y prevenir el acoso escolar en las escuelas.

Full text

ARTICLE IN PRESS
G Model
Revista
de
Psicodidáctica
xxx
(xxxx)
xxx–xxx
www.elsevier.es/psicod
Original
Bidirectional
association
between
normative
adjustment
and
bullying
perpetration
in
adolescence:
A
prospective
longitudinal
study夽
Eva
M.
Romera∗,
Manuel
Carmona-Rojas,
Rosario
Ortega-Ruiz,
and
Antonio
Camacho
Universidad
de
Córdoba,
Spain
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
22
November
2021
Accepted
2
March
2022
Available
online
xxx
Keywords:
Bullying
Norms
Adolescence
Prevention
School
climate
Random
Intercept
Cross-Lagged
a
b
s
t
r
a
c
t
Normative
adjustment
stimulates
the
development
of
attitudes
and
behaviours
that
promote
school
cli-
mate.
Previous
research
has
shown
that
it
is
a
relevant
factor
in
preventing
involvement
in
risk
behaviours
that
affect
the
quality
of
peer
relationships
in
classrooms
and
schools.
Previous
the
development
of
behaviour
adjusted
to
the
norms
which
promotes
interaction
processes
fostering
a
positive
atmosphere
in
the
classroom
and
in
the
school.
The
aim
of
this
study
is
to
analyse
the
prospective
influence
of
norma-
tive
adjustment
on
bullying
perpetration
over
four
time
periods
spaced
six
months
apart
(18
months).
A
total
of
3017
adolescents
between
11
and
16
years
(49.5%
girls;
MageT1 =
13.15,
SD
=
1.09)
are
involved
in
the
present
study.
The
Random
Intercept
Cross-Lagged
Model
results
indicate
an
influential
bidirectional
association
between
normative
adjustment
and
bullying
perpetration
over
time.
When
the
adolescents’
normative
adjustment
increases,
their
involvement
in
bullying
perpetration
decreases
six
months
later.
On
the
other
hand,
when
the
adolescents’
bullying
perpetration
increases
over
time,
a
decrease
in
nor-
mative
adjustment
is
evident
later.
The
unconditional
univariate
growth
results
report
that
normative
adjustment
increases,
while
bullying
perpetration
decreases.
These
findings
are
discussed
in
terms
of
the
need
to
consider
contextual
factors
and
how
they
interact
in
our
understanding
and
prevention
of
bullying
in
schools.
©
2022
Universidad
de
Pa´
ıs
Vasco.
Published
by
Elsevier
Espa˜
na,
S.L.U.
All
rights
reserved.
Asociación
bidireccional
entre
el
ajuste
normativo
y
la
agresión
en
acoso
escolar
en
la
adolescencia:
un
estudio
longitudinal
prospectivo
Palabras
clave:
Acoso
escolar
Normas
Adolescencia
Prevención
Convivencia
Random
Intercept
Cross-Lagged
r
e
s
u
m
e
n
El
ajuste
normativo
estimula
el
desarrollo
de
actitudes
y
comportamientos
que
promueven
la
convivencia
escolar.
Estudios
previos
subrayan
su
relevancia
para
prevenir
la
implicación
en
comportamientos
de
riesgo
que
afectan
a
la
calidad
de
las
relaciones
entre
iguales
en
el
aula
y
en
el
centro
escolar.
El
objetivo
del
estudio
es
analizar
la
influencia
prospectiva
entre
el
ajuste
normativo
y
la
perpetración
de
acoso
durante
cuatro
períodos
de
tiempo
con
un
intervalo
de
seis
meses
(18
meses).
Han
participado
un
total
de
3.017
adolescentes
entre
11
y
16
a˜
nos
(49.5%
ni˜
nas;
MedadT1
=
13.15,
DT
=
1.09).
Los
resultados
del
Modelo
Random
Intercept
Cross-Lagged
indican
una
asociación
bidireccional
entre
el
ajuste
normativo
y
la
perpetración
del
acoso
a
lo
largo
del
tiempo.
Cuando
los
adolescentes
aumentan
su
ajuste
normativo,
disminuye
su
participación
en
la
perpetración
del
acoso
seis
meses
después.
A
su
vez,
cuando
aumenta
la
implicación
en
agresión,
se
registra
una
disminución
en
su
ajuste
normativo
a
lo
largo
del
tiempo.
Los
resultados
de
crecimiento
univariado
incondicional
informan
que
el
ajuste
normativo
aumenta
mientras
que
la
agresión
en
acoso
escolar
disminuye.
Los
hallazgos
se
discuten
en
términos
de
la
necesidad
de
considerar
la
interacción
longitudinal
con
factores
contextuales
para
comprender
y
prevenir
el
acoso
escolar
en
las
escuelas.
©
2022
Universidad
de
Pa´
ıs
Vasco.
Publicado
por
Elsevier
Espa˜
na,
S.L.U.
Todos
los
derechos
reservados.
PII
of
original
article:S1136-1034(22)00012-0.
夽Please
cite
this
article
as:
Romera
EM,
Carmona-Rojas
M,
Ortega-Ruiz
R,
Camacho
A.
Asociación
bidireccional
entre
el
ajuste
normativo
y
la
agresión
en
acoso
escolar
en
la
adolescencia:
un
estudio
longitudinal
prospectivo.
Rev
Psicodidáctic.
2022.
https://doi.org/10.1016/j.psicod.2022.03.001
∗Corresponding
author.
E-mail
address:
eva.romera@uco.es
(E.M.
Romera).
2530-3805/©
2022
Universidad
de
Pa´
ıs
Vasco.
Published
by
Elsevier
Espa˜
na,
S.L.U.
All
rights
reserved.
PSICOE-104;
No.
of
Pages
8

ARTICLE IN PRESS
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E.M.
Romera,
M.
Carmona-Rojas,
R.
Ortega-Ruiz
et
al.
Revista
de
Psicodidáctica
xxx
(xxxx)
xxx–xxx
Introduction
Bullying
is
defined
as
aggressive
behaviour
intended
to
cause
harm
to
the
victim.
This
type
of
undesirable
behaviour
occurs
against
a
background
of
a
power
imbalance,
usually
long-term,
between
bully
and
victim
(Olweus,
1994).
A
substantial
body
of
research
has
focused
on
the
individual
characteristics
linked
to
bullying
perpetration,
but
more
studies
are
needed
to
understand
students’
behaviour
in
their
own
school
context.
The
adherence
to
school
norms
based
on
the
respect
to
others
and
the
setting
guides
behaviours
considered
appropriate
and
desirable
in
schools
and
classrooms
(Herrera-López
et
al.,
2016).
However,
it
is
necessary
to
further
investigate
its
bidirectional
relationship
with
involve-
ment
in
bullying
perpetration.
Recent
research
has
shown
that
the
lack
of
adjustment
with
school
norms
has
been
identified
as
a
risk
factor
for
involvement
in
bullying
perpetration
(Menesini
&
Salmivalli,
2017;
Pouwels
et
al.,
2018;
Smith,
2016).
Nevertheless,
to
understand
the
bidirectional
association
between
the
behaviour
of
schoolchildren
who
defiantly
exhibit
deviant
behaviour
towards
the
educational
system
of
norms
and
peer
aggression
may
help
identify
its
relevance
to
understand
bullying
behaviour
and
guide
prevention
programs
(Låftman
et
al.,
2017;
Teng
et
al.,
2020).
Bullying
perpetration
and
normative
adjustment
Normative
adjustment
is
defined
as
the
set
of
attitudes
and
behaviours
associated
with
compliance
with
social
systems
aimed
at
achieving
coexistence
in
schools
(Herrera-López
et
al.,
2016).
These
social
norms
are
linked
to
displaying
values
of
respect
and
tolerance
so
that
interpersonal
relationships
can
flourish
in
schools
(Longobardi
et
al.,
2018).
Previous
studies
have
shown
that
adopt-
ing
behaviour
adjusted
to
the
norms
designed
to
foster
interaction
processes
among
individuals
is
positively
related
to
high
levels
of
support
and
social
adaptation
and
low
levels
of
bullying
perpe-
tration,
improves
the
quality
of
relationships
between
peers,
and
creates
a
positive
atmosphere
in
the
classroom
and
the
school
(Dawes,
2017;
Laninga-Wijnen
et
al.,
2018;
Mayeux
&
Kraft,
2018;
Pozzoli
et
al.,
2012).
Although
it
is
assumed
that
normative
adjustment
acts
as
encouragement
for
positive
social
interactions
in
the
classroom,
its
relationship
with
bullying
perpetration
in
schools
needs
to
be
explored
further.
It
has
been
shown
that
pupils
who
display
less
adjustment
to
school
norms
have
a
higher
probability
of
being
involved
in
bullying
perpetration
(Låftman
et
al.,
2017;
Longobardi
et
al.,
2018;
Müller
et
al.,
2018;
Wang
et
al.,
2018).
However,
these
are
cross-sectional
studies
which
limit
the
possibility
of
exploring
causal
relationships
between
the
variables.
The
few
longitudinal
studies
carried
out
take
into
account
the
perception
of
the
school
atmosphere
as
a
factor
linked
to
involvement
in
bullying
perpetra-
tion
(Romera,
Luque-González
et
al.,
2022;
Teng
et
al.,
2020),
but
not
so
much
the
behaviour
and
attitudes
of
schoolchildren
towards
the
basic
norms
that
guarantee
a
positive
atmosphere
in
school,
such
as
respect
for
others
and
for
the
school
itself;
nor
do
they
take
into
account
whether
involvement
in
bullying
perpetration
could
account
for
a
greater
degree
of
divergence
with
classroom
and
school
rules.
In
order
to
explore
the
possible
reciprocal
association
between
normative
adjustment
and
bullying
perpetration,
we
need
to
apply
methodological
approaches
which
take
into
account
a
between-
and
within-level
approach.
The
between-person
level
records
trait
characteristics
through
the
inter-subject
effect,
i.e.,
comparing
schoolchildren
with
their
peers.
Meanwhile,
the
within-person
level
records
state
characteristics
and
approaches
the
link
between
normative
adjustment
and
bullying
perpetration
from
an
intra-
subject
approach,
i.e.,
analysing
whether
longitudinal
changes
in
a
variable
in
one
particular
individual
lead
to
subsequent
changes
in
another
variable.
Uncontrolled
discrimination
between
the
between-
and
within-
person
level
results
in
the
absence
of
time-invariant
individual
differences
being
assumed.
This
fails
to
consider
how
the
involve-
ment
of
adolescents
in
bullying
may
tend
to
be
a
sporadic
rather
than
a
stable
trait
over
time
(Zych
et
al.,
2020).
Consequently,
in
the
analysis
of
the
mechanisms
involved
in
bullying
research,
special
consideration
must
be
given
to
separating
between-
and
within-person
level
effects
to
enable
us
to
explore
the
prospective
associations
between
the
constructs
when
time-dependent
char-
acteristics
such
as
state
are
considered
(Romera
et
al.,
2021).
The
effects
of
sex
and
age
should
also
be
studied
when
con-
sidering
the
reciprocal
association
between
normative
adjustment
and
bullying
perpetration,
as
clear
differences
have
been
identi-
fied
between
boys
and
girls.
In
general,
indiscipline
and
lack
of
adjustment
to
norms
tend
to
occur
more
frequently
in
boys
than
in
girls,
mainly
in
those
educational
contexts
in
which
the
social
bonds
are
weaker
(Jiménez
&
Estévez,
2017;
Longobardi
et
al.,
2018;
Mucherah
et
al.,
2018).
In
the
case
of
bullying,
significant
differ-
ences
have
been
identified
as
regards
sex
and
age
in
adolescents.
Indeed,
previous
results
show
that
peer
aggressive
behaviour
tends
to
decrease
as
adolescence
progresses
(Cho
&
Lee,
2020).
On
the
other
hand,
although
there
is
no
consensus
in
studies
on
bullying
about
gender
differences,
cross-cultural
studies
indicate
a
general
tendency
for
boys
to
be
more
frequent
perpetrators
of
bullying
(Smith
et
al.,
2019).
Despite
gender
differences
in
bullying
perpetra-
tion,
the
moderating
effect
of
gender
has
been
recognised,
with
girls
having
a
greater
social
influence
on
levels
of
aggressive
behaviour
(Busching
&
Krahé,
2015).
The
longitudinal
study
of
bullying
and
normative
adjustment
also
demands
a
developmental
approach
to
understand
how
both
variables
are
connected
over
time.
Through
growth
curve
analysis
previous
studies
have
shown
that
bullying
perpetration
tends
to
decrease
over
adolescence
(Cho
&
Lee,
2020),
while
the
adjustment
to
normative
behaviours
in
schools
tend
to
increase
(Ettekal
&
Shi,
2020).
However,
more
studies
are
needed
to
understand
the
com-
mon
trajectory
of
bullying
perpetration
and
normative
adjustment
through
parallel
growth
curve.
The
present
study
The
few
longitudinal
studies
that
analyse
these
associations
over
time
deal
with
within-
and
between-person
effects
together,
which
may
cause
difficulties
in
the
interpretation
of
the
results
(Berry
&
Willoughby,
2017).
In
this
study,
we
followed
statistical
meth-
ods
to
differentiate
these
effects
further
so
that
the
developmental
processes
occurring
in
adolescents
may
be
interpreted
more
accu-
rately.
The
objective
of
this
study
was
to
address
the
temporal
associations
between
normative
adjustment
and
bullying
perpe-
tration
to
identify
the
developmental
process
that
increases
the
risk
of
individuals
becoming
involved
in
aggressive
behaviour.
Based
on
the
above
literature,
after
controlling
the
between-person
variance,
it
was
expected
that
normative
adjustment
would
predict
bully-
ing
perpetration
(Hypothesis
1),
while
bullying
perpetration
would
predict
the
subsequent
normative
adjustment
(Hypothesis
2)
at
the
within-person
level.
As
found
in
previous
studies,
it
was
expected
that
these
effects
would
be
stronger
for
boys
and
early
adoles-
cents
(Hypothesis
3).
Based
on
the
longitudinal
trajectories,
we
predicted
that
normative
adjustment
would
tend
to
increase
over
time
(Hypothesis
4),
while
bullying
perpetration
would
decrease
(Hypothesis
5).
After
controlling
the
effects
of
gender
and
age,
we
also
expected
to
find
a
negative
common
development
between
normative
adjustment
and
bullying
perpetration;
in
other
words,
2

ARTICLE IN PRESS
G Model
E.M.
Romera,
M.
Carmona-Rojas,
R.
Ortega-Ruiz
et
al.
Revista
de
Psicodidáctica
xxx
(xxxx)
xxx–xxx
that
an
increase
in
normative
adjustment
over
time
would
be
asso-
ciated
with
a
decrease
in
bullying
perpetration
(Hypothesis
6).
Method
Participants
The
sample
consisted
of
a
total
of
3017
pupils
(49.5%
girls)
from
the
four
years
of
compulsory
secondary
education,
attending
thir-
teen
different
schools
in
the
province
of
Córdoba
(Spain)
during
the
2017/2018
and
2018/2019
academic
years.
The
students’
ages
ranged
from
11
to
16
years
old
(MT1 =
13.15,
SD
=
1.09).
Schools
were
selected
by
incidental
sampling,
inviting
the
schools
to
participate.
The
85.45%
of
the
students
belong
to
public
schools,
while
14.55%
to
private
schools.
The
21.5%
of
the
students
belong
to
environments
with
a
low
socioeconomic
level,
54.8%
to
neighbourhoods
with
a
medium
socioeconomic
level
and
23.8%
to
environments
with
a
high
economic
level.
The
distribution
of
the
population
according
to
the
town
population
size
was:
19.1%
belong
to
small
towns
(less
than
10,000
inhabitants),
33%
to
medium-sized
towns,
and
the
rest,
47.9%,
to
large
towns
(more
than
100,000
inhabitants).
Instruments
Normative
adjustment
was
measured
using
the
scale
with
this
name
in
the
Adolescent
Multidimensional
Social
Competence
Ques-
tionnaire
(AMSC-Q)
(Gómez-Ortiz
et
al.,
2017),
which
consists
of
5
Likert-type
items
1–7
(1
=
completely
false,
7
=
completely
true).
This
scale
measures
the
students’
level
of
compliance
with
class-
room
norms,
the
respect
for
the
opinions
of
their
peers
and
care
for
the
school’s
material
and
facilities.
One
item,
for
instance,
reads:
“I
respect
the
opinion
of
others
even
if
I
do
not
share
it”.
This
norma-
tive
adjustment
subscale
has
been
previously
validated
with
Spanish
adolescents
as
a
unidimensional
structure
(Herrera-López
et
al.,
2016).
To
measure
the
pupils’
bullying
perpetration,
we
used
the
aggression
scale
of
the
European
Bullying
Intervention
Project
Ques-
tionnaire
(EBIPQ)
(Ortega-Ruiz
et
al.,
2016)
(␻T1 =
.77).
The
EBIPQ
measures
the
involvement
of
schoolchildren
in
victimization
and
aggression
bullying
behaviours,
associated
with
actions
such
as
hit-
ting,
name-calling,
threatening,
spreading
rumours,
or
excluding
during
the
last
three
months.
Students
were
previously
informed
that
bullying
refers
to
harmful
behaviours
that
occur
repeatedly,
intentionally
and
with
an
imbalance
of
power.
The
aggression
scale
is
made
up
of
7
Likert-type
items
0–4
(0
=
no,
4
=
yes,
more
than
once
a
week).
An
example
item
of
the
aggression
scale
is:
“I
have
insulted
a
fellow
pupil”.
This
bullying
perpetration
subscale
has
been
previously
validated
with
Spanish
adolescents
as
a
unidimensional
structure
(Romera
et
al.,
2021).
Procedure
A
four-time
longitudinal
research
design
was
used,
with
time
periods
spaced
six
months
apart.
Permission
was
granted
by
the
schools
and
the
families
of
the
pupils
who
took
part,
and
the
study
was
approved
by
the
Ethics
Committee
from
the
institution
where
the
authors
work.
Data
collection
was
carried
out
by
the
pupils
fill-
ing
in
a
questionnaire
in
normal
classroom
time,
supervised
by
one
of
the
research
team.
The
students
were
fully
informed
of
the
vol-
untary,
confidential,
and
anonymous
nature
of
the
questionnaire
and
that
they
could
opt
out
of
the
study
at
any
time.
The
time
spent
completing
the
questionnaire
did
not
exceed
40
minutes,
in
all
cases.
Data
analysis
In
the
preliminary
analyses,
internal
consistency
and
psycho-
metric
properties
of
both
scales
were
explored.
Internal
consistency
was
measured
through
Cronbach’s
alpha,
McDonald’s
omega,
com-
posite
reliability
whose
appropriate
values
are
indicated
by
indices
above
.70
(Bacon
et
al.,
1995).
In
addition,
the
average
variance
extracted
was
also
reported
with
the
recommendation
that
it
should
exceed
a
value
of
50%
(Hair
et
al.,
2006).
The
psycho-
metric
properties
of
the
scales
were
also
explored.
Model
fit
was
estimated
using
the
indices:
comparative
fit
index
(CFI
>
.90),
the
Tucker–Lewis
index
(TLI
>
.90),
the
root
mean
square
error
of
approximation
(RMSEA
<
.08)
and
the
standardized
root
mean
square
residual
(SRMR
<
.08)
(Chen,
2007).
The
association
between
the
variables
was
also
subjected
to
a
correlation
analysis
and
the
differences
in
the
variables
based
on
gender
and
age
were
tested
through
latent
mean
differences
from
scalar
invariance.
Cohen’s
d
was
calculated
to
explore
the
effect
size
of
the
differences.
As
recommended
as
a
previous
step
to
the
longitudinal
analyses,
the
independent
invariance
of
the
instruments
over
time
was
explored
through
a
confirmatory
factor
analysis
(CFA)
using
a
sequence
of
hierarchical
steps
(Little,
2013).
A
Random
Intercept
Cross-Panel
Model
(RI-CLPM;
Hamaker
et
al.,
2015)
was
conducted
to
explore
the
reciprocal
contribu-
tion
between
normative
adjustment
and
bullying
perpetration
at
the
between-
and
within-person
levels.
In
contrast
to
the
traditional
cross-lagged
panel
model
(CLPM),
RI-CLPM
is
sensitive
to
the
dif-
ferences
of
within-
and
between-person
variance
by
splitting
into
a
random
intercept
(Berry
&
Willoughby,
2017).
The
random
inter-
cept
captures
stable
between-individual
differences
in
normative
adjustment
and
bullying
perpetration
across
all
time
points,
while
in
the
within-person
level,
the
residuals
at
each
measurement
capture
the
intraindividual
deviations
from
a
person’s
stable
level
within
each
time
point.
Regarding
the
between-person
effect,
RI-CLPM
provides
two
random
intercept
factors
by
fixing
the
loading
fac-
tor
to
1.0.
The
within-person
effect
contains
autoregressive
and
cross-lagged
parameters,
as
well
as
covariances
between
the
out-
comes
at
the
same
time.
The
autoregressive
parameters
indicate
the
temporal
stability
of
the
variable.
Cross-lagged
effects
estimate
the
bidirectional
influence
of
normative
adjustment
and
bullying
per-
petration
in
a
subsequent
measurement
with
the
aim
of
analysing
the
causal
effect
of
one
variable
on
another.
Finally,
variables
are
associated
in
each
time
to
reflect
within-person
change
covariances
between
the
variables.
Due
to
the
segregation
of
the
within-and
between-person,
the
cross-lagged
and
autoregressive
effects
in
the
RI-CLPM
are
entirely
located
at
the
within-person
level.
We
com-
pare
a
series
of
models
through
which
the
same
parameters
are
constrained
to
be
equal
across
time
based
on
the
principle
of
par-
simony.
Provided
that
the
simplified
model
remains
conceptually
consistent,
the
simplified
model
is
generally
considered
best
as
the
greater
degrees
of
freedom
increase
the
likelihood
of
its
rejection
(Kline,
2015).
Thus,
when
performing
these
model
comparisons,
the
aim
is
to
analyse
whether
a
simplified
model
rather
than
the
more
complex
model
can
be
selected
and
whether
there
are
any
significant
differences
between
the
two
model
fits.
Model
build-
ing
involved
four
steps.
First,
we
estimated
the
RI-CLPM
by
freely
estimating
all
the
effects.
Second,
the
autoregressive
parameters
within
the
person
were
constrained
to
be
equal
over
time.
Third,
we
constrained
the
within-person
cross-lagged
paths.
Fourth,
the
covariances
between
the
residuals
of
the
within-person
centred
variables
at
the
same
time
from
second
to
fourth
times
were
con-
strained
to
be
equal
over
time.
Finally,
to
test
for
age
and
gender
differences,
we
performed
multiple
group
analyses
by
constrain-
ing
the
coefficients
to
be
equal
across
gender
(boys
versus
girls)
and
age
(early
versus
middle
adolescence).
The
post
hoc
Wald
2
3

ARTICLE IN PRESS
G Model
E.M.
Romera,
M.
Carmona-Rojas,
R.
Ortega-Ruiz
et
al.
Revista
de
Psicodidáctica
xxx
(xxxx)
xxx–xxx
test
(Chou
&
Bentler,
1990)
was
used
to
determine
if
there
would
be
a
significant
differences
across
the
groups
in
the
RI-CLPM.
The
Growth
Curve
Model
(Preacher
et
al.,
2008)
was
performed
to
explore
the
developmental
changes
of
normative
adjustment
and
bullying
perpetration.
The
mean
and
variance
of
the
intercept
and
slope
was
considered,
as
well
as
the
covariance
between
the
inter-
cept
and
slope.
The
intercept
shows
the
initial
level
of
a
variable,
while
the
slope
refers
to
the
global
magnitude
of
change
(positive
or
negative)
during
the
time
covered
by
the
study
(18
months
in
our
study).
The
variance
of
both
parameters
reflects
inter-individual
differences.
The
linear
slope
factors
were
quantified
as
0,
0.5,
1.0,
and
1.5
to
provide
the
evenly
spaced
six-month
measurement
intervals.
The
growth
curve
analyses
involved
two
steps.
First,
we
conducted
a
univariate
growth
curve
to
explore
the
changes
in
each
variable
separately,
to
test
whether
the
pattern
of
the
hypothetical
trajectory
fits
the
data.
For
each
outcome,
we
analysed
the
changes
of
the
variable
over
time
and
its
relationship
to
the
initial
levels
(e.g.,
covariance
between
the
intercept
and
slope
of
bullying
perpe-
tration).
In
the
second
step,
we
performed
a
parallel
growth
curve
to
capture
the
co-development
of
changes
in
the
target
outcomes
with
gender
and
age
as
covariates
(e.g.,
the
covariance
between
the
slopes
of
normative
adjustment
and
bullying
perpetration),
and
because
the
initial
values
of
one
variable
are
associated
with
hypo-
thetical
changes
in
the
other
(e.g.,
covariance
between
the
intercept
of
normative
adjustment
and
the
slope
of
bullying
perpetration).
Gen-
der
and
age
were
introduced
to
control
for
the
effect
on
intercept
and
slope
of
each
variable.
Parallel
growth
modelling
supports
the
concurrent
estimation
of
growth
rate
parameters
among
a
group
of
variables.
The
analyses
were
performed
using
the
Lavaan
R
package
(Rosseel,
2012).
Robust
standard
errors
with
maximum
likelihood
(MLR)
were
addressed
to
account
for
data
non-normality.
Model
fit
was
evaluated
according
to
the
standard
fit
indices
comparative
fit
index
(CFI),
the
Tucker–Lewis
index
(TLI),
the
root
mean
square
error
of
approximation
(RMSEA)
and
the
standardized
root
mean
square
residual
(SRMR).
Values
above
.90
in
CFI
and
TLI
were
con-
sidered
an
acceptable
fit
and
above
.95
a
good
fit.
Values
below
.08
were
considered
acceptable
in
RMSEA
and
SRMR,
while
values
below
.05
indicated
a
good
fit.
Differences
of
<
.01
CFI
and
<
.015
RMSEA
were
considered
as
references
to
determine
the
differ-
ence
between
the
models
explored
(Chen,
2007).
The
low
levels
of
normed
2(2/df
=
1.59)
in
Little’s
MCAR
test
indicate
that
this
missing
data
was
random
(MAR)
(Bollen,
1989).
The
method
used
to
deal
with
the
missing
data
was
full
information
maximum
likeli-
hood
(FIML),
using
the
valid
data
without
removing
any
individual,
instead
of
imputing
data
(Enders,
2010).
Results
Preliminary
results
The
bullying
perpetration
subscale
had
good
internal
consis-
tency
through
Cronbach’s
alpha
(␣T1 =
.82,
␣T2 =
.80,
␣T3 =
.82,
and
␣T4 =
.78),
McDonald’s
omega
(␻T1 =
.83,
␻T2 =
.83,
␻T3 =
.83,
and
␻T4 =
.82),
composite
reliability
(CRT1 =
.95,
CRT2 =
.94,
CRT3 =
.95,
and
CRT4 =
.95)
and
average
variance
extracted
(AVET1 =
64.95%,
AVET2 =
60.67%,
AVET3 =
66.64%,
and
AVET4 =
64.47%).
The
bullying
perpetration
subscale
also
showed
good
psychometric
proper-
ties
through
CFA:
T1,
2(14)
=
301.790,
p
<
.001,
CFI
=
.984,
TLI
=
.976,
RMSEA
=
.076,
[90%
CI
.068-083],
and
SRMR
=
.071;
T2,
2(14)
=
274.239,
p
<
.001,
CFI
=
.983,
TLI
=
.975,
RMSEA
=
.076,
[90%
CI
.068-084],
and
SRMR
=
.074;
T3,
2(14)
=
260.526,
p
<
.001,
CFI
=
.986,
TLI
=
.979,
RMSEA
=
.074,
[90%
CI
.067-082],
and
SRMR
=
.075;
T4,
2(14)
=
235.495,
p
<
.001,
CFI
=
.984,
TLI
=
.976,
RMSEA
=
.072,
[90%
CI
.064-080],
and
SRMR
=
.080).
The
normative
adjustment
subscale
had
good
internal
consis-
tency
through
Cronbach’s
alpha
(␣T1 =
.81,
␣T2 =
.84,
␣T3 =
.83,
and
␣T4 =
.85),
McDonald’s
omega
(␻T1 =
.82,
␻T2 =
.85,
␻T3 =
.85,
and
␻T4 =
.86),
composite
reliability
(CRT1 =
.93,
CRT2 =
.92,
CRT3 =
.93,
and
CRT4 =
.93)
and
average
variance
extracted
(AVET1 =
53.47%,
AVET2 =
58.61%,
AVET3 =
59.62%,
and
AVET4 =
61.06%).
The
norma-
tive
adjustment
subscale
also
showed
good
psychometric
properties
through
confirmatory
factor
analysis
(CFA):
T1,
2(5)
=
51.000,
p
<
.001,
CFI
=
.997,
TLI
=
.995,
RMSEA
=
.049,
[90%
CI
.037-062],
and
SRMR
=
.026;
T2,
2(5)
=
75.635,
p
<
.001,
CFI
=
.998,
TLI
=
.995,
RMSEA
=
.058,
[90%
CI
.047-070],
and
SRMR
=
.027;
T3,
2(5)
=
99.255,
p
<
.001,
CFI
=
.997,
TLI
=
.994,
RMSEA
=
.066,
[90%
CI
.055-077],
and
SRMR
=
.029;
T4,
2(5)
=
98.213,
p
<
.001,
CFI
=
.997,
TLI
=
.995,
RMSEA
=
.066,
[90%
CI
.055-078],
and
SRMR
=
.028).
The
descriptive
statistics
of
the
study
variables
are
shown
in
Table
1.
After
successfully
achieving
scalar
invariance
between
boys
and
girls,
and
early
and
middle
adolescents
(see
Tables
S1
and
S2
in
supplementary
material),
gender
and
age
differences
were
anal-
ysed
with
latent
mean
difference
(from
scalar
invariance).
In
terms
of
gender,
boys
showed
greater
involvement
in
bullying
(from
T1
to
T3),
with
a
low
effect
size.
Girls
showed
higher
levels
of
normative
adjustment,
with
a
moderate
effect.
Two
groups
were
established
to
explore
differences
based
on
age,
early
adolescents
(from
11
to
13
years)
and
middle
adolescents
(from
14
to
16
years).
Low
effect
size
was
found
by
rating
middle
adolescents
with
greater
bully-
ing
perpetration
(from
T1
to
T3).
Early
adolescents
reported
more
normative
adjustment
with
a
low
effect
size.
Stability
correlations
also
show
how
normative
adjustment
(r
=
.57
–
.71)
and
bullying
perpetration
remain
stable
over
time
(r
=
.29
–
.35).
The
results
obtained
show
a
moderate
negative
rela-
tionship
between
bullying
perpetration
and
normative
adjustment
(r
=
-29
–
-.39
within
time;
r
=
-.24
–
-.36
across
time).
The
correlation
analysis
highlighted
the
presence
of
high
values
in
the
two
study
variables
over
time
(see
Table
2)
thus
determining
their
temporal
consistency.
Measurement
invariance
The
measurement
invariance
of
each
construct
was
estimated
over
time
using
CFA,
including
covariances
between
the
latent
indi-
cators
of
each
time
period
(Little,
2013).
A
series
of
restrictive
steps
were
applied
to
obtain
the
measurement
invariance
of
the
con-
structs
over
time
(see
Table
3).
The
CFA
was
developed
by
loading
all
the
items
of
the
same
scale
into
an
indicator,
as
done
in
previous
studies
with
normative
adjustment
(Gómez-Ortiz
et
al.,
2017)
and
bullying
perpetration
(Ortega-Ruiz
et
al.,
2016).
The
model
fits
are
shown
in
Table
3.
First,
the
configural
model
was
estimated
without
restrictions,
where
factor
loadings
and
intercepts
were
freely
esti-
mated
for
both
normative
adjustment
and
bullying
perpetration.
The
results
of
configural
invariance
show
an
excellent
model
fit.
Second,
the
metric
model
estimated
after
constraint
that
the
factor
loading
was
equivalent
across
time.
Such
constraints
did
not
significantly
change
the
model
fit
in
any
construct
in
comparison
with
config-
ural
invariance
as
CFI
and
RMSEA
was
lower
than
<
.01
and
<
.015
respectively.
Finally,
the
intercepts
were
constrained
in
the
scalar
model.
The
model
fit
indicates
that
there
are
no
significant
differences
between
the
metric
and
scalar
invariance.
Random
intercept
cross-lagged
model
A
series
of
sequential
models
were
performed
with
the
aim
of
obtaining
the
most
parsimonious
model
fit
when
interpreting
the
results
(see
Table
3).
Model
1
represents
the
free
estimation
of
all
parameters.
The
model
fit
indicates
a
good
fit.
The
first
constraint
was
applied
to
the
autoregressive
paths
in
model
2,
which
showed
no
significant
differences
with
respect
to
the
unconstrained
model.
4

ARTICLE IN PRESS
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M.
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R.
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et
al.
Revista
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(xxxx)
xxx–xxx
Table
1
Descriptive
statistics
and
latent
mean
differences
across
gender
and
age
Gender
differencesaAge
differencesb
Total
sample
Boys
Girls
Early
adolescents
Middle
adolescents
S
K
M
(SD)
M
(SD)
M
(SD)
z
d
M
(SD)
M
(SD)
z
d
Normative
adjustment
T1
−1.15
1.38
5.79
(1.07)
5.54
(1.13)
6.04
(.94)
8.09***
0.49
5.92
(1.02)
5.59
(1.11)
−6.39***
0.38
Normative
adjustment
T2
−1.03
0.96
5.81
(1.02)
5.59
(1.06)
6.00
(.93)
8.08***
0.46
5.91
(1.02)
5.65
(.98)
−5.88***
0.33
Normative
adjustment
T3
−1.14
1.20
5.94
(.99)
5.73
(1.07)
6.12
(.89)
7.74***
0.48
6.05
(.97)
5.75
(1.01)
−6.66***
0.38
Normative
adjustment
T4 −1.17 1.55
5.88
(1.01) 5.67
(1.08) 6.02
(.91)
7.52***
0.45
5.95
(.99)
5.76
(1.06)
−4.05***
0.23
Bullying
perpetration
T1 3.45
16.52
0.26
(.44)
0.33
(.53)
0.19
(.32)
−4.11***
0.38
0.23
(.30)
0.31
(.46)
4.11***
0.38
Bullying
perpetration
T2
3.33
15.96
0.28
(.45)
0.34
(.45)
0.23
(.37)
−2.98**
0.24
0.26
(.39)
0.32
(.45)
2.98**
0.24
Bullying
perpetration
T3
3.56
16.67
0.20
(.38)
0.26
(.45)
0.15
(.29)
−2.32*
0.23
0.19
(.36)
0.22
(.36)
2.32*
0.23
Bullying
perpetration
T4
3.48
19.27
0.22
(.36)
0.25
(.41)
0.17
(.30)
−0.69
0.07
0.20
(.28)
0.23
(.38)
0.69
0.07
aFor
boys
the
latent
means
variables
were
fixed
at
0
and
freely
estimated
for
girls.
bFor
middle
adolescents
the
latent
means
variables
were
fixed
at
0
and
freely
estimated
for
early
adolescents.
S
=
Skewness;
K
=
Kurtosis.
*p
<
.05.
** p
<
.01.
*** p
<
.001.
Table
2
Correlations
for
normative
adjustment
and
bullying
perpetration
across
four
times
1
2
3
4
5
6
7
1.
Normative
adjustment
T1
–
2.
Normative
adjustment
T2
0.69***
–
3.
Normative
adjustment
T3
0.61***
0.71***
–
4.
Normative
adjustment
T4 0.57*** 0.66*** 0.65*** –
5.
Bullying
perpetration
T1
−0.35***
−0.36***
−0.32***
−0.24***
–
6.
Bullying
perpetration
T2
−0.32***
−0.39***
−0.31***
−0.30***
0.32***
–
7.
Bullying
perpetration
T3
−0.24***
−0.36***
−0.35***
−0.27***
0.35***
0.34***
–
8.
Bullying
perpetration
T4
−0.23***
−0.29***
−0.29***
−0.28***
0.29***
0.29***
0.34***
*** p
<
.001.
Table
3
Goodness-of-fit
indices
of
the
measurement
invariance,
random
intercept
cross-lagged
panel
model
and
growth
curve
model
Model
fit
Model
comparison
2S-B df
CFI
TLI
RMSEA
SRMR
2S-B (df)
CFI
RMSEA
Measurement
Invariance
Normative
adjustment
Configural
2792.245*** 147
0.987
0.985
0.081
[0.078,
0.084]
0.058
–
–
–
Metric
2307.593***
159
0.986
0.984
0.080
[0.077,
0.082]
0.060
35.506
(12)***
0.001
0.001
Scalar
2481.751***
171
0.986
0.985
0.077
[0.074,
0.079]
0.060
0.46
(12)
0.000
0.003
Bullying
perpetration
Configural
2074.931***
319
0.974
0.969
0.049
[0.047,
0.051]
0.083
–
–
–
Metric
1867.141***
337
0.974
0.971
0.048
[0.046,
0.050]
0.084
16.619
(18)
0.000
0.001
Scalar
1966.869***
355
0.974
0.973
0.047
[0.045,
0.049]
0.084
0.84
(18)
0.000
0.000
Random
Intercept
Cross-Lagged
Model
Model
1
143.293***
19
0.955
0.933
0.073
[.062,
.085]
0.070
–
–
–
Model
2
142.594***
23
0.952
0.942
0.068
[.058,
.069]
0.067
0.699
(4)
0.003
0.005
Model
3
145.064***
27
0.954
0.952
0.062
[.052,
.072]
0.070
2.47
(4)
0.002
0.006
Model
4
148.159***
29
0.953
0.954
0.061
[.051,
.070]
0.073
3.095
(2)
0.001
0.001
Growth
Curve
Model
Unconditional
normative
adjustment
54.019***
5
0.983
0.979
0.070
[0.054,
0.088]
0.039
–
–
–
Unconditional
bullying
perpetration
23.681***
5
0.968
0.962
0.057
[0.036,
0.080]
0.034
–
–
–
Parallel
growth
curve
129.110***
30
0.974
0.961
0.046
[0.038,
0.054]
0.035
–
–
–
Note.
2=
Robust
chi-square
test
of
exact
fit;
df
=
Degrees
of
freedom;
CFI
=
comparative
fit
index;
TLI
=
Tucker–Lewis
index;
RMSEA
=
root
mean
square
error
of
approximation;
SRMR
=
standardized
root
mean
square
residual;

=
Change
in
fit
indices.
*** p
<
.001.
In
model
3
the
cross-lagged
effects
were
constrained,
showing
no
significant
differences
compared
to
model
2.
Finally,
in
model
4,
the
covariances
between
the
residuals
in
the
same
time
period
were
constrained.
Considering
that
model
4
presented
no
significant
dif-
ferences
to
model
3,
it
was
adopted
as
the
most
parsimonious
model,
as
a
reference
to
explore
the
associations
between
normative
adjustment
and
bullying
perpetration.
The
results
of
the
random
intercept
cross-lagged
model
are
reported
in
Figure
1.
At
the
between-person
level,
the
covari-
ance
among
the
intercepts
was
significant
and
negative,
indicating
that
adolescents
with
greater
involvement
in
bullying
perpetration
across
the
four
times
reported
less
normative
adjustment
compared
to
other
adolescents.
The
significant
negative
covariances
between
construct
residues
at
the
within-person
level
indicate
that
when
adolescents
reported
a
high
degree
of
bullying
perpetration,
they
also
consistently
revealed
lower
than
average
levels
of
normative
adjustment.
With
respect
to
cross-lagged
effects,
when
adolescents
showed
an
increase
in
normative
adjustment,
this
subsequently
pre-
5

ARTICLE IN PRESS
G Model
E.M.
Romera,
M.
Carmona-Rojas,
R.
Ortega-Ruiz
et
al.
Revista
de
Psicodidáctica
xxx
(xxxx)
xxx–xxx
Figure
1.
Results
of
random
intercept
cross-lagged
model.
Note.
Standardized
coefficients
based
on
constrained
unstandardized
coefficients
are
shown.
*
p
<
.05;
**
p
<
.01;
***
p
<
.001.
dicted
a
decrease
in
bullying
perpetration
compared
to
their
own
levels
six
months
later.
Likewise,
changes
in
bullying
perpetration
predicted
later
inverse
changes
in
normative
adjustment.
The
results
of
the
Wald
tests
indicated
that
there
were
no
differences
in
gen-
der,
Wald
2(5)
=
4.87,
p
=
.43
or
age,
Wald
2(5)
=
1.36,
p
=
.93
in
the
reciprocal
association
between
normative
adjustment
and
bullying
perpetration.
Growth
curve
model
A
series
of
growth
curve
analyses
were
performed
to
examine
the
longitudinal
trajectories
of
normative
adjustment
and
bullying
perpetration.
First,
we
performed
unconditional
univariate
growth
curves
for
each
variable.
The
model
fit
for
each
model
indicated
a
good
fit
of
the
data
(see
Table
3).
The
significant
and
positive,
ˇ
=
.18,
t
=
4.25,
p
<
.001,
and
negative,
ˇ
=
-.18,
t
=
-5.18,
p
<
.001,
slopes
suggest
that
normative
adjustment
and
bullying
perpetra-
tion
tended
to
increase
and
decrease
respectively
during
the
study
period.
The
variances
of
the
slopes
(M
=
.10,
SE
=
.03,
t
=
3.73,
p
<
.001,
and
M
=
.04,
SE
=
.01,
t
=
4.27,
p
<
.001,
respectively)
support
the
idea
that
these
changes
did
not
occur
equally
for
all
adolescents
in
normative
adjustment
and
bullying
perpetration.
In
Figure
2,
the
shaded
arrows
illustrate
the
covariances
between
the
intercept
and
slope
for
each
variable
through
the
unconditional
univariate
growth
model.
The
covariance
between
the
intercept
and
slope
in
normative
adjustment
was
negative,
suggesting
that
those
adoles-
cents
with
higher
baseline
levels
reported
a
reduced
increase
in
normative
adjustment
over
time.
The
negative
covariance
between
the
slope
and
intercept
in
bullying
perpetration
indicates
that
higher
scoring
at
baseline
reported
a
lower
decrease
in
bullying
perpetra-
tion
over
time.
To
test
the
relationships
between
the
trajectories
of
normative
adjustment
and
bullying
perpetration,
we
performed
a
parallel
growth
curve
analysis.
The
resulting
model
fit
indicated
a
good
fit
of
the
data
(see
Table
3).
The
bold
arrows
in
Figure
2
show
the
covariances
between
the
intercepts
and
slopes
across
variables
and
the
effects
of
gender
and
age
as
covariates
through
the
parallel
growth
model.
The
negative
association
between
the
intercepts
indicates
that
individuals
with
higher
initial
levels
of
nor-
mative
adjustment
have
lower
initial
levels
of
bullying
perpetration
and
vice
versa.
The
significant
covariance
between
the
slope
factors
indicates
that
individuals
who
experienced
the
greatest
increases
in
normative
adjustment
reported
the
greatest
decreases
in
bullying
perpetration.
The
positive
covariance
between
the
slope
of
bully-
ing
perpetration
and
the
intercept
of
normative
adjustment
supports
the
idea
that
higher
baseline
levels
in
normative
adjustment
were
associated
with
a
greater
decrease
in
bullying
perpetration.
The
neg-
ative
covariance
between
the
slope
of
normative
adjustment
and
the
intercept
of
bullying
perpetration
indicates
that
higher
base-
line
levels
in
bullying
perpetration
were
associated
with
a
lower
increase
in
normative
adjustment.
Being
a
girl
was
associated
with
a
greater
decrease
in
bullying
perpetration,
while
no
gender
differ-
ences
were
found
in
the
changes
in
normative
adjustment.
Being
a
middle
adolescent
was
associated
with
a
greater
increase
in
nor-
mative
adjustment,
and
a
lower
decrease
in
bullying
perpetration.
Discussion
The
aim
of
this
study
was
to
explore
the
bidirectional
rela-
tionship
between
the
involvement
of
adolescents
in
bullying
perpetration
and
normative
adjustment,
using
longitudinal
mod-
els
which
allowed
us
to
verify
their
interdependence
and
evolution
over
time.
The
RI-CLPM
enabled
us
to
relate
pupils’
aggressive
behaviours
with
their
levels
of
normative
adjustment
in
four
time
periods,
while
considering
the
possible
differentiated
effects
at
between-
and
within-person
level.
In
line
with
the
results
of
pre-
vious
studies
(Laninga-Wijnen
et
al.,
2018;
Mayeux
&
Kraft,
2018;
Pozzoli
et
al.,
2012),
the
model
confirmed
the
negative
relationship
between
the
study
variables
and
their
continuity
over
time,
which
conditions
the
mutual
influence
on
state
characteristics.
On
the
between-person
level,
the
involvement
of
adolescents
in
acts
of
bullying
is
linked
to
lower
normative
adjustment.
The
results
also
show
that
this
inter-subject
behaviour
is
replicated
at
the
intra-
subject
level
through
the
within-person
level,
so
that
there
is
a
cycle
of
influence
between
the
two
constructs.
Students
who
dis-
played
a
greater
increase
in
normative
adjustment
tended
to
show
less
involvement
in
undesirable
behaviour
such
as
aggression,
and
6

ARTICLE IN PRESS
G Model
E.M.
Romera,
M.
Carmona-Rojas,
R.
Ortega-Ruiz
et
al.
Revista
de
Psicodidáctica
xxx
(xxxx)
xxx–xxx
Figure
2.
Results
of
growth
curve
analyses.
Note.
Standardized
coefficients
based
on
unstandardized
coefficients
are
shown.
Shaded
covariances
correspond
to
the
unconditional
univariate
growth
model.
Covariances
and
predictors
in
bold
correspond
to
the
parallel
growth
model.
For
covariates,
the
results
are
presented
in
gender/age.
*
p
<
.05;
**
p
<
.01;
***
p
<
.001.
vice
versa.
That
is,
according
to
the
Hypothesis
1,
normative
adjust-
ment
predicts
bullying
perpetration,
in
the
same
way
that
bullying
perpetration
predicts
the
subsequent
normative
adjustment
at
the
within-person
level
(Hypothesis
2).
Although
previous
stud-
ies
have
highlighted
the
need
to
focus
on
adolescents
with
high
levels
of
bullying
aggression
and
low
normative
adjustment
(at
the
between-person
level),
the
findings
of
the
present
study
stress
the
importance
of
noticing
the
possible
changes
that
may
occur
in
nor-
mative
adjustment
and
bullying
perpetration
among
adolescents
(at
a
within-person
level),
as
this
can
influence
changes
between
the
two
phenomena
without
the
need
for
high
or
low
levels
com-
pared
to
their
peers.
The
present
findings
highlight
the
relevant
role
of
compliance
with
school
norms,
as
a
cause
and
a
consequence
to
bullying
behaviours.
To
prevent
peer
aggression
is
necessary
to
pay
attention
to
students’
motives
and
attitudes
toward
school
norms,
but
also
to
be
involved
in
bullying
will
worsen
the
level
of
compli-
ance
with
a
system
that
regulates
the
quality
of
peer
relationships
(Herrera-López
et
al.,
2016).
The
approach
of
a
longitudinal
analy-
sis
is
a
potentiality
of
this
study
as
it
allows
to
know
the
direction
and
evolution
of
the
influence
of
normative
adjustment
on
bully-
ing
perpetration
over
time.
The
results
identified
also
that
gender
and
age
did
not
moderate
the
negative
association
between
norma-
tive
adjustment
and
bullying
perpetration,
contrary
to
Hypothesis
3.
Despite
previous
and
our
descriptive
results
identify
differences
in
bullying
and
normative
adjustment
(Romera,
Luque
et
al.,
2022;
Smith
et
al.,
2019),
it
does
not
imply
that
the
association
between
both
is
influenced
by
gender
and
age.
Conducting
a
growth
curve
analysis
of
the
variables
has
enabled
us
to
overcome
the
limitations
inherent
to
previous
cross-sectional
investigations
and
to
verify
the
trend
of
these
behaviours
over
time.
Here,
the
trajectory
of
bullying
tends
to
decrease
over
time,
while
normative
adjustment
tends
to
increase.
These
results
confirm
the
hypothesis
4
and
5.
Previous
studies
have
identified
a
decreasing
tendence
in
bullying
in
middle
school,
explained
by
the
social
and
cognitive
development
at
these
ages
(Cho
&
Lee,
2020)
and
a
more
adjusted
behaviour
to
school
norms
(Ettekal
&
Shi,
2020).
Moreover,
according
to
hypothesis
6,
we
found
a
negative
common
devel-
opment
between
normative
adjustment
and
bullying
perpetration
over
time.
The
increase
in
normative
adjustment
over
time
was
associated
with
a
decrease
in
bullying
perpetration.
These
results
support
the
overlap
between
both
variables,
implying
that
changes
in
one
variable
imply
inversely
changes
in
the
other
one.
This
research
has
certain
limitations.
Firstly,
there
is
a
bias
in
the
selection
of
the
sample,
which
was
deliberately
limited
to
one
specific
geographical
area:
if
the
models
proposed
were
applied
to
schoolchildren
from
other
communities,
this
would
give
greater
validity
to
the
results
obtained.
Second,
it
should
be
noted
that
self-reports
were
used
exclusively
for
the
adolescents’
behaviour,
with
a
single
group
of
informants.
Thirdly,
only
two
variables
were
explored.
It
would
be
interesting
to
analyse
the
effect
of
other
vari-
ables
whose
relationship
with
bullying
and
normative
adjustment
is
identified,
as
popularity.
Need
for
popularity
could
explain
the
relationship
between
both
variables
precisely
because
adolescents
continually
strive
for
prominence
and
prestige
within
their
peer
group
and
going
against
norms
may
be
considered
as
a
strategy
to
achieve
this
popularity
(Romera
et
al.,
2021).
It
would
also
be
of
interest
to
extend
the
study
of
the
effect
of
normative
adjust-
ment
to
prosocial
defensive
behaviour,
and
to
teachers
views
of
adolescents’
attitudes
towards
classroom
norms.
The
results
of
this
study
may
guide
educational
intervention
programs
towards
fostering
improvements
in
peer
relationships
in
schools
and
bullying
prevention.
This
study
highlights
the
impor-
tance
of
engage
students
in
school
norms
in
a
way
that
they
value
them
and
incorporate
in
their
lifestyle
(Llorent
et
al.,
2021).
It
is
also
essential
to
establish
school
norms
accepted
and
trans-
ferred
to
their
daily
relationships
to
prevent
undesirable
behaviour
like
bullying
behaviour
(Mora-Merchán
et
al.,
2021).
The
chal-
lenge
for
education
is
therefore
to
try
adolescents
recognise
an
7

ARTICLE IN PRESS
G Model
E.M.
Romera,
M.
Carmona-Rojas,
R.
Ortega-Ruiz
et
al.
Revista
de
Psicodidáctica
xxx
(xxxx)
xxx–xxx
interdependence
between
their
attitude
to
school
and
their
psycho-
logical,
social
and
emotional
well-being,
which
encourages
them
to
develop
supportive
links
with
the
school
in
order
to
improve
school
climate
in
schools.
Funding
This
study
was
supported
by
the
Spanish
National
Research
Agency—Ministerio
de
Ciencia
e
Innovación
(PDC2021-121741-
I00).
Funding
for
open
access
charge:
Universidad
de
Córdoba
/
CBUA.
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8