The Humour and bullying project:
Modelling cross-lagged and dyadic data.
Dr Simon C. Hunter
School of Psychological Sciences and Health,
University of Strathclyde
email: simon.hunter@strath.ac.uk
This research was funded by the Economic and Social Research Council, award
reference RES-062-23-2647.
Project team and info
P.I.: Dr Claire Fox, Keele University
Research Fellow: Dr Siân Jones
Project team: Sirandou Saidy Khan, Hayley Gilman, Katie Walker,
Katie Wright-Bevans, Lucy James, Rebecca Hale, Rebecca Serella,
Toni Karic, Mary-Louise Corr, Claire Wilson, and Victoria Caines.
Thanks and acknowledgements:
Teachers, parents and children in the participating schools.
The ESRC.
More info:
Project blog: http://esrcbullyingandhumourproject.wordpress.com/
Twitter: @Humour_Bullying
Overview
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Background and rationale to the Humour & Bullying project
Methods used in the project
AMOS – what is it, why use it (and pertinently, why not)?
Measurement models – achieving fit.
Cross-lagged analyses
Dyadic data – issues and analyses
Summary
Humour
What functions does humour serve?
Social: Strengthening relationships,
but also excluding, humiliating, or
manipulating others (Martin, 2007).
Personal: To cope with dis/stress,
esp. in reappraisal and in ‘replacing’
negative feelings (Martin, 2007).
Both of these functions are directly relevant to bullying and peervictimisation contexts.
Humour
Multi-dimensional (Fox et al., in press; Martin, 2007):
• Self-enhancing: Not detrimental toward others (e.g. ‘I find that
laughing and joking are good ways to cope with problems’).
• Aggressive: Enhancing the self at the expense of others (e.g. ‘If
someone makes a mistake I often tease them about it’).
• Affiliative: Enhances relationships and can reduce interpersonal
tensions (e.g. ‘I often make people laugh by telling jokes or funny stories’).
• Self-defeating: Enhances relationships, but at the expense of
personal integrity or one’s own emotional needs (e.g. ‘I often put
myself down when making jokes or trying to be funny’).
Peer-victimisation
• Repeated attacks on an individual.
• Conceptualised as a continuum rather than a category.
Also multi-dimensional in nature:
• Verbal: Being teased or called names.
• Physical: Hitting, kicking etc. Also
includes property damage.
• Social: Exclusion, rumour spreading.
Peer-victimisation
• Clearly a stressful experience for many young people,
associated with depressive symptomatology (Hunter et al., 2007, 2010),
anxiety (Visconti et al., 2010), self-harm (Viljoen et al., 2005) and suicidal
ideation (Dempsey et al., 2011; Kaltiala-Heino et al., 2009), PTSD (Idsoe et al.,
2012; Tehrani et al., 2004), loneliness (Catterson & Hunter, 2010; Woodhouse et al.,
2012), psychosomatic problems (Gini & Pozzoli, 2009), ...etc
• Also a very social experience – peer roles can be broader than
just victim or aggressor (Salmivalli et al., 1996).
Peer-victimisation
Klein and Kuiper (2008):
• Children who are bullied have much less opportunity to interact
with their peers and so are at a disadvantage with respect to the
development of humour competence.
 Cross-sectional data support: Peer-victimisation is negatively
correlated with both affiliative and self-enhancing humour (Fox &
Lyford, 2009).
 May be particularly true for victims of social aggression.
Victims gravitate toward more use of self-defeating humour?
 May be particularly true for victims of verbal aggression as
peers directly supply the victim with negative self-relevant
cognitions such as “You’re a loser”, “You’re stupid” etc which
are internalised (see also Rose & Abramson, 1992, re. depressive cognitions).
Research aims
Primarily, to evaluate the relationship between humour use,
involvement in bullying (as victim or aggressor), and adjustment
 Testing causal hypotheses, e.g., verbal victimisation will cause
an increase in levels of self-defeating humour (Rose & Abramson,
1992)
 Evaluating proposed explanatory causal pathways, e.g. the
effect of victimisation on mental health is mediated via negative
humour styles
 Evaluating humour as a risk / resilience factor, e.g. high levels
of positive humour may buffer young people against the
negative effects of peer-victimisation
 Assessing whether friendships serve as a contextual risk factor
for peer-victimisation
Research aims
Primarily, to evaluate the relationship between humour use,
involvement in bullying (as victim or aggressor), and adjustment
 Testing causal hypotheses, e.g., verbal victimisation will cause
an increase in levels of self-defeating humour (Rose & Abramson,
1992)
 Evaluating proposed explanatory causal pathways, e.g. the
effect of victimisation on mental health is mediated via negative
humour styles
 Evaluating humour as a risk / resilience factor, e.g. high levels of
positive humour may buffer young people against the negative
effects of peer-victimisation
 Assessing whether friendships serve as a contextual risk factor
for peer-victimisation
Methods
• N=1241 (612 male), 11-13 years old, from six Secondary schools
in England.
• Data collected at two points in time: At the start and at the end of
the 2011-2012 school session.
• Data collection spread over two sessions at each time point due
to number of tasks.
• N=807 present at all four data collection sessions.
Measures
Self-Report:
• 24-item Child Humour Styles Questionnaire (Fox et al., in press).
• 10-item Children’s Depression Inventory
– Short Form (Kovacs, 1985).
• 36-item Victimisation and Aggression
(Owens et al., 2005).
• 10-item Self-esteem (Rosenberg, 1965).
• 4-item Loneliness
et al., 2005).
(Asher et al., 1984; Rotenberg
Measures
Peer-nomination:
• Rated liking of all peers (Asher & Dodge, 1986).
• Nominated friends and very best friend (Parker & Asher, 1993).
• Peer-victimisation and use of aggression (Björkqvist et al., 1992),
participants nominated up to three peers for Verbal, Physical, and
Indirect. This was an 8-item measure.
 Verbal: “Gets called nasty names by other children.”
 Physical: “Gets kicked, hit and pushed around by other children.”
 Indirect – “Gets left out of the group by other children” and “Has nasty
rumours spread about them by other children.”
• Humour (adapted from Fox et al., in press). This was a 4-item measure,
young people nominated up to three peers for each item.
AMOS
• Easy to use graphical interface, comes as an SPSS bolt-on.
• Can use for path analysis, assessment of measurement models,
and structural equation modeling.
• Includes features such as bootstrapping, modification indices,
assessment of multivariate normality etc.
 But… these can’t be used if you have missing data, on
relevant items, in your SPSS data file!
Measurement models
Measurement models describe the relationships between
indicators and latent variables.
Latent variable 
Depression
Manifest indicators 
Item 1
Item 2
Error 
error1
error2
Item 3
error3
Measurement models
Measurement models may have more complex structures.
Physical
Victimisation
Verbal
Victimisation
Item 1
Item 2
Item 3
Item 1
Item 2
Item 3
error1
error2
error3
error4
error5
error6
Measurement models
General
Victimisation
Resid2
Resid1
Physical
Victimisation
Verbal
Victimisation
Item 1
Item 2
Item 3
Item 1
Item 2
Item 3
error1
error2
error3
error4
error5
error6
Measurement models
Measurement models may fit well when you model them in a
straightforward manner in AMOS (like those just shown).
If they don’t fit well, there are different ways to try and improve fit.
Measurement models
Correlate error terms:
Physical
Victimisation
Verbal
Victimisation
Item 1
Item 2
Item 3
Item 1
Item 2
Item 3
error1
error2
error3
error4
error5
error6
Measurement models
Model the method variance:
Depression
Item 1
[R]
Item 2
Item 3
[R]
Item 4
Item 5
[R]
Item 6
error1
error2
error3
error4
error5
error6
Method
Measurement models
Create ‘parcels’ (Bandalos, 2002; Little et al., 2002) so that this…
Depression
Item 1
Item 2
Item 3
Item 4
Item 5
Item 6
error1
error2
error3
error4
error5
error6
Measurement models
…becomes this
Depression
Parcel 1
Parcel 2
Parcel 3
error1
error3
error5
Parcelling
• Most likely to do this if you have a factor which has lots of items.
• Need unidimensional construct: Parcelling is problematic if you
are unsure of the factor structure. Little et al. (2002) suggest this
is the biggest threat in terms of model misspecification.
 Clearly, cannot be used when the goal of your analysis is to
understand fully the relations among items
• Some measures actually come with instructions to parcel
Control, Agency, and Means–Ends Interview: Little et al., 1995)
(e.g. the
Parcelling
• May improve fit because fewer parameters are being estimated
(so better sample size to variable ratio). This can therefore also
be a way to deal with smaller sample sizes when you have
measures with lots of indicators.
 But, likely to improve fit across all models regardless of
whether they are correctly specified – increasing the chances
that we will fail to reject a model which should be rejected
(Type II error)
Cross-lagged analyses
Cross-sectional data are restricted in terms of unpacking causation
relating to two correlated variables. Three explanations:
• Omitted variable accounts for correlation
• Both variables influence the other
• One variable influences the other
Verbal
Victimisation
Self-Defeating
Humour
Symptoms of
Depression
Cross-lagged analyses
Cross-lagged data, sometimes called panel data, allow us to move
forward in our understanding of how the variables influence each
other.
• ‘A happened, followed by B’ design
• More complex to analyse than cross-sectional data
Critique
• Omitted variable bias still a problem.
• Only looks at group level change, not individual level (where
latent growth curve models might be more appropriate)
Cross-lagged analyses
The cross-lagged model (also referred to as a simplex model, an
autoregressive model, a conditional model, or a transition model).
T1
Victimisation
T2
Victimisation
e
e
T1
Depression
T2
Depression
Can the history of victimisation predict depression, taking into
consideration the history of depression (and vice-versa)?
Cross-lagged analyses
Can also include time-invariant predictors in the model.
T1
Victimisation
T2
Victimisation
e
e
T1
Depression
T2
Depression
Gender
Cross-lagged analyses
NB – the model can be extended to incorporate further time points.
e
e
T1
Victimisation
T2
Victimisation
T3
Victimisation
T1
Depression
T2
Depression
T3
Depression
e
e
Cross-lagged analyses
Analysis 1: Victimisation and Internalising
Internalising = withdrawal, anxiety, fearfulness, and depression
(Rapport et al., 2001). Operationalised here as symptoms of depression
and loneliness.
Competing models:
A stability-only model
• Stability paths
T1 Social
Victimisation
T2 Social
Victimisation
T1 Verbal
Victimisation
T2 Verbal
Victimisation
T1 Physical
Victimisation
T2 Physical
Victimisation
T1
Internalising
T2
Internalising
Competing models:
A stability and a restricted cross-lagged model
• Stability paths
• PLUS cross-lagged within related concept only (victimisation)
T1 Social
Victimisation
T2 Social
Victimisation
T1 Verbal
Victimisation
T2 Verbal
Victimisation
T1 Physical
Victimisation
T2 Physical
Victimisation
T1
Internalising
T2
Internalising
Competing models:
A fully cross-lagged model
• Stability paths, cross-lagged within related concept
• Cross-lagged across all variables
T1 Social
Victimisation
T2 Social
Victimisation
T1 Verbal
Victimisation
T2 Verbal
Victimisation
T1 Physical
Victimisation
T2 Physical
Victimisation
T1
Internalising
T2
Internalising
Cross-lagged analyses
Fit indices
• Chi-square: ideally, non-significant.
• CMIN/DF: under 2 or 3.
• CFI: > .95 = good, >.90 = adequate.
• RMSEA: < .050 = good, < .080 = adequate.
Results:
• Model comparisons: All models significantly different from each
other (ΔX2, p < .001).
Cross-lagged analyses
Results:
X2
CMIN/DF
CFI
RMSEA
Model 1
105.98 (df = 23),
p < .001
4.608
.987
.054
(.044, .065)
Model 2
57.51 (df = 17),
p < .001
3.383
.994
.044
(.032, .057)
Model 3
10.24 (df = 11),
p = .509
0.931
1.000
.000
(.000, .028)
Cross-lagged analyses
Cross-sectional results:
• Different forms of peer-victimisation all positively associated with
each other (T1 = .69 to .78; T2 = .57 to .69).
• Different forms of peer-victimisation all positively associated with
internalising. Verbal = .54 (T2 = .39), Physical = .46 (T2 = .23),
Social = .59 (T2 = .43).
 Social and verbal seem most problematic
Cross-lagged analyses
Cross-Lagged Results (only significant paths shown)
T1 Verbal
Victimisation
T2 Verbal
Victimisation
.11
.36
-.14
T1 Social
Victimisation
T1 Physical
Victimisation
.37
T2 Social
Victimisation
.47
T2 Physical
Victimisation
.12
.10
.15
.17
.13
T1
Internalising
.57
T2
Internalising
Cross-lagged analyses
Analysis 2: Victimisation, Humour, and Internalising
Cross-lagged analyses
Results:
• Model comparisons: All models were again significantly different
from each other (ΔX2, p < .001).
X2
CMIN/DF
CFI
RMSEA
Model 1
283.54 (df = 83),
p < .001
3.416
.977
.044
(.039, .050)
Model 2
175.54 (df = 63),
p < .001
2.786
.987
.038
(.031, .045)
Model 3
36.58 (df = 27),
p = .103
1.355
.999
.017
(.000, .030)
Cross-lagged analyses
Cross-sectional associations: T1 (T2)
2. Agg
3. SD
4. SE
1. Aff Hum
.13 (.06)
-.16 (-.22)
.35 (.26)
2. Agg Hum
-
.14 (.19)
.04 (-.04)
.07 (.04)
.09 (.07)
.03 (.01)
-.05 (.02)
-
.09 (.01)
.38 (.28)
.31 (.17)
.34 (.23)
.49 (.48)
3. SD Hum
4. SE Hum
5. Verbal
6. Physical
7. Social
8. Interlsng
-
5. Verb
6. Phys
7. Soc
8. Int
-.15 (-.12) -.14 (-.10) -.16 (-.17) -.38 (-.31)
-.06 (-.04) -.04 (-.04) -.07 (-.06) -.20 (-.25)
-
.73 (.65)
.78 (.69)
.53 (.38)
-
.69 (.57)
.46 (.23)
-
.59 (.43)
-
Time 2
Time 1
Self-Defeating
Humour
Self-Defeating
Humour
.11
.13
Aggressive
Humour
.07
Aggressive
Humour
.07
Self-Enhancing
Humour
Affiliative
Humour
Self-Enhancing
Humour
Affiliative
Humour
.08
.20
Verbal
Victimisation
-.14
-.14
Social
Victimisation
-.13
.13
Physical
Victimisation
T1
Internalising
-.17
.09
Verbal
Victimisation
Social
Victimisation
.12
.15
.12
Physical
Victimisation
T2
Internalising
Cross-lagged analyses
Method summary
• Useful for beginning to disentangle cause and effect
• Not a panacea – still has limitations
Results summary
• Humour may be self-reinforcing (virtuous cycle…of sorts)
• (Mal)adjustment appears to be an important driver of both
humour use and peer-victimisation
 Implications for intervention re. adolescent mental health and
adolescent attitudes toward those with mental health issues
Dyadic analyses - APIM
Children in friendships are likely to produce data
which are related in some way, violating the
normal assumption that all data are independent.
Usually, we just ignore this.
Shared experiences may shape friends’ similarity
or their similarity may be what the attraction was to
begin with.
The Actor-Partner Independence Model (APIM: Kenny,
1996) makes a virtue of this data structure.
Can conduct APIM analyses in SEM, or using MLM (where individual
scores are seen as nested within groups with an n of 2)
Dyadic analyses
Looks a lot like the cross-lagged analysis
T1
Victimisation
T2
Victimisation
e
e
Friend’s T1
Victimisation
Friend’s T2
Victimisation
However, the data structure in SPSS is very different.
Dyadic analyses
Standard data entry in SPSS:
ParticipantT1
ParticipantT2
Person 1
Data
Data
Person 2
Data
Data
Person 3
Data
Data
Person 4
Data
Data
Dyadic analyses
For APIM, data is entered by dyad, not person:
ParticipantT1
FriendT1
ParticipantT2
FriendT2
Dyad 1
Data
Data
Data
Data
Dyad 2
Data
Data
Data
Data
Dyad 3
Data
Data
Data
Data
Dyad 4
Data
Data
Data
Data
Dyadic analyses
We can evaluate “actor effects”
T1
Victimisation
T2
Victimisation
e
e
Friend’s T1
Victimisation
Friend’s T2
Victimisation
Dyadic analyses
We can evaluate “partner effects”
T1
Victimisation
T2
Victimisation
e
e
Friend’s T1
Victimisation
Friend’s T2
Victimisation
Dyadic analyses
We can evaluate the simple correlation between partners
T1
Victimisation
T2
Victimisation
e
e
Friend’s T1
Victimisation
Friend’s T2
Victimisation
Dyadic analyses
An important issue is the nature of the dyads you have, either
indistinguishable or distinguishable.
Analyses differ according to the type of dyad you have.
Dyadic analyses
Indistinguishable dyads: Best friends.
ParticipantT1
FriendT1
ParticipantT2
FriendT2
Dyad 1
Data
Data
Data
Data
Dyad 2
Data
Data
Data
Data
Dyad 3
Data
Data
Data
Data
Dyad 4
Data
Data
Data
Data
Dyadic analyses
Indistinguishable dyads: Best friends.
ParticipantT1
FriendT1
ParticipantT2
FriendT2
Dyad 1
Data
Data
Data
Data
Dyad 2
Data
Data
Data
Data
Dyad 3
Data
Data
Data
Data
Dyad 4
Data
Data
Data
Data
Dyadic analyses
Distinguishable dyads: Victim and Aggressor.
VictimT1
AgrsorT1
VictimT2
AgrsorT2
Dyad 1
Data
Data
Data
Data
Dyad 2
Data
Data
Data
Data
Dyad 3
Data
Data
Data
Data
Dyad 4
Data
Data
Data
Data
Dyadic analyses
Indistinguishable dyads
T1
Victimisation
T2
Victimisation
e
e
Friend’s T1
Victimisation
Friend’s T2
Victimisation
Within-person effects must be constrained to be equal
Dyadic analyses
Indistinguishable dyads
T1
Victimisation
T2
Victimisation
e
e
Friend’s T1
Victimisation
Partner effects must be constrained to be equal
Friend’s T2
Victimisation
Dyadic analyses
Indistinguishable dyads
T1
Victimisation
T2
Victimisation
e
e
Friend’s T1
Victimisation
Friend’s T2
Victimisation
Intercepts for the Time 2 variables must be constrained to be equal
Dyadic analyses
Indistinguishable dyads
T1
Victimisation
T2
Victimisation
e
e
Friend’s T1
Victimisation
Friend’s T2
Victimisation
The means and variances of both Time 1 variables must be
constrained to be equal
Dyadic analyses
Indistinguishable dyads
T1
Victimisation
T2
Victimisation
e
e
Friend’s T1
Victimisation
Friend’s T2
Victimisation
The variances of the residual variances must be equal
Dyadic analyses
Distinguishable dyads: e.g. Victim with Non-Victimised Best Friend
Victim’s
Depression
T1
Victim’s
Depression
T2
e
e
Victim’s Friend’s
Depression T1
Victim’s Friend’s
Depression T1
We implement none of the preceding constraints.
We can now have more complex patterns: e.g. victim’s level of
depression may predict non-victim’s depression but not vice-versa.
Dyadic analyses
• ‘Couple’ pattern (actor and partner effects are equal and of the
same sign).
• ‘Contrast’ pattern (actor and partner effects are equal but have
opposite signs).
• ‘Actor-only’ pattern (an actor effect but no partner effect)
• ‘Partner-only’ pattern (a partner effect but no actor effect)
Kenny & Ledermann (2010) recommend calculating a parameter
they introduce called k to quantitatively assess what kind of patternn
you have:
To calculate k, you use ‘phantom variables’
(not going into this today)
Dyadic analyses
Humour & Bullying Data
Indistinguishable dyads: Best friends.
• Ndyad = 457 (best friends at T1)
First APIM:
• Depressive symptomatology of best friend dyads.
Dyadic analyses
This is a saturated model, therefore there is ‘perfect fit’
Dyadic analyses
Depression
.59
T2 Depression
.59
T2 Friend’s
Depression
.12
.12
Friend’s
Depression
Actor effect is significant: .59, p < .001
Partner effect is also significant: .12, p < .001
Dyadic analyses
Second APIM:
• Depressive Symptomatology of Best Friend Dyads.
• Victimisation of Best Friend Dyads
 Earlier analyses suggested that mental health
victimisation. True for friend effects too?
drove
Dyadic analyses
Cross-lagged analyses
Cross-sectional ACTOR (& PARTNER) correlations at T1
1. Depression
2. Social
3. Verbal
4. Physical
1. Depression
2. Social
3. Verbal
4. Physical
N/A (.18)
.44 (.09)
.40 (.10)
.36 (.06)
N/A (.12)
.80 (.12)
.68 (.05)
N/A (.16)
.70 (.12)
N/A (.14)
• Strong actor correlations between constructs, all positive
• Partner correlations between social/verbal victimisation and
depression, and between verbal and physical victimisation
Time 2
Time 1
Depression
Friend’s
Depression
Verbal
Victimisation
Friend’s Verbal
Victimisation
Social
Victimisation
Friend’s Social
Victimisation
.58
.08
.08
.58
.28
.34
.34
-.12
.28
.11
Friend’s Physical
Victimisation
.11
Friend’s
Depression
Verbal
Victimisation
Friend’s Verbal
Victimisation
.52
Social
Victimisation
.52
Friend’s Social
Victimisation
.29
Physical
Victimisation
.29
Friend’s Physical
Victimisation
-.12
Physical
Victimisation
Depression
Time 2
Time 1
.58
Depression
Friend’s
Depression
Verbal
Victimisation
Depression
.08
.08
Friend’s
Depression
.58
.24
.24
Friend’s Verbal
Victimisation
Verbal
Victimisation
Friend’s Verbal
Victimisation
.34
Social
Victimisation
Social
Victimisation
.34
Friend’s Social
Victimisation
Physical
Victimisation
Friend’s Physical
Victimisation
.22
.22
Friend’s Social
Victimisation
Physical
Victimisation
Friend’s Physical
Victimisation
Time 1
Time 2
Depression
Depression
.23
Friend’s
Depression
Verbal
Victimisation
Friend’s Verbal
Victimisation
Social
Victimisation
.23
Verbal
Victimisation
.28
.34
.28
Friend’s
Depression
Friend’s Verbal
Victimisation
.34
.12
Social
Victimisation
.12
Friend’s Social
Victimisation
Friend’s Social
Victimisation
.16
Physical
Victimisation
Friend’s Physical
Victimisation
.16
Physical
Victimisation
Friend’s Physical
Victimisation
Time 1
Time 2
Depression
Depression
Friend’s
Depression
Friend’s
Depression
.24
.24
-.19
-.19
Verbal
Victimisation
-.35
Friend’s Verbal
Victimisation
Social
Victimisation
Friend’s Social
Victimisation
Physical
Victimisation
Friend’s Physical
Victimisation
.16
.16
-.35
.52
-.12
Verbal
Victimisation
Friend’s Verbal
Victimisation
Social
Victimisation
Friend’s Social
Victimisation
-.12
.52
-.25
-.25
Physical
Victimisation
Friend’s Physical
Victimisation
Time 1
Time 2
Depression
Depression
Friend’s
Depression
Friend’s
Depression
Verbal
Victimisation
Verbal
Victimisation
Friend’s Verbal
Victimisation
Friend’s Verbal
Victimisation
Social
Victimisation
-.16
Social
Victimisation
-.16
Friend’s Social
Victimisation
Friend’s Social
Victimisation
Physical
Victimisation
Friend’s Physical
Victimisation
.29
.11
.11
.29
Physical
Victimisation
Friend’s Physical
Victimisation
Dyadic analyses
Summary
• Friendships as context for development of worsening victimisation
(except for social victimisation)
• Verbal victimisation seems to be most problematic for friends of
victims, not those experiencing it
• Conversely, social victimisation seems to be ‘good’ for friends of
victims
• Physical victimisation has fewer effects
• Can be... challenging to report results!
Summary
AMOS
• Easy to use, accessible, though can be limited
• Trouble shooting fairly straightforward
Cross-lagged analyses
• Good way to address limitations of cross-sectional designs
• Pretty straightforward to analyse, even with a number of variables
• Still has limitations
APIM analyses
• Can reveal very different picture to cross-lagged analyses
• Can be quite complex to build model in AMOS, especially when
multiple variables included
Further reading
Bandalos, D.L. (2002). The effect of item parceling on goodness-of-fit and parameter estimate bias in
structural equation modeling. Structural Equation Modeling, 9, 78-102.
Berrington, A. (2006). An overview of methods for the analysis of panel data. ESRC National Centre for
Research Methods Briefing Paper / 007.
Cook, W.L., & Kenny, D.A. (2005). The Actor-Independence Model: A model of bidirectional effects in
developmental studies. International Journal of Behavioral Development, 29, 101-109.
Farrell, A.D. (1994). Structural equation modeling with longitudinal data: Strategies for examining group
differences and reciprocal relationships. Journal of Consulting and Clinical Psychology, 62, 477-487.
Holt, J.K. (2004). Item parceling in structural equation models for optimum solutions. Paper presented at
the Annual Meeting of the Mid-Western Educational Research Association, October 13 – 16,
Columbus, OH.
Kenny, D.A. (1996). Models of non-independence in dyadic research. Journal of Social and Personal
Relationships, 13, 279.
Lederman, T., Macho, S., & Kenny, D.A. (N/A) Assessing mediation in dyadic data using APIM.
[powerpoint slides]
Little, T.D., Cunningham, W.A., Shahar, G., & Widaman, K.F. (2002). To parcel or not to parcel: Exploring
the question, weighing the merits. Structural Equation Modeling, 9, 151-173.