1. 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.

2. 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

3. 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

4. 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.

5. 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

6. 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.

7. 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

8. 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).

9. 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

10. 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

11. 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.

12. 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).

13. 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.

14. 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

15. Measurement models describe the relationships between indicators and latent variables. Latent variable  Manifest indicators  Error  Measurement models Depression Item 1Item 2Item 3 error1error2error3

16. Measurement models may have more complex structures. Measurement models Item 1Item 2Item 3 error1error2error3 Verbal Victimisation Item 1Item 2Item 3 error4error5error6 Physical Victimisation

17. Measurement models Item 1Item 2Item 3 error1error2error3 Verbal Victimisation Item 1Item 2Item 3 error4error5error6 Physical Victimisation General Victimisation Resid2 Resid1

18. 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

19. Item 1Item 2Item 3 error1error2error3 Verbal Victimisation Item 1Item 2Item 3 error4error5error6 Physical Victimisation Correlate error terms:

20. Measurement models Model the method variance: Item 1 [R] Item 2 Item 3 [R] error1 error2error3 Item 4 Item 5 [R] Item 6 error4 error5 error6 Depression Method

21. Measurement models Create ‘parcels’ (Bandalos, 2002; Little et al., 2002) so that this… Item 1 Item 2 Item 3 error1 error2error3 Item 4 Item 5Item 6 error4 error5 error6 Depression

22. Measurement models …becomes this Parcel 1 Parcel 2 error1 error3 Parcel 3 error5 Depression

23. 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

24. 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

25. 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 Verbal Victimisation Omitted variable accounts for correlation Self-Defeating Humour Symptoms of Depression

26. 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

27. T1 Victimisation T2 Depression T2 Victimisation T1 Depression 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)?

28. Cross-lagged analyses T1 Victimisation T2 Depression T2 Victimisation T1 Depression e e Can also include time-invariant predictors in the model. Gender

29. Cross-lagged analyses NB – the model can be extended to incorporate further time points. T1 Victimisation T2 Depression T2 Victimisation T1 Depression e e T3 Depression T3 Victimisation e e

30. 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

32. A stability-only model Stability paths Competing models: T1 Physical Victimisation T2 Physical Victimisation T1 Internalising T1 Verbal Victimisation T2 Verbal Victimisation T1 Social Victimisation T2 Social Victimisation T2 Internalising

33. A stability and a restricted cross-lagged model Stability paths PLUS cross-lagged within related concept only (victimisation) Competing models: T1 Physical Victimisation T2 Physical Victimisation T1 Verbal Victimisation T2 Verbal Victimisation T1 Social Victimisation T2 Social Victimisation T1 Internalising T2 Internalising

34. A fully cross-lagged model Stability paths, cross-lagged within related concept Cross-lagged across all variables Competing models: T1 Physical Victimisation T2 Physical Victimisation T1 Verbal Victimisation T2 Verbal Victimisation T1 Social Victimisation T2 Social Victimisation T1 Internalising T2 Internalising

35. 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 (ΔX 2, p <.001). Cross-lagged analyses

36. Results: Cross-lagged analyses X2X2 CMIN/DFCFIRMSEA Model 1105.98 (df = 23), p <.001 4.608.987.054 (.044,.065) Model 257.51 (df = 17), p <.001 3.383.994.044 (.032,.057) Model 310.24 (df = 11), p =.509 0.9311.000.000 (.000,.028)

37. 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

38. Cross-Lagged Results (only significant paths shown) T1 Physical Victimisation T2 Physical Victimisation T1 Social Victimisation T2 Social Victimisation T1 Verbal Victimisation T2 Verbal Victimisation Cross-lagged analyses.11 -.14.12.10.15.17.13.57.47.37.36 T1 Internalising T2 Internalising

39. Analysis 2: Victimisation, Humour, and Internalising Cross-lagged analyses

41. Results: Model comparisons: All models were again significantly different from each other (ΔX 2, p <.001). Cross-lagged analyses X2X2 CMIN/DFCFIRMSEA Model 1283.54 (df = 83), p <.001 3.416.977.044 (.039,.050) Model 2175.54 (df = 63), p <.001 2.786.987.038 (.031,.045) Model 336.58 (df = 27), p =.103 1.355.999.017 (.000,.030)

42. Cross-sectional associations: T1 (T2) Cross-lagged analyses 2. Agg3. SD4. SE5. Verb6. Phys7. Soc8. 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-

43. Physical Victimisation Social Victimisation Verbal Victimisation -.13.13.09.12.15.12 Self-Enhancing Humour Affiliative Humour Aggressive Humour Self-Defeating Humour Physical Victimisation Social Victimisation Verbal Victimisation Self-Enhancing Humour Affiliative Humour Aggressive Humour Self-Defeating Humour Time 1 Time 2.13.08.07 -.14.20 -.17 -.14.11 T1 Internalising T2 Internalising

44. 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

45. 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)

46. Dyadic analyses T1 Victimisation Friend’s T2 Victimisation T2 Victimisation Friend’s T1 Victimisation e e Looks a lot like the cross-lagged analysis However, the data structure in SPSS is very different.

47. Dyadic analyses Standard data entry in SPSS: Participant T1 Participant T2 Person 1Data Person 2Data Person 3Data Person 4Data

48. Dyadic analyses For APIM, data is entered by dyad, not person: Participant T1 Friend T1 Participant T2 Friend T2 Dyad 1Data Dyad 2Data Dyad 3Data Dyad 4Data

49. Dyadic analyses We can evaluate “actor effects” T1 Victimisation Friend’s T2 Victimisation T2 Victimisation Friend’s T1 Victimisation e e

50. Dyadic analyses We can evaluate “partner effects” T1 Victimisation Friend’s T2 Victimisation T2 Victimisation Friend’s T1 Victimisation e e

51. Dyadic analyses We can evaluate the simple correlation between partners T1 Victimisation Friend’s T2 Victimisation T2 Victimisation Friend’s T1 Victimisation e e

52. 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.

53. Dyadic analyses Indistinguishable dyads: Best friends. Participant T1 Friend T1 Participant T2 Friend T2 Dyad 1Data Dyad 2Data Dyad 3Data Dyad 4Data

54. Dyadic analyses Indistinguishable dyads: Best friends. Participant T1 Friend T1 Participant T2 Friend T2 Dyad 1Data Dyad 2Data Dyad 3Data Dyad 4Data

55. Dyadic analyses Distinguishable dyads: Victim and Aggressor. Victim T1 Agrsor T1 Victim T2 Agrsor T2 Dyad 1Data Dyad 2Data Dyad 3Data Dyad 4Data

56. Dyadic analyses Indistinguishable dyads Within-person effects must be constrained to be equal T1 Victimisation Friend’s T2 Victimisation T2 Victimisation Friend’s T1 Victimisation e e

57. Dyadic analyses Indistinguishable dyads Partner effects must be constrained to be equal T1 Victimisation Friend’s T2 Victimisation T2 Victimisation Friend’s T1 Victimisation e e

58. Dyadic analyses Indistinguishable dyads Intercepts for the Time 2 variables must be constrained to be equal T1 Victimisation Friend’s T2 Victimisation T2 Victimisation Friend’s T1 Victimisation e e

59. Dyadic analyses Indistinguishable dyads The means and variances of both Time 1 variables must be constrained to be equal T1 Victimisation Friend’s T2 Victimisation T2 Victimisation Friend’s T1 Victimisation e e

60. Dyadic analyses Indistinguishable dyads The variances of the residual variances must be equal T1 Victimisation Friend’s T2 Victimisation T2 Victimisation Friend’s T1 Victimisation e e

61. Dyadic analyses Victim’s Depression T1 Victim’s Friend’s Depression T1 Victim’s Depression T2 Victim’s Friend’s Depression 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.

62. 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)

63. Dyadic analyses Humour & Bullying Data Indistinguishable dyads: Best friends. N dyad = 457 (best friends at T1) First APIM: Depressive symptomatology of best friend dyads.

64. Dyadic analyses This is a saturated model, therefore there is ‘perfect fit’

65. Dyadic analyses Depression T2 Friend’s Depression T2 Depression Friend’s Depression.59.12 Actor effect is significant:.59, p <.001 Partner effect is also significant:.12, p <.001

66. 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?

67. Dyadic analyses

68. Cross-sectional ACTOR (& PARTNER) correlations at T1 Cross-lagged analyses 1. Depression2. Social3. Verbal4. Physical 1. DepressionN/A (.18).44 (.09).40 (.10).36 (.06) 2. SocialN/A (.12).80 (.12).68 (.05) 3. VerbalN/A (.16).70 (.12) 4. PhysicalN/A (.14) Strong actor correlations between constructs, all positive Partner correlations between social/verbal victimisation and depression, and between verbal and physical victimisation

69. Physical Victimisation Friend’s Physical Victimisation Friend’s Social Victimisation Social Victimisation Verbal Victimisation Friend’s Verbal Victimisation Friend’s Depression Depression Physical Victimisation Friend’s Physical Victimisation Friend’s Social Victimisation Social Victimisation Verbal Victimisation Friend’s Verbal Victimisation Friend’s Depression Depression Time 1 Time 2.34.11.08 -.12.58.28.52.29

70. Physical Victimisation Friend’s Physical Victimisation Friend’s Social Victimisation Social Victimisation Verbal Victimisation Friend’s Verbal Victimisation Friend’s Depression Depression Physical Victimisation Friend’s Physical Victimisation Friend’s Social Victimisation Social Victimisation Verbal Victimisation Friend’s Verbal Victimisation Friend’s Depression Depression Time 1 Time 2.08.34.24.22.08.58

71. Physical Victimisation Friend’s Physical Victimisation Friend’s Social Victimisation Social Victimisation Verbal Victimisation Friend’s Verbal Victimisation Friend’s Depression Depression Physical Victimisation Friend’s Physical Victimisation Friend’s Social Victimisation Social Victimisation Verbal Victimisation Friend’s Verbal Victimisation Friend’s Depression Depression Time 1 Time 2.23.12.16.34.28

72. Physical Victimisation Friend’s Physical Victimisation Friend’s Social Victimisation Social Victimisation Verbal Victimisation Friend’s Verbal Victimisation Friend’s Depression Depression Physical Victimisation Friend’s Physical Victimisation Friend’s Social Victimisation Social Victimisation Verbal Victimisation Friend’s Verbal Victimisation Friend’s Depression Depression Time 1 Time 2.16 -.35 -.12 -.25.24 -.19.52 -.12

73. Physical Victimisation Friend’s Physical Victimisation Friend’s Social Victimisation Social Victimisation Verbal Victimisation Friend’s Verbal Victimisation Friend’s Depression Depression Physical Victimisation Friend’s Physical Victimisation Friend’s Social Victimisation Social Victimisation Verbal Victimisation Friend’s Verbal Victimisation Friend’s Depression Depression Time 1 Time 2.11 -.16.29

74. 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!

75. 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

76. 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.The effect of item parceling on goodness-of-fit and parameter estimate bias in structural equation modeling Berrington, A. (2006). An overview of methods for the analysis of panel data. ESRC National Centre for Research Methods Briefing Paper / 007.An overview of methods for the analysis of panel data 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.The Actor-Independence Model: A model of bidirectional effects in developmental studies 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.Item parceling in structural equation models for optimum solutions 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]Assessing mediation in dyadic data using APIM 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.To parcel or not to parcel: Exploring the question, weighing the merits Further reading