A L I S O N BO W L I N G

MODERATION AND MEDIATION IN REGRESSION

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.

MODERATION IN REGRESSION

• Interactions in regression1. One continuous predictor and one categorical predictor• The effects of the continuous predictor may be assessed at

each level of the categorical predictor2. Two continuous predictors• The effects of one predictor may be assessed at specified

values of the other (moderator) predictor

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.

MBCOPING.SAV

• Investigated the effects of• Gender• Negative life events• Ways of coping• Resilience (cognitive hardiness)• On

• Psychological distress (ghq)

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

CONTINUOUS + CATEGORICAL PREDICTORS

• Interaction involving one continuous and 1 categorical variable• Coghardc and Gender ( 2 = female)• Using GLM Univariate….

GENDER X COGHARD INTERACTION

• The effects of cognitive hardiness on ghq differ for males and females.

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)

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)

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•

TWO CONTINUOUS VARIABLES

• Effect of Emotional coping (emotcopec) and Cognitive Hardiness on ghq.

Ghq = 47.04 - .33(coghardc) + .22 (emotcopec) - .013 (coghardc x emotcopec)

SCATTERPLOT

Effect of cognitive hardiness on ghq at different levels of emotion coping

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

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

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

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

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•

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

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

MEDIATION MODEL

Cognitive hardiness ghq

Emotional coping

MEDIATION MODEL IN SPSS

1. Regress emotcope on cognitive hardiness

2. Regress ghq on cognitive hardiness

REGRESSION MODEL IN SPSS

3. Regress ghq on both cognitive hardiness and emotional coping.

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

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

RUN THE ANALYSIS IN AMOS

• The regression weights are the same as those obtained by the regression analysis.

EXAMINE THE OUTPUT (VIEW TEXT)

Regression weights Estimate S.E. C.R. P Label

emotcope <--- coghard -.596 .059 -

10.110 ***

ghq <--- emotcope .232 .064 3.593 ***ghq <--- coghard -.377 .065 -5.842 ***

Unstandardised regression weights Estimate

emotcope <--- coghard -.596ghq <--- emotcope .259ghq <--- coghard -.422

VARIANCES AND R2

R2 Estimate

emotcope .355ghq .375

INDIRECT EFFECT OF COGHARD ON GHQ

Indirect effect coghard emotcopeemotcope .000 .000ghq -.138 .000

Standardized indirect effect coghard emotcope

emotcope .000 .000ghq -.154 .000

MORE COMPLICATED MODELS

MORE COMPLICATED MODELS – REGRESSION WEIGHTS

Estimate S.E. C.R. P Label

emotcope <--- les_neg .100 .107 .936 .349

taskcope <--- les_neg .241 .113 2.131 .033

emotcope <--- coghard -.580 .061 -9.443 ***

taskcope <--- coghard .359 .065 5.513 ***

ghq <--- emotcope .210 .061 3.434 ***

ghq <--- coghard -.304 .066 -4.636 ***

ghq <--- les_neg .425 .090 4.706 ***

ghq <--- taskcope -.051 .058 -.890 .373