The Humour and bullying project: Modelling cross-lagged and dyadic data.
Dr Simon C. HunterSchool of Psychological Sciences and Health,
University of Strathclydeemail: [email protected]
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 UniversityResearch Fellow: Dr Siân JonesProject 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
• 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
Overview
Humour
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).
What functions does humour serve?
Both of these functions are directly relevant to bullying and peer-victimisation contexts.
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’).
Humour
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.
• 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
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).
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
Research aims
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 (Asher et al., 1984; Rotenberg et
al., 2005).
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.
• 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!
AMOS
Measurement models describe the relationships between indicators and latent variables.
Latent variable
Manifest indicators
Error
Measurement models
Depression
Item 1 Item 2 Item 3
error1 error2 error3
Measurement models may have more complex structures.
Measurement models
Item 1 Item 2 Item 3
error1 error2 error3
Verbal Victimisation
Item 1 Item 2 Item 3
error4 error5 error6
PhysicalVictimisation
Measurement models
Item 1 Item 2 Item 3
error1 error2 error3
Verbal Victimisation
Item 1 Item 2 Item 3
error4 error5 error6
PhysicalVictimisation
General Victimisation
Resid2Resid1
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
Measurement models
Item 1 Item 2 Item 3
error1 error2 error3
Verbal Victimisation
Item 1 Item 2 Item 3
error4 error5 error6
PhysicalVictimisation
Correlate error terms:
Measurement modelsModel the method variance:
Item 1[R] Item 2 Item 3
[R]
error1 error2 error3
Item 4 Item 5[R] Item 6
error4 error5 error6
Depression
Method
Measurement modelsCreate ‘parcels’ (Bandalos, 2002; Little et al., 2002) so that this…
Item 1 Item 2 Item 3
error1 error2 error3
Item 4 Item 5 Item 6
error4 error5 error6
Depression
Measurement models…becomes this
Parcel 1 Parcel 2
error1 error3
Parcel 3
error5
Depression
• 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 (e.g. the Control, Agency, and Means–Ends Interview: Little et al., 1995)
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)
Parcelling
Cross-sectional data are restricted in terms of unpacking causation relating to two correlated variables. Three explanations:
Cross-lagged analyses
• Both variables influence the other• One variable influences the other
VerbalVictimisation
• Omitted variable accounts for correlation
Self-DefeatingHumour
Symptoms ofDepression
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
Cross-lagged analyses
T1Victimisation
T2Depression
T2Victimisation
T1Depression
e
e
The cross-lagged model (also referred to as a simplex model, an autoregressive model, a conditional model, or a transition model).
Can the history of victimisation predict depression, taking into consideration the history of depression (and vice-versa)?
Cross-lagged analyses
T1Victimisation
T2Depression
T2Victimisation
T1Depression
e
e
Can also include time-invariant predictors in the model.
Gender
Cross-lagged analyses
NB – the model can be extended to incorporate further time points.
T1Victimisation
T2Depression
T2Victimisation
T1Depression
e
e
T3Depression
T3Victimisation
e
e
Analysis 1: Victimisation and Internalising
Internalising = withdrawal, anxiety, fearfulness, and depression (Rapport et al., 2001). Operationalised here as symptoms of depression and loneliness.
Cross-lagged analyses
A stability-only model• Stability paths
Competing models:
T1 PhysicalVictimisation
T2 PhysicalVictimisation
T1Internalising
T1 VerbalVictimisation
T2 VerbalVictimisation
T1 SocialVictimisation
T2 SocialVictimisation
T2Internalising
A stability and a restricted cross-lagged model• Stability paths• PLUS cross-lagged within related concept only (victimisation)
Competing models:
T1 PhysicalVictimisation
T2 PhysicalVictimisation
T1 VerbalVictimisation
T2 VerbalVictimisation
T1 SocialVictimisation
T2 SocialVictimisation
T1Internalising
T2Internalising
A fully cross-lagged model• Stability paths, cross-lagged within related concept • Cross-lagged across all variables
Competing models:
T1 PhysicalVictimisation
T2 PhysicalVictimisation
T1 VerbalVictimisation
T2 VerbalVictimisation
T1 SocialVictimisation
T2 SocialVictimisation
T1Internalising
T2Internalising
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:
Cross-lagged analyses
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-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 PhysicalVictimisation
T2 PhysicalVictimisation
T1 SocialVictimisation
T2 SocialVictimisation
T1 VerbalVictimisation
T2 VerbalVictimisation
Cross-lagged analyses
.11
-.14
.12
.10
.15.17
.13
.57
.47
.37
.36
T1Internalising
T2Internalising
Analysis 2: Victimisation, Humour, and Internalising
Cross-lagged analyses
Results:• Model comparisons: All models were again significantly different
from each other (ΔX2, p < .001).
Cross-lagged analyses
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-sectional associations: T1 (T2)
Cross-lagged analyses
2. Agg 3. SD 4. SE 5. Verb 6. Phys 7. Soc 8. Int
1. Aff Hum .13 (.06) -.16 (-.22) .35 (.26) -.15 (-.12) -.14 (-.10) -.16 (-.17) -.38 (-.31)
2. Agg Hum - .14 (.19) .04 (-.04) .07 (.04) .09 (.07) .03 (.01) -.05 (.02)
3. SD Hum - .09 (.01) .38 (.28) .31 (.17) .34 (.23) .49 (.48)
4. SE Hum - -.06 (-.04) -.04 (-.04) -.07 (-.06) -.20 (-.25)
5. Verbal - .73 (.65) .78 (.69) .53 (.38)
6. Physical - .69 (.57) .46 (.23)
7. Social - .59 (.43)
8. Interlsng -
PhysicalVictimisation
SocialVictimisation
VerbalVictimisation
-.13
.13
.09 .12
.15
.12
Self-Enhancing Humour
Affiliative Humour
Aggressive Humour
Self-Defeating Humour
PhysicalVictimisation
SocialVictimisation
VerbalVictimisation
Self-Enhancing Humour
Affiliative Humour
Aggressive Humour
Self-Defeating Humour
Time 1 Time 2
.13
.08
.07
.07
-.14
.20 -.17-.14
.11
T1Internalising
T2Internalising
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
T1Victimisation
Friend’s T2Victimisation
T2Victimisation
Friend’s T1Victimisation
e
e
Looks a lot like the cross-lagged analysis
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”
T1Victimisation
Friend’s T2Victimisation
T2Victimisation
Friend’s T1Victimisation
e
e
Dyadic analyses
We can evaluate “partner effects”
T1Victimisation
Friend’s T2Victimisation
T2Victimisation
Friend’s T1Victimisation
e
e
Dyadic analyses
We can evaluate the simple correlation between partners
T1Victimisation
Friend’s T2Victimisation
T2Victimisation
Friend’s T1Victimisation
e
e
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
Within-person effects must be constrained to be equal
T1Victimisation
Friend’s T2Victimisation
T2Victimisation
Friend’s T1Victimisation
e
e
Dyadic analyses
Indistinguishable dyads
Partner effects must be constrained to be equal
T1Victimisation
Friend’s T2Victimisation
T2Victimisation
Friend’s T1Victimisation
e
e
Dyadic analyses
Indistinguishable dyads
Intercepts for the Time 2 variables must be constrained to be equal
T1Victimisation
Friend’s T2Victimisation
T2Victimisation
Friend’s T1Victimisation
e
e
Dyadic analyses
Indistinguishable dyads
The means and variances of both Time 1 variables must be constrained to be equal
T1Victimisation
Friend’s T2Victimisation
T2Victimisation
Friend’s T1Victimisation
e
e
Dyadic analyses
Indistinguishable dyads
The variances of the residual variances must be equal
T1Victimisation
Friend’s T2Victimisation
T2Victimisation
Friend’s T1Victimisation
e
e
Dyadic analyses
Victim’s Depression
T1
Victim’s Friend’sDepression T1
Victim’s Depression
T2
Victim’s Friend’sDepression T1
e
e
Distinguishable dyads: e.g. Victim with Non-Victimised Best Friend
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
T2 Friend’s Depression
T2 Depression
Friend’s Depression
.59
.59
.12
.12
Actor effect is significant: .59, p < .001Partner 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 drove victimisation. True for friend effects too?
Dyadic analyses
Cross-sectional ACTOR (& PARTNER) correlations at T1
Cross-lagged analyses
1. Depression 2. Social 3. Verbal 4. Physical
1. Depression N/A (.18) .44 (.09) .40 (.10) .36 (.06)
2. Social N/A (.12) .80 (.12) .68 (.05)
3. Verbal N/A (.16) .70 (.12)
4. Physical N/A (.14)
• Strong actor correlations between constructs, all positive• Partner correlations between social/verbal victimisation and
depression, and between verbal and physical victimisation
PhysicalVictimisation
Friend’s PhysicalVictimisation
Friend’s SocialVictimisation
Social Victimisation
Verbal Victimisation
Friend’s Verbal Victimisation
Friend’s Depression
Depression
PhysicalVictimisation
Friend’s PhysicalVictimisation
Friend’s SocialVictimisation
SocialVictimisation
Verbal Victimisation
Friend’s Verbal Victimisation
Friend’s Depression
Depression
Time 1 Time 2
.34
.34
.11
.11
.08
.08
-.12
-.12
.58
.58
.28
.28
.52
.52
.29
.29
PhysicalVictimisation
Friend’s PhysicalVictimisation
Friend’s SocialVictimisation
Social Victimisation
Verbal Victimisation
Friend’s Verbal Victimisation
Friend’s Depression
Depression
PhysicalVictimisation
Friend’s PhysicalVictimisation
Friend’s SocialVictimisation
SocialVictimisation
Verbal Victimisation
Friend’s Verbal Victimisation
Friend’s Depression
Depression
Time 1 Time 2
.08
.34
.34
.24
.24
.22
.22
.08
.58
.58
PhysicalVictimisation
Friend’s PhysicalVictimisation
Friend’s SocialVictimisation
Social Victimisation
Verbal Victimisation
Friend’s Verbal Victimisation
Friend’s Depression
Depression
PhysicalVictimisation
Friend’s PhysicalVictimisation
Friend’s SocialVictimisation
SocialVictimisation
Verbal Victimisation
Friend’s Verbal Victimisation
Friend’s Depression
Depression
Time 1 Time 2
.23
.23
.12
.12
.16
.16
.34
.34.28
.28
PhysicalVictimisation
Friend’s PhysicalVictimisation
Friend’s SocialVictimisation
Social Victimisation
Verbal Victimisation
Friend’s Verbal Victimisation
Friend’s Depression
Depression
PhysicalVictimisation
Friend’s PhysicalVictimisation
Friend’s SocialVictimisation
SocialVictimisation
Verbal Victimisation
Friend’s Verbal Victimisation
Friend’s Depression
DepressionTime 1 Time 2
.16
.16
-.35
-.35
-.12
-.25
-.25
.24 .24
-.19 -.19
.52
.52-.12
PhysicalVictimisation
Friend’s PhysicalVictimisation
Friend’s SocialVictimisation
Social Victimisation
Verbal Victimisation
Friend’s Verbal Victimisation
Friend’s Depression
Depression
PhysicalVictimisation
Friend’s PhysicalVictimisation
Friend’s SocialVictimisation
SocialVictimisation
Verbal Victimisation
Friend’s Verbal Victimisation
Friend’s Depression
Depression
Time 1 Time 2
.11
.11
-.16
-.16
.29
.29
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
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.
Further reading