1. ALISON BOWLING MODERATION AND MEDIATION IN REGRESSION

2. MODERATION In a 2-way ANOVA If the interaction is significant we can say that any effect of one of the IVs on the DV is moderated by the second IV. That is, the effect of an IV on the DV differs for different levels of the second IV. Follow up by an analysis of simple effects This analyses the effect of an IV for different levels of the second IV.

3. MODERATION IN REGRESSION Interactions in regression 1.One continuous predictor and one categorical predictor The effects of the continuous predictor may be assessed at each level of the categorical predictor 2.Two continuous predictors The effects of one predictor may be assessed at specified values of the other (moderator) predictor

4. CENTRING VARIABLES It is often useful to centre a variable to facilitate interpretation of the parameters. Individual predictors represent the effect on the outcome when the other predictor is zero. Zero should be meaningful E.g. in the bird count data, the years were 1981 – 2014. Year 0 would have been 1981 years ago! It makes sense to recode (centre) year to range from 0 – 35. Now year = 0 represents the bird count at the start of the survey. For other data, it makes sense to centre a variable at another value – e.g. the mean.

5. MBCOPING.SAV Investigated the effects of Gender Negative life events Ways of coping Resilience (cognitive hardiness) On Psychological distress (ghq)

6. CENTRING AT THE MEAN Cognitive hardiness (coghard) Scores range from 58 – 127 Nobody has zero resilience! It makes sense to centre this at the mean. Create a new variable coghardc

7. CONTINUOUS + CATEGORICAL PREDICTORS Interaction involving one continuous and 1 categorical variable Coghardc and Gender ( 2 = female) Using GLM Univariate….

8. GENDER X COGHARD INTERACTION The effects of cognitive hardiness on ghq differ for males and females.

9. INTERPRETING THE INTERACTION Ghq = 48.57 -.65 (Gender) -.43 (Coghardc) -.25 (Gender x Coghardc) For females ( Gender = 0, reference group) Ghq = 48.57 -.43 (coghardc)

10. INTERPRETING THE INTERACTION Ghq = 48.57 -.65 (Gender) -.43 (Coghardc) -.25 (Gender x Coghardc) For males ( Gender = 1) Ghq = 48.57 -.65(1) -.43 (coghardc) -.25 (1 x coghardc) Ghq = 47.92 -.68 (coghardc)

11. USING PROCESS (FIELD) Outcome: ghq Model Summary R R-sq F df1 df2 p.59.35 32.96 3.00 183.00.00 Model coeff se t p LLCI ULCI constant 47.28 2.19 21.58.00 42.96 51.60 gender.65 1.33.49.63 -1.98 3.28 coghardc -.93.19 -4.84.00 -1.31 -.55 int_1.25.11 2.26.03.03.47 Interactions: int_1 coghardc X gender R-square increase due to interaction(s): R2-chng F df1 df2 p int_1.02 5.09 1.00 183.00.03 ************************************************************************* Conditional effect of X on Y at values of the moderator(s): gender Effect se t p LLCI ULCI 1.00 -.68.09 -7.52.00 -.85 -.50 2.00 -.43.07 -6.43.00 -.56 -.29

12. TWO CONTINUOUS VARIABLES Effect of Emotional coping (emotcopec) and Cognitive Hardiness on ghq. Ghq = 47.04 -.33(coghardc) +.22 (emotcopec) -.013 (coghardc x emotcopec)

13. SCATTERPLOT Effect of cognitive hardiness on ghq at different levels of emotion coping

14. EFFECT OF COGHARD ON GHQ The effect of cognitive hardiness on ghq depends on emotion coping. Effect is : - 33 -.013 emotcopec (This is the derivative of Ghq = 47.04 -.33(coghardc) +.22 (emotcopec) -.013 (coghardc x emotcopec) With respect to cognardc

15. EFFECTS FOR DIFFERENT LEVELS OF EMOTIONAL COPING To find the effect (slope) of the predictor (cognitive hardiness) at different levels of the moderator (emotional coping) Formula is : - 33 -.013 emotcopec Let’s take values of Emotcopec of -10, 0 and + 10

16. EFFECT OF COGHARD AT DIFFERENT LEVELS OF EMOTCOPE Effect is : - 33 -.013 emotcopec Effect of coghard when emotcopec = -10 = -.33 -.013 (emotcopec) = -.33 -.013 ( -10) = -.33 +.13 = -.20

17. EFFECT OF COGNITIVE HARDINESS Effect of coghard when emotcopec = 0 = -.33 -.013 (emotcopec) = -.33 -.013 ( 0) = -.33 Effect of coghard when emotcopec = 10 = -.33 -.013 (emotcopec) = -.33 -.013 ( 10) = -.33 -.13 = -.46

18. USING PROCESS Outcome: ghq Model Summary R R-sq F df1 df2 p.64.41 41.63 3.00 183.00.00 Model coeff se t p LLCI ULCI constant 47.04.74 63.65.00 45.58 48.50 emotco_1.22.06 3.47.00.10.35 coghardc -.33.06 -5.14.00 -.46 -.21 int_1 -.01.00 -3.07.00 -.02.00 Interactions: int_1 coghardc X emotco_1 R-square increase due to interaction(s): R2-chng F df1 df2 p int_1.03 9.41 1.00 183.00.00 ************************************************************************* Conditional effect of X on Y at values of the moderator(s): emotco_1 Effect se t p LLCI ULCI -12.43 -.17.09 -1.89.06 -.35.01.00 -.33.06 -5.14.00 -.46 -.21 12.43 -.49.07 -6.67.00 -.64 -.35

19. MEDIATION Mediation occurs when the relationship between a dependent variable and a DV can be explained by their relationship to a third variable (the mediator). Barron, R.M and Kenny, D.A. (1986). The moderator- Mediator ….. Journal of Personality and Social Psychology, 51, 1173 - 1182 Independent variable Dependent variable Mediator

20. EMOTION COPING AS A MEDIATOR Let us assume that the researcher theorised that emotion coping is a mediator of the effect of cognitive hardiness on ghq. i.e. that cognitive hardiness influences emotional coping, and that this influences ghq. The indirect effect. Cognitive hardiness may also influence ghq in addition to its indirect effect The direct effect

21. MEDIATION MODEL Cognitive hardiness ghq Emotional coping

22. MEDIATION MODEL IN SPSS 1.Regress emotcope on cognitive hardiness 2.Regress ghq on cognitive hardiness

23. REGRESSION MODEL IN SPSS 3. Regress ghq on both cognitive hardiness and emotional coping.

24. COMPLETE MEDIATION MODEL Cognitive hardiness ghq Emotional coping -.596**.23** -.377** Cognitive hardiness has both an indirect effect on ghq, and a direct effect on ghq. Indirect effect = -.596 *.23 = -.137

25. MEDIATION IN AMOS Use Amos graphics. Create the graphic Read in the SPSS data file, MBCoping.sav Go to: View/Set Analysis Properties… Click the Output tab Check: Minimization history Check: Standardized estimates Check: Squared multiple correlations

26. RUN THE ANALYSIS IN AMOS The regression weights are the same as those obtained by the regression analysis.

27. EXAMINE THE OUTPUT (VIEW TEXT) Regression weights EstimateS.E.C.R.PLabel emotc ope <---coghard-.596.059-10.110*** ghq<---emotcope.232.0643.593*** ghq<---coghard-.377.065-5.842*** Unstandardised regression weights Estimate emotcope<---coghard-.596 ghq<---emotcope.259 ghq<---coghard-.422

28. VARIANCES AND R 2 R2R2 Estimate emotcope.355 ghq.375

29. INDIRECT EFFECT OF COGHARD ON GHQ Indirect effect coghardemotcope.000 ghq-.138.000 Standardized indirect effect coghardemotcope.000 ghq-.154.000

30. MORE COMPLICATED MODELS

31. MORE COMPLICATED MODELS – REGRESSION WEIGHTS EstimateS.E.C.R.PLabel emotcope<---les_neg.100.107.936.349 taskcope<---les_neg.241.1132.131.033 emotcope<---coghard-.580.061-9.443*** taskcope<---coghard.359.0655.513*** ghq<---emotcope.210.0613.434*** ghq<---coghard-.304.066-4.636*** ghq<---les_neg.425.0904.706*** ghq<---taskcope-.051.058-.890.373