Slide 2 Mediation That is, Indirect Effects Slide 3 What is a
Mediator? An intervening variable. X causes M and then M causes Y.
Slide 4 MacKinnon et al., 2002 14 different ways to test mediation
models Grouped into 3 general approaches Causal Steps (Judd, Baron,
& Kenney) Differences in Coefficients Product of Coefficients
Slide 5 Causal Steps X must be correlated with Y. X must be
correlated with M. M must be correlated with Y, holding constant
any direct effect of X on Y. When the effect of M on Y is removed,
X is no longer correlated with Y (complete mediation) or the
correlation between X and Y is reduced (partial mediation). Slide 6
First you demonstrate that the zero-order correlation between X and
Y (ignoring M) is significant. Next you demonstrate that the
zero-order correlation between X and M (ignoring Y) is significant.
Slide 7 Now you conduct a multiple regression analysis, predicting
Y from X and M. The partial effect of M (controlling for X) must be
significant. Finally, you look at the direct effect of X on Y. This
is the Beta weight for X in the multiple regression just mentioned.
For complete mediation, this Beta must be (not significantly
different from) 0. For partial mediation, this Beta must be less
than the zero-order correlation of X and Y. Slide 8 Criticisms Low
power. Should not require that X be correlated with Y X could have
both a direct effect and an indirect effect on Y With the two
effects being opposite in direction but equal in magnitude. Slide 9
Differences in Coefficients Compare The correlation between Y and X
(ignoring M) With the for predicting Y from X (partialled for M)
The assumptions of this analysis are not reasonable. Can lead to
conclusion that M is mediator even when M is unrelated to Y. Slide
10 Product of Coefficients The best approach Compute the indirect
path coefficient for effect of X on Y through M The product of r XM
and for predicting Y from M partialled for X This product is the
indirect effect of X through M on Y Slide 11 The Test Statistic
(TS) TS is usually evaluated by comparing it to the standard normal
distribution (z) There is more than one way to compute TS. Slide 12
Sobels (1982) first-order approximation The standard error is
computed as is b M.X or r M.X, 2 is its standard error is b Y.M(X)
or Y.M(X), 2 is its standard error Slide 13 Alternative Error Terms
Aroians (1944) second-order exact solution Goodmans (1960) unbiased
solution Slide 14 Ingram, Cope, Harju, and Wuensch (2000) Theory of
Planned Behavior -- Ajzen & Fishbein (1980) The model has been
simplified for this lesson. The behavior was applying for graduate
school. The subjects were students at ECU Slide 15 Slide 16 Causal
Steps Attitude is significantly correlated with behavior, r =.525.
Attitude is significantly correlated with intention, r =.767. Slide
17 The partial effect of intention on behavior, holding attitude
constant, falls short of statistical significance, =.245, p =.16.
The direct effect of attitude on behavior (removing the effect of
intention) also falls short of statistical significance, =.337, p
=.056. No strong evidence of mediation. Slide 18 Product of
Coefficients Slide 19 Aroians second-order exact solution Slide 20
http://quantpsy.org/sobel/sobel.htm Slide 21 Or, Using Values of t
Merde, short of statistical significance. Slide 22 Mackinnon et al.
(1998) TS is not normally distributed Monte Carlo study to find the
proper critical values. For a.05 test, the proper critical value is
0.9 Wunderbar, our test is statistically significant after all.
Slide 23 Mackinnon et al. (1998) Distribution of Products Find the
product of the t values for testing and Compare to the critical
value, which is 2.18 for a.05 test. Significant ! Slide 24 Shrout
and Bolger (2002) With small sample sizes, best to bootstrap. If X
and Y are temporally proximal, good idea to see if they are
correlated. If temporally distal, not a good idea, because More
likely that X Y has more intervening variables, and More likely
that the effect of extraneous variables is great. Slide 25 Opposite
Direct and Indirect Effects X is the occurrence of an environmental
stressor, such as a major flood, and which has a direct effect of
increasing Y, the stress experienced by victims of the flood. M is
coping behavior on part of the victim, which is initiated by X and
which reduces Y. Slide 26 Partial Mediation ? X may really have a
direct effect upon Y in addition to its indirect effect on Y
through M. X may have no direct effect on Y, but may have indirect
effects on Y through M 1 and M 2. If, however, M 2 is not included
in the model, then the indirect effect of X on Y through M 2 will
be mistaken as being a direct effect of X on Y. Slide 27 There may
be two subsets of subjects. In the one subset there may be only a
direct effect of X on Y, and in the second subset there may be only
an indirect effect of X on Y through M. Slide 28 Causal Inferences
from Nonexperimental Data? I am very uncomfortable making causal
inferences from non-experimental data. Sure, we can see if our
causal model fits well with the data, But a very different causal
model may fit equally well. For example, these two models fit the
data equally well: Slide 29 Slide 30 Bootstrap Analysis Shrout and
Bolger recommend bootstrapping when sample size is small. They and
Kris Preacher provide programs to do the bootstrapping. Ill
illustrate Preachers SPSS macro. He has an SAS macro too. Slide 31
Slide 32 Direct, Indirect, and Total Effects IMHO, these should
always be reported, and almost always standardized. the direct
effect of attitude is.337 The indirect effect is (.767)(.245)
=.188. The total effect =.337 +.188 =.525. r xy =.525: we have
partitioned that correlation into two distinct parts, the direct
effect and the indirect effect. Slide 33 Preacher & Kelleys 2
This statistic is the ratio of the indirect effect to the maximum
value that the indirect effect could assume given the constraints
imposed by variances and covariance of X, M, and Y. It has the
advantage of ranging from 0 to 1, as a proportion should. Slide 34
Preacher & Kelleys 2 Notice that for our data this statistic is
significantly greater than zero. Preacher and Kelley (2011)
Kappa-squared EffectBoot SEBootLLCIBootULCI
INTENT0.14160.08130.00940.3163 Slide 35 Parallel Multiple Mediation
Experimental Manipulation: Subjects told article they are to read
will be (1) on the front page of newspaper or (0) in an internal
supplement. Importance: Subjects rating of how important the
article is. Mediator. Influence: Subjects rating how influential
the article will be. Mediator. Slide 36 Parallel Multiple Mediation
(2) The article was about an impending sugar shortage. Reaction:
Subjects intention to modify their own behavior (stock up on sugar)
based on the article. Dependent variable. Slide 37 Process Hayes
%process (data=pmi2, vars=cond pmiZ importZ reactionZ, y=reactionZ,
x=cond, m=importZ pmiZ, boot=10000,
total=1,normal=1,contrast=1,model=4); Slide 38 Slide 39 Serial
Multiple Mediation %process (data=pmi2, vars=cond pmiZ importZ
reactionZ, y=reactionZ, x=cond, m=importZ pmiZ, boot=10000,
total=1,normal=1,contrast=1,model=6); Slide 40 Slide 41 Moderated
Mediation Female attorney loses promotion because of sex
discrimination. Protest Condition: experimentally manipulated,
attorney does (1) or does not (0) protest the decision. Independent
Variable. Response Appropriateness: Subjects rating of how
appropriate the attorneys response was. Mediator. Slide 42
Moderated Mediation (2) Liking: Subjects ratings of how much they
like the attorney. Dependent variable. Sexism: Subjects ratings of
how pervasive they think sexism is. Moderator. Slide 43 Process
Hayes %process (data=protest2, vars=protest RespapprZ SexismZ
LikingZ, y=LikingZ, x=protest, w=SexismZ, m=RespapprZ,
quantile=1,model=8, boot=10000); Slide 44 Slide 45 Slide 46 A Fly
in the Ointment Slide 47 Cross-Sectional Data Most published tests
of mediation models have used data where X, M, and Y were all
measured at the same time and X not experimentally manipulated. But
what we really need is longitudinal data. Mediation tests done with
cross-sectional data produce biased results. Slide 48 a, b, and c
are direct effects x, m, and y are autoregressive effects
