1. Research Methods in Business Fall 2011 Hypothesis Development: Moderation & Mediation
Dr. Stefan Wuyts
Associate Professor Marketing
Koç University

2. Agenda Mediation Moderation
Baron & Kenny 1986
Zhao, Lynch & Chen 2010
Moderation
Wuyts & Geyskens 2005
Simple slopes
Mediated moderation and moderated mediation
Muller, Judd & Yzerbyt 2005
Edwards & Lambert 2007

3. Mediation Baron & Kenny 1986
Third variable represents generative mechanism through which the focal independent variable is able to influence the dependent variable.
Conditions:
X influence Y
X influences M
M influences Y
When M is controlled, X no longer influences Y X M Y a b c

4. The significance of the indirect effect can be estimated (Sobel)
Assumption of normality for the standard error of the indirect effect ab
Assumption that the DV does not cause the mediator X M Y a b c

5. Zhao et al. 2010: myths and truths of BK86
Critique 1: Supervisor to student: “Once you have the effect, then you can look for mediation”
Wrong!
Strength of mediation measured by size of the indirect effect, not by lack of main effect;
X need not influence Y directly;
Direct effect and indirect effect can have opposite signs:
Own research on the effect of alliance portfolio diversity on profitability: positive indirect effect through radical product innovation and direct negative effect due to cost.

6. Correct: Incorrect:

7. Critique 2: “full mediation is best scenario” Wrong
Critique 2: “full mediation is best scenario” Wrong! Theory building is gradual process. Take Morgan & Hunt 1994: Later on Palmatier et al. 2006:
Relationship marketing activities
Trust, commitment
Business outcomes
Relationship marketing activities
Trust, commitment
Business outcomes
Consumer gratitude

8. Zhao et al. distinguish between:
Complementary mediation
Competitive mediation
Indirect-only mediation
Direct-only nonmediation
No-effect nonmediation

9. Critique 3: Sobel test assumes normal distribution with 95% confidence interval symmetrically around the mean estimates of a*b, while the sampling distribution of the product of two parameters is not normal. Better use bootstrap test (random sampling with replacement, 5000 samples of size N  empirical distribution of a x b estimates)

10. Bootstrapping Intuition:
Randomly draw a sample of size n with replacement out of the original sample N, with each element i being selected at most t times.
Replicate this r times.
Calculate the target statistic s, e.g., indirect effect a*b, in each replication r.
Determine the distribution of s over r.
Determine Mean, se of M, and Confidence interval (CI) of s.
Advantage:
Simple estimation of complex statistics (even in N < 20)
Disadvantage:
Tends to be overly optimistic (no finite-sample guarantees)

11. See Figure 2!
Main conclusion:
All you need to do is conduct bootstrap test of the indirect effect a*b.

12. Moderation
A moderator affects the direction and/or strength of the relation between an independent variable and a dependent variable (Baron & Kenny 1986)
Remember: try not to dichotomize
Focus on predictor x moderator, but that assumes that the effect of the independent variable on the dependent variable changes linearly with respect to the moderator.

13. Interaction effects are important to advance theory:
Governance forms as hedges against different forms of uncertainty
Higher-order interaction effects can help clarify mechanism behind main or lower-order interaction effects

14. Technological uncertainty
Cultural distance
Control variables
R&D know-how
Labor cost savings
Firm size
Governance
Minority equity stake
Outsourcing
performance
Relationship history

15. Hypothesized Sign
ba)
t-Value
Intercept
-.19
-.66
Governance mechanism
Equity participation (EqPart)
.98
1.67
Prior tie selection (Tie)
-.07
-.20
Uncertainty
Technological uncertainty (TechUnc)
-5.33
-.72
Cultural distance (CulDis)
-.21
-.88
Interaction Effects
EqPart * TechUnc +
128.80***
3.40
Tie * TechUnc -
-29.18**
-2.01
EqPart * CulDis
-1.13**
-2.19
Tie * CulDis
.54*
1.63
EqPart * Tie
-.17
EqPart * Tie * TechUnc
+/-
***
-3.07
EqPart * Tie * CulDis
2.71***
2.59
Control Variablesb
Labor cost savings
.02
.89
Firm size
-.11
-1.21
Profitability
.28
1.37

16. Technological uncertainty
Cultural distance
Control variables
R&D know-how
Labor cost savings
Firm size
Governance
Minority equity stake
Outsourcing
performance
Relationship history

17. Hypothesized Sign
ba)
t-Value
Intercept
-.19
-.66
Governance mechanism
Equity participation (EqPart)
.98
1.67
Prior tie selection (Tie)
-.07
-.20
Uncertainty
Technological uncertainty (TechUnc)
-5.33
-.72
Cultural distance (CulDis)
-.21
-.88
Interaction Effects
EqPart * TechUnc +
128.80***
3.40
Tie * TechUnc -
-29.18**
-2.01
EqPart * CulDis
-1.13**
-2.19
Tie * CulDis
.54*
1.63
EqPart * Tie
-.17
EqPart * Tie * TechUnc
+/-
***
-3.07
EqPart * Tie * CulDis
2.71***
2.59
Control Variablesb
Labor cost savings
.02
.89
Firm size
-.11
-1.21
Profitability
.28
1.37

18. Calculating simple slopes (Aiken & West 1991):
Insightful to know the sign, size, and significance of the effect of X on Y at different levels of moderator Z.
Standard error of simple slope is given as:

19. Calculating simple slopes (Aiken & West 1991):
Insightful to know the sign, size, and significance of the effect of X on Y at different levels of moderator Z.
Standard error of simple slope is given as:
in which , and

20. Calculating simple slopes (Aiken & West 1991):
Insightful to know the sign, size, and significance of the effect of X on Y at different levels of moderator Z.
Standard error of simple slope is given as:
in which , and
with
~ t(n-k-1)

21. Mediated moderation / moderated mediation
Example of mediated moderation (Muller et al.)
X = morality vs might primes
Y = cooperation vs competition
Mo = pro-self vs pro-social

22. Mediated moderation / moderated mediation
Example of moderated mediation (Muller et al.) People low in need for cognition: People high in need for cognition:
Positive mood
Persuasion
Positive mood
Positively valenced thoughts
Persuasion

23. Mediated moderation / moderated mediation
Muller et al start again from BK1986:
Interestingly, the following holds with regard to the indirect effect of X on Y:
In case of moderation:

24. Situation gets somewhat complicated:
Simple treatment effects can be estimated at different levels of Mo. For example, the moderated indirect effect of X via the mediator is:

25. Ultimately, let the theory speak:
If we want to understand the process behind moderation, mediated moderation is called for;
If we expect that the mediation process depends on a moderator, moderated mediation is called for.

26. Edwards and Lambert (2007) criticize the Muller et al. approach:
First of all, similar flaws as Baron & Kenny
Second, see Figure 1 for many alternative possibilities
E&L also criticize so-called subgroup approach (as in multi-group SEM, see later)
Lower statistical power
Death to dichotomizing
Does not provide a formal test of difference in mediation between subgroups

27. They propose mediation in terms of path models and moderation by supplementing the equations with moderator variables. Then integrate the equations to reduced form equations.
For example, if moderation occurs at both stages (X on Me and Me on Y), then the reduced form equation includes Mo*Mo.
Since the reduced form equations can contain products of regression coefficients, bootstrapping is called for.