Hui Bian

Office for Faculty Excellence

• Reference –Hayes, A. F. (2013). Introduction to

mediation, moderation, and conditional process analysis: A regression-based approach. New York: The Guilford Press

• Software

–SPSS

–SAS

–SEM software: such as AMOS

–We use SPSS macro developed by Dr. Andrew Hayes

• Process

• Go to his website http://www.afhayes.com

• Moderation

–The magnitude of association between X and Y is influenced by or dependent on moderator.

• Example

–The intervention intensity moderated the effect of self-efficacy on physical activity.

• The effect of X on Y is moderated by M

X Y

M

M is moderator. X is predictor. Y is dependent variable.

• Statistical diagram of moderation model

M

X

MX

Y

MX is interaction of M and X.

• Moderation model

–Y = a + b1X + b2M + b3XM + e

For the moderation effect, we want to test if b3 is significantly different from zero.

• Example: we have three variables: protest, liking, and sexism.

–Data file name is “protest”.

– Two groups: one group (no protest) learned that the female lawyer didn’t take any action to against sex discrimination. The other group (protest) learned that the female lawyer did take action.

• Then the participants were asked to complete a survey which examines Liking.

• The participants were also asked to complete Modern Sexism Scale (sexism) (higher score means more pervasive he or she believes sex discrimination in society.

• The research question is whether the effect of protest on liking depends on a person’s beliefs about the pervasiveness of sex discrimination in society.

• SPSS syntax

–process vars=protest liking sexism/y=liking/x=protest/m=sexism/model=1/jn=1/quantile=1/plot=1.

Y is liking, x is protest, and moderator is sexism. Jn means Johnson-Neyman.

• Results

• Visualize moderation effect: pick-a-point approach

• Results

• Visualize moderation effect: Johnson-Neyman technique

• Visualize moderation effect: Johnson-Neyman technique

–The region of significant moderation effect is M <= 3.509 and M >=4.975

• Graph based on JN

95%CI lower limit

95%CI Upper limit

Point estimate

• Mediation answers question about how X influences Y through a mechanism.

–Variation in X causes variation in one or more mediators , which in turn causes variation in Y.

• Simple mediation diagram

M is mediator. X is predictor. Y is dependent variable.

X Y

M

• There are two distinct pathways of X effect on Y.

–Direct effect: from X to Y without passing through M.

–Indirect effect: from X to Y passing through M.

• Estimate direct, indirect, and total effects of X

X Y

M a b

c’

• Two regression equations

–M = i1 + aX + eM

–Y = i2 + c’X + bM + eY

• The indirect effect of X on Y through M is the product of a and b.

• The direct effect is c’.

• The total effect c = ab + c’

• For the direct effect: we want to test whether the coefficient of X is different from zero.

• For indirect effect: we want to test whether X effect on Y is through the mechanism represented by X -> M -> Y.

• How to calculate indirect effect

–Normal theory approach: Sobel test

• Assuming ab is normally distributed

–Bootstrap confidence interval

• No assumption for the shape of the sampling distribution of ab.

• Sobel test: we can use the SPSS macro developed by Dr. Andrew Hayes.

• Bootstrapping: resampling method –Original sample size n –Observations of this sample is resampled

with replacement. – Statistics are calculated based on the new

sample. – Repeated this resampling procedure

thousands of times. –A representation of the sampling distribution

of the statistics is constructed.

• We use Bootstrapping to get 95% confidence interval for ab.

• Process developed by Dr. Andrew Hayes is used to calculate indirect effect.

• Simple mediation model

– Example: two groups of students were given two conditions separately. We want to look at the effect of conditions on intention to buy sugar through media influence.

–X is conditions (cond)

– Y is intention to buy sugar (reaction)

–M is media influence (pmi)

• Let’s use PROCESS from Dr. Andrew Hayes

–Install PROCESS first

–Go to Analyze > Regression > Preachers and Hayes (2008)

• Outputs: direct and total effects

• The different effect of x on y

–C’=.2544, t(120) = .9943, p = .32

–This means X doesn’t affect y independent of M’s effect on Y.

• Outputs: indirect effect

• Indirect effect

–C = .2424 (boot), 95% BC bootstrap confidence interval is .0183-.5372

–This means there is indirect effect of X on Y through M.

• We also can use syntax to get mediation results

• From File > New > Syntax, then type

–process vars = cond pmi reaction/y=reaction/x=cond/m=pmi/model=4/total=1/effsize=1/boot=10000.

• We can use AMOS to get direct and indirect effects. The model is like this in AMOS.

• Outputs from AMOS: total effects

• Outputs from AMOS: direct effect

• Outputs from AMOS: indirect effect

• From AMOS we also can get bootstrapping results

• Bootstrapping results from AMOS

• Multiple mediator model

– Two or more mediators in the model

X

M1

Y

Mk

• Parallel multiple mediator model

–No relationships between or among mediators.

–Indirect effects = a1b1+ a2b2 +…+ aibi

i means number of mediators

• Example: same study, but two mediators in the model

–X is conditions (cond)

– Y is intention to buy sugar (reaction)

–M1 is media influence (pmi) and M2 is perceived importance (import).

• Results

• Results