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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.

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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 SiânJones

Project team: SirandouSaidy 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

  • 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


What functions does humour serve?

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).

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


  • Repeated attacks on an individual.

  • Conceptualised as a continuum rather than a category.

Peer-victimisation

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).


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).

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

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


  • 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.

Methods


Self-Report:

  • 24-item Child Humour Styles Questionnaire (Fox et al., in press).

Measures

  • 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).


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.

Measures


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

Depression

Measurement models describe the relationships between indicators and latent variables.

Latent variable 

Manifest indicators 

Error 

Item 1

Item 2

Item 3

error1

error2

error3


Verbal

Victimisation

Physical

Victimisation

Item 1

Item 1

Item 2

Item 2

Item 3

Item 3

error1

error4

error2

error5

error3

error6

Measurement models

Measurement models may have more complex structures.


Item 1

Item 2

Item 3

error1

error2

error3

General

Victimisation

Measurement models

Resid2

Resid1

Physical

Victimisation

Verbal

Victimisation

Item 1

Item 2

Item 3

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.


Verbal

Victimisation

Physical

Victimisation

Item 1

Item 1

Item 2

Item 2

Item 3

Item 3

error1

error4

error2

error5

error3

error6

Measurement models

Correlate error terms:


Depression

Measurement models

Model the method variance:

Item 1

[R]

Item 2

Item 4

Item 3

[R]

Item 5

[R]

Item 6

error4

error5

error1

error2

error3

error6

Method


Depression

Measurement models

Create ‘parcels’ (Bandalos, 2002; Little et al., 2002) so that this…

Item 1

Item 2

Item 4

Item 3

Item 5

Item 6

error4

error5

error1

error2

error3

error6


Measurement models

Depression

…becomes this

Parcel 1

Parcel 2

Parcel 3

error5

error1

error3


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 (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)


Cross-lagged analyses

  • Omitted variable accounts for correlation

Cross-sectional data are restricted in terms of unpacking causation relating to two correlated variables. Three explanations:

  • 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

T1

Victimisation

T2

Victimisation

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)?

e

e

T1

Depression

T2

Depression


Cross-lagged analyses

T1

Victimisation

T2

Victimisation

Can also include time-invariant predictors in the model.

e

e

T1

Depression

T2

Depression

Gender


Cross-lagged analyses

e

e

NB – the model can be extended to incorporate further time points.

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:


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

T1 Verbal

Victimisation

T2 Verbal

Victimisation

.11

.36

Cross-Lagged Results (only significant paths shown)

-.14

T1 Social

Victimisation

T2 Social

Victimisation

.37

.12

.10

T1 Physical

Victimisation

T2 Physical

Victimisation

.47

.15

.17

.13

T1

Internalising

T2

Internalising

.57


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).


Cross-lagged analyses

Cross-sectional associations: T1 (T2)


Time 2

Self-Defeating Humour

Self-Defeating Humour

.11

.13

.07

Aggressive Humour

Aggressive Humour

.07

Self-Enhancing Humour

Self-Enhancing Humour

Time 1

Affiliative Humour

.08

Affiliative Humour

.20

-.17

Verbal

Victimisation

-.14

Verbal

Victimisation

-.14

.09

Social

Victimisation

.12

Social

Victimisation

-.13

.13

.15

Physical

Victimisation

Physical

Victimisation

.12

T1

Internalising

T2

Internalising


  • 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

Cross-lagged analyses


  • 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.

Dyadic analyses - APIM

  • 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

  • However, the data structure in SPSS is verydifferent.

T1

Victimisation

T2

Victimisation

e

e

Friend’s T1

Victimisation

Friend’s T2

Victimisation


Standard data entry in SPSS:

Dyadic analyses


For APIM, data is entered by dyad, not person:

Dyadic analyses


  • We can evaluate “actor effects”

Dyadic analyses

T1

Victimisation

T2

Victimisation

e

e

Friend’s T1

Victimisation

Friend’s T2

Victimisation


  • We can evaluate “partner effects”

Dyadic analyses

T1

Victimisation

T2

Victimisation

e

e

Friend’s T1

Victimisation

Friend’s T2

Victimisation


  • We can evaluate the simple correlation between partners

Dyadic analyses

T1

Victimisation

T2

Victimisation

e

e

Friend’s T1

Victimisation

Friend’s T2

Victimisation


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.

Dyadic analyses


  • Indistinguishable dyads: Best friends.

Dyadic analyses


  • Distinguishable dyads: Victim and Aggressor.

Dyadic analyses


  • Indistinguishable dyads

  • Within-person effects must be constrained to be equal

Dyadic analyses

T1

Victimisation

T2

Victimisation

e

e

Friend’s T1

Victimisation

Friend’s T2

Victimisation


  • Indistinguishable dyads

  • Partner effects must be constrained to be equal

Dyadic analyses

T1

Victimisation

T2

Victimisation

e

e

Friend’s T1

Victimisation

Friend’s T2

Victimisation


  • Indistinguishable dyads

  • Intercepts for the Time 2 variables must be constrained to be equal

Dyadic analyses

T1

Victimisation

T2

Victimisation

e

e

Friend’s T1

Victimisation

Friend’s T2

Victimisation


  • Indistinguishable dyads

  • The means and variances of both Time 1 variables must be constrained to be equal

Dyadic analyses

T1

Victimisation

T2

Victimisation

e

e

Friend’s T1

Victimisation

Friend’s T2

Victimisation


  • Indistinguishable dyads

  • The variances of the residual variances must be equal

Dyadic analyses

T1

Victimisation

T2

Victimisation

e

e

Friend’s T1

Victimisation

Friend’s T2

Victimisation


  • 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

Victim’s Depression

T1

Victim’s Depression

T2

e

e

Victim’s Friend’s

Depression T1

Victim’s Friend’s

Depression T1


  • ‘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


Dyadic analyses

This is a saturated model, therefore there is ‘perfect fit’


Depression

T2 Depression

Dyadic analyses

.59

.12

.12

Friend’s Depression

T2 Friend’s Depression

.59

Actor effect is significant: .59, p < .001

  • Partner effect is also significant: .12, p < .001


  • 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


Dyadic analyses


Cross-lagged analyses

Cross-sectional ACTOR (& PARTNER) correlations at T1

  • Strong actor correlations between constructs, all positive

  • Partner correlations between social/verbal victimisation and depression, and between verbal and physical victimisation


Time 2

Depression

Depression

.58

.08

Friend’s Depression

Friend’s Depression

.08

.58

Verbal Victimisation

.28

Verbal Victimisation

.34

Time 1

Friend’s Verbal Victimisation

Friend’s Verbal Victimisation

.34

.28

Social Victimisation

Social

Victimisation

.52

-.12

-.12

Friend’s Social

Victimisation

Friend’s Social

Victimisation

.52

Physical

Victimisation

.29

Physical

Victimisation

.11

.11

Friend’s Physical

Victimisation

Friend’s Physical

Victimisation

.29


Time 2

.58

Depression

Depression

.08

.08

Friend’s Depression

Friend’s Depression

.58

.24

Verbal Victimisation

Verbal Victimisation

.24

Time 1

Friend’s Verbal Victimisation

Friend’s Verbal Victimisation

.34

Social Victimisation

Social

Victimisation

.34

Friend’s Social

Victimisation

Friend’s Social

Victimisation

.22

Physical

Victimisation

Physical

Victimisation

.22

Friend’s Physical

Victimisation

Friend’s Physical

Victimisation


Time 2

Depression

Depression

.23

Friend’s Depression

Friend’s Depression

.23

.28

Verbal Victimisation

Verbal Victimisation

.34

Time 1

Friend’s Verbal Victimisation

Friend’s Verbal Victimisation

.34

.28

.12

Social Victimisation

Social

Victimisation

.12

Friend’s Social

Victimisation

Friend’s Social

Victimisation

.16

Physical

Victimisation

Physical

Victimisation

.16

Friend’s Physical

Victimisation

Friend’s Physical

Victimisation


Time 2

Depression

Depression

Friend’s Depression

Friend’s Depression

.24

.24

-.19

-.19

.16

Verbal Victimisation

Verbal Victimisation

-.35

Time 1

Friend’s Verbal Victimisation

Friend’s Verbal Victimisation

.16

-.35

Social Victimisation

Social

Victimisation

.52

-.12

Friend’s Social

Victimisation

Friend’s Social

Victimisation

-.12

.52

Physical

Victimisation

Physical

Victimisation

-.25

-.25

Friend’s Physical

Victimisation

Friend’s Physical

Victimisation


Time 2

Depression

Depression

Friend’s Depression

Friend’s Depression

Verbal Victimisation

Verbal Victimisation

Time 1

Friend’s Verbal Victimisation

Friend’s Verbal Victimisation

Social Victimisation

Social

Victimisation

-.16

Friend’s Social

Victimisation

Friend’s Social

Victimisation

-.16

.29

Physical

Victimisation

Physical

Victimisation

.11

.11

Friend’s Physical

Victimisation

Friend’s Physical

Victimisation

.29


  • 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!

Dyadic analyses


  • AMOS

  • Easy to use, accessible, though can be limited

  • Trouble shooting fairly straightforward

Summary

  • 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.


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