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Mediation Mediation

Mediation - PowerPoint Presentation

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Mediation - PPT Presentation

That is Indirect Effects What is a Mediator An intervening variable X causes M and then M causes Y MacKinnon et al 2002 14 different ways to test mediation models Grouped into 3 general approaches ID: 241575

mediation effect direct indirect effect mediation indirect direct data correlated behavior causal multiple model correlation effects product subjects

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Slide1

Mediation

That is, Indirect EffectsSlide2

What is a Mediator?

An intervening variable.

X causes M and then M causes Y.Slide3

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 CoefficientsSlide4

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).Slide5

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.Slide6

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.Slide7

Criticisms

Low power.

Should not require that X be correlated with Y

X could have both a direct effect and an indirect effect on YWith the two effects being opposite in direction but equal in magnitude.Slide8

Differences in Coefficients

Compare

The correlation between Y and X (ignoring M)

With the β 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.Slide9

Product of Coefficients

The best approach

Compute the indirect path coefficient for effect of X on Y through M

The product ofr

XM

and

β

for predicting Y from M

partialled

for X

This product is the indirect effect

of X through M on YSlide10

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

.Slide11

Sobel’s

(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 errorSlide12

Alternative Error Terms

Aroian’s

(1944) second-order exact solution

Goodman’s (1960) unbiased solutionSlide13

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 ECUSlide14
Slide15

Causal Steps

Attitude is significantly correlated with behavior,

r

= .525.Attitude is significantly correlated with intention,

r

= .767.Slide16

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.Slide17

Product of CoefficientsSlide18

Aroian’s second-order exact solutionSlide19

http://quantpsy.org/sobel/sobel.htmSlide20

Or, Using Values of t

Merde

, short of statistical significance.Slide21

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.Slide22

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 !Slide23

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.Slide24

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.Slide25

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.Slide26

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.Slide27

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:Slide28
Slide29

Andrew F. Hayes

      If X is not determined through manipulation and random assignment, then any sequence of causal ordering of X, M, and Y must be entertained as a potential candidate for the direction of causal flow.

See

Mediation-Nonexperimental

and

Correlation-Causation-Mediation

.Slide30

Bootstrap Analysis

Shrout

and Bolger recommend bootstrapping when sample size is small.

They and Kris Preacher provide programs to do the bootstrapping.I’ll illustrate Preacher’s SPSS macro.

He has an SAS macro too.Slide31
Slide32

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.Slide33

%process

(

data

=

Ingram,y

=

Behavior,x

=Attitude,

m=

Intent,model

=

4

,

total=1,

boot=

10000

,effsize=

1

,

seed=

28513

);

Total=1 asks for total, direct, and indirect

effects

Effsize

=1 asks SAS to compute several effect size statisticsSlide34

Outcome: Intent

Model

 

coeff

t

p

LLCI

ULCI

Constant

3.3895

2.2309

0.0296

0.3483

6.4308

ATTITUDE

0.4225

9.1078

0.0000

0.3296

0.5154

Path

 = .4225.

The coefficients here are unstandardized. If you want standardized coefficients, standardize the data prior to analysis. Proc StandardSlide35

Outcome: Behavior

Path

 = 1.065

,

direct effect = .8066

,

neither are significant.

Model

 

coeff

t

p

LLCI

ULCI

constant

0.0747

0.0082

0.9934

-18.0600

18.2095

INTENT

1.0650

1.4179

0.1617

-0.4391

2.5691

ATTITUDE

0.8066

1.9500

0.0561

-0.0217

1.6350Slide36

Total effect of X on Y

Effect

t

p

LLCI

ULCI

1.2566

4.6948

0.0000

0.7208

1.7924

Indirect effect of X on Y

 

Effect

BootLLCI

BootULCI

INTENT

0.4500

-0.1081

1.0815

This is the unstandardized slope for predicting Behavior from Attitude ignoring Intention.

(Path

)(Path ) = .4225( 1.065) = .4500 Slide37

The Total Effect = 1.2566

Direct Effect = .8066

Indirect Effect = .4500

.8066 + .4500 = 1.2566Slide38

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 of how

influential the article will be. Mediator.Slide39

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.Slide40

Process Hayes

%

process

(data=pmi2,y=reactionZ,x

=

cond

,

m=

importZ

pmiZ,

boot

=

10000

,total=

1

,

normal=

1

,contrast=

1,model=

4

);

If you do not provide a custom seed, Process selects one for you.Slide41
Slide42

Parallel Multiple Mediation

Go over the output:

Annotated OutputSlide43

Serial Multiple Mediation

%

process

(data=pmi2,y=

reactionZ

,

x=

cond,m

=

importZ

pmiZ,

boot

=

10000

,

total=

1

,normal=

1

,contrast=

1

,model=6);Slide44
Slide45

Serial Multiple Mediation

Go over the output

Annotated OutputSlide46

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 attorney’s response was. Mediator.Slide47

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.Slide48

Process Hayes

%

process

(data=protest2,y=

LikingZ

,

x=

protest,w

=

SexismZ,m

=

RespapprZ

,

plot=

1

,model=

8

, boot=

10000

);Slide49
Slide50
Slide51

Multicategorical

X

(Protest = 0) subjects were told that the attorney did not protest the decision

(Protest = 1, individual protest) they were told that the attorney protested, complaining that the decision was not fair to her.

(Protest = 2, collective protest) they were told that the attorney protested, complaining that the decision was not fair to women. Slide52

%

process

(

data

=protest2,y=

Zliking,x

=protest,

m=

Zrespappr,mcx

=

1

,total=

1

,model=

4

,

seed=

28513

);

 

“mcx=1” indicates that there are more than two groups and that the grouping variable should be dummy coded with the group with the smallest numeric code (0, no protest) being the reference group.Slide53

Unlike Hayes, I standardized the continuous variables.

*********** PROCESS v3.1 for SAS **********

Model and Variables

Model: 4

Y: ZLIKING

X: PROTEST

M: ZRESPAPPRSlide54

Coding

X1 contrasts the individual protest group with the no protest group. X2 contrasts the collective protest group with the no protest group.

Coding of categorical X variable

for analysis:

PROTEST

X1

X2

0

0

0

1

1

0

2

0

1Slide55

Outcome ZRESPAPPR

Model

 

coeff

se

t

p

LLCI

ULCI

constant

-0.7285

0.1353

-5.3828

0.0000

-0.9964

-0.4607

X1

0.9355

0.1892

4.9456

0.0000

0.5612

1.3099

X2

1.1945

0.1871

6.3842

0.0000

0.8242

1.5647

Mean response appropriateness was .94 standard deviations higher in the individual protest group than in the no protest group

and 1.19 standard deviations higher in the collective protest group than in the no protest group. Slide56

Outcome ZLIKING

Model

 

coeff

se

t

p

LLCI

ULCI

constant

0.0744

0.1515

0.4909

0.6244

-0.2254

0.3741

X1

-0.0035

0.2086

-0.0169

0.9865

-0.4164

0.4093

X2

-0.2098

0.2172

-0.9658

0.3360

-0.6397

0.2201

ZRESPAPPR

0.5290

0.0899

5.8844

0.0000

0.3511

0.7069

Response appropriateness is strongly and significantly associated with liking. The coefficient here is a beta weight.

The groups’ partial effects are small, negative, and not significant.Slide57

Total Effects

Relative total effects of X on Y:

 

Effect

se

t

p

LLCI

ULCI

X1

0.4914

0.2149

2.2870

0.0239

0.0662

0.9166

X2

0.4221

0.2125

1.9863

0.0492

0.0016

0.8427

Omnibus test of total effect of X on Y:

R2-chng

F

df1

df2

p

0.0463

3.0552

2.0000

126.0000

0.0506Slide58

Direct Effects

Relative direct effects of X on Y

Effect

se

t

p

LLCI

ULCI

-0.0035

0.2086

-0.0169

0.9865

-0.4164

0.4093

-0.2098

0.2172

-0.9658

0.3360

-0.6397

0.2201

Omnibus test of direct effect of X on Y:

R2-chng

F

df1

df2

p

0.0087

0.7286

2.0000

125.0000

0.4846Slide59

Relative indirect effects of X on Y

 

 

Effect

BootSE

BootLLCI

BootULCI

X1

0.4949

0.1459

0.2441

0.8137

X2

0.6319

0.1600

0.3506

0.9730

The indirect effects for both X1 and X2 are significant. Each of these is the product of (the beta weight for predicting the mediator from X) times (the beta weight for predicting liking from the mediator).

X1: .9355(.529) = .4949

X2: 1.1945(.529) = .6319Slide60

A Fly in the OintmentSlide61

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.Slide62

a, b, and c are direct effects

x, m, and y are autoregressive effects