Research Methods in Business Fall 2011 Hypothesis Development: Moderation & Mediation Dr. Stefan Wuyts Associate Professor Marketing Koç University swuyts@ku.edu.tr

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

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

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

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.

Correct: Incorrect:

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

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

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)

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)

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

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.

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

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

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 +/- -154.93*** -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

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

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 +/- -154.93*** -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

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:

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

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)

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

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

Mediated moderation / moderated mediation Muller et al. 2005 start again from BK1986: Interestingly, the following holds with regard to the indirect effect of X on Y: In case of moderation:

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:

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.

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

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.