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• Reference –Hayes, A. F. (2013). Introduction to
mediation, moderation, and conditional process analysis: A regression-based approach. New York: The Guilford Press
• 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.
• The effect of X on Y is moderated by M
X Y
M
M is moderator. X is predictor. Y is dependent variable.
• 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.
• Visualize moderation effect: Johnson-Neyman technique
–The region of significant moderation effect is M <= 3.509 and M >=4.975
• 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.
• 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.
• 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.
• 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)
• 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.
• 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.
• 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).
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