MediationPaul Jose

PSYC 325

Thought for the day:“You know the world is going crazy when

the best rapper is a white guy, the best golfer is a black guy, the tallest guy in the NBA is Chinese, the Swiss hold the America’s Cup, France is accusing the U.S. of arrogance, and

Germany doesn’t want to go to war.”

Chris Rock

Are mediation and moderation cousins?

• People are thrown off a bit by the fact that moderation and mediation sound alike. It makes it seem that they are very similar.

• In actuality, they are somewhat similar. Well, it’s confusing, I admit.

• Statistically they are cousins, but they are designed to answer different questions.

Similarities and differences

Similarities:• They both involve three variables;• You can use regression to compute both;• There is no statistics programme (other than ModGraph)

designed to tackle either one.Differences:• You create a product term in moderation; not in mediation;• You don’t have to centre anything in mediation;• Moderation can be used on concurrent data, but mediation

is best used on longitudinal data.

So let’s focus on mediation now

• The question you wish to answer is whether the effect of the IV is at least partially mediated by the mediating variable on the DV.

• You can answer this question with two regressions (and a correlation matrix).

• Let’s consider a specific example.

Does rumination mediate the effect of stress on depression?

Stress Depression

Rumination

The theories

• Susan Nolen-Hoeksema believes that an individual who does more rumination ends up with more depression. Simple direct effect.

• I don’t disagree with her, but I think that this simple effect should be embedded within the stress and coping context.

• In other words, stress affects both rumination and depression. Can the effect of rumination on depression be contextualized by examining the larger model (previous page)?

Baron and Kenny (1984)

• Baron and Kenny are the people responsible for systematizing the research approach to mediation.

• They claim that three preconditions must exist before one tests for mediation:

1. Significant correlation between IV and DV;

2. Significant correlation between IV and mediator; and

3. Significant correlation between mediator and DV.

Do we have data that meet these preconditions?

Stress Depression

Rumination

.473***

.481*** .475***

Seems so. So now what?

The test

• Baron and Kenny say that if the relationship between IV and DV is reduced to non-significance when the potential mediator is included in the regression equation, then mediation has been demonstrated.

• This is somewhat misleading, but I will show you what they mean.

Hierarchical regression again

• First step: regress depression on stress (emuch).• Second step: add the mediating variable to the

equation (rumination).• Check to see whether the beta weight of stress

goes down at the second step. If it does, then you have mediation. Easy to tell when the beta becomes non-significant, but what if it stays significant (see next page)?

Results of regression

Coefficientsa

-.560 .031 -17.863 .000

3.117E-02 .001 .476 23.439 .000

-1.374 .064 -21.467 .000

2.116E-02 .001 .323 14.669 .000

4.253E-02 .003 .316 14.363 .000

(Constant)

EMUCH

(Constant)

EMUCH

RUMINATE

Model1

2

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: CDIZa.

Different levels of mediation

• There are actually three types of mediation:– No mediation (no change in beta);– Partial mediation (a significant drop in beta, but it stays

significant); and– Full mediation (a significant drop in beta, and it

becomes non-significant).

• The first type is quite frequent; the second type occurs occasionally; and the last type is as rare as hen’s teeth.

• What we have here is the second type.

But how do we know that it’s a significant drop?

• Well, one uses a test called the Sobel’s t-test.• You can find it in stat texts, but you can also find

it on-line at Preacher and Leonardelli’s web-site: http://www.unc.edu/~preacher/sobel/sobel.htm

• The programme computes whether the drop in beta (or B) is significant or not.

• You have to give it very specific information to obtain a result, however. You have to compute two regressions (see next page):

Two regressions

1. First regression: regress the mediator on the IV. Take the unstandardized regression coefficient (the B, not the ) and the standard error (se).

2. Second regression: regress the DV on both the IV and the mediator simultaneously, and take the B and se for the mediator on the DV.

3. Then you can input these four numbers into the window, and it will compute Sobel’s t for you.

4. So let’s do it.

First regression

Coefficientsa

19.018 .224 84.744 .000

.235 .010 .481 24.659 .000

(Constant)

EMUCH

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: RUMINATEa.

Second regression

Coefficientsa

.222 .496 .449 .654

.164 .011 .323 14.669 .000

.329 .023 .316 14.363 .000

(Constant)

EMUCH

RUMINATE

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: CDIa.

Input

• B (IV to rum.): .235

• B (rum. to DV): .329

• SE (IV to rum.): .010

• SE (rum. to DV): .023

Sobel’s t = 12.22, p < .00001

So what does it mean . . . ?

• Well, I have several problems with this web-site, despite the fact that it computes the t quickly and accurately:– You don’t know what kind of mediation you have: full

or partial.– You don’t know what the new beta weight is.

• So I’ve written something called MedGraph that will answer all of those questions, plus more.

• You’ll probably eventually see advertisements on late-nite TV for ModGraph/MedGraph (like the vegetable slicers, knives that cut through steel, CDs for classic rock music, etc.).

MedGraph will do this: ta-da!

Stress Depression

Rumination

.473***

.481*** .475***

(.323**)

(.316**)

Sobel’s t = 12.22, p < .00001; partial mediation; indirect effect = .120

Now, isn’t that much better?

• You can see in a glance whether and how much the beta decreased.

• You can see what the Sobel’s t value is, and whether it is significant.

• You will learn whether you have no, partial, or full mediation.

• You will see an estimate of the indirect effect (how much variance in the DV does the IV explain through the mediator).

• It doesn’t slice and dice vegetables yet, but I’m working on that.

So is everybody clear on mediation and moderation now?

• Let me summarize both, and give you a chance to ask questions.

• Both approaches are used to explore the interrelationships among 3 variables.

• Two variables? Do a simple correlation.• Having three variables means that one can examine

their various relationships in more complicated ways.• Mediation and moderation are tests of association,

but structured so that particular questions can be answered.

Why do moderation and mediation?

• Researchers are increasingly using these approaches because they wish to understand “mechanisms” of how variables affect each other.

• However, most researchers:1. Are confused about what mediation and

moderation do;2. Use one or the other incorrectly;3. Overuse one or the other (they have a

“favourite” approach); and/or4. Misinterpret the results.

Structural equation modeling

• Some researchers think that mediation is the pinnacle of statistical achievement in an investigation of “mechanisms”. Wrong.

• Mediation is a special case of path analysis, and more researchers should be examining mechanisms by including more than 3 variables in their analyses.

• Here is an example.

The case for path analysis• I predicted that four coping strategies might

mediate between Individualism and/or Collectivism and Negative adjustment.

• I and C are higher order constructs descriptive of how people relate to others in their particular culture.

• Western societies are high in I, and Asian societies are high in C, according to Harry Triandis.

• So I could conduct 8 separate mediation analyses (I to Rumination to NegAdj; etc.) to see whether mediation occurred.

• The problem is that this inflates Type 1 error.

The answer: Path analysis

Individ-ualism

Collect-ivism

Extern.

Problem-solving

Rumin.

Socialsupport

Neg.adjustment

-.07*

.65**

.29*

-.20*

.16*

.14*-.23*

.13*.23*

.44**

How manymediations areshown here?Answer: 4

Why is this better?• It’s better insofar as one is considering all of these

variables together.• Whenever one does an associational analysis

(correlation, regression, etc.), one must consider the “third variable” problem.

• When one does a mediation analysis with three variables, one should think about whether one has included all relevant variables.

• Inclusion of other variables can wash out (or intensify) relationships identified with a simple mediation.

• The real world has more than 3 variables in it.

The world of mediation and moderation

• The distinctions between these two techniques should be clearer for you now. For more information check out my “Help Centre”. It presents some clear examples.

• Confidence in this area is obtained by doing both techniques on the same dataset (permissible), and examining the results.

• Keep experimenting and pushing the limits.• And watch for advertisements for ModGraph and

MedGraph!