1. Quantitative Marketing Seminar
MKT 8543
Quantitative Marketing Seminar
Mediators, Moderators, and Multi-Group Analysis March 24, Mediation March 31, Moderation and Multi-Group Analysis
Mississippi State University
Nicole Ponder

2. Helpful, Key Article
Baron, R. and D. Kenny (1986), “The Moderator-Mediator Variable Distinction in Social Psychology Research: Conceptual, Strategic, and Statistical Considerations,” Journal of Personality and Social Psychology,” 51,
The standard to cite when you are referring to the testing of mediation and/or moderation.

3. Mediation
A mediator explains or causes the relationship – the effects take place through the mediator. A mediator “comes between.”
Independent
Construct
Dependent
Construct
Independent
Construct
Mediator
Dependent
Construct

4. Both direct and indirect effects; partial mediation
There can be partial mediation as well as full mediation, or direct as well as indirect effects
Indirect effect;
complete mediation
Independent
Construct
Dependent
Construct
Mediator
Independent
Construct
Mediator
Both direct and indirect effects; partial mediation
Dependent
Construct

5. Testing for Mediation a b c
Mediator a b
Independent
Construct
Dependent
Construct c
Direct effects: if c is significant when the mediator is omitted from the model, then the independent construct directly affects the dependent construct
Indirect effects: can be either full mediation or partial mediation
Full mediation: If a and b are significant, but c becomes non-significant when the mediator is included, then the mediator completely mediates the relationship between the indep. and dep. constructs
a*b is the indirect effect of the indep. construct on the dep. construct, which you can get by stating EF on the LISREL output line (effect sizes)
Partial mediation: If c becomes smaller but is still significant, then the mediator partially mediates the effect of indep. on dep. construct

6. Example of Mediation H4
β = 0.279
t = 2.542 H1
γ = 0.576
t =
Interactive
Communication H3
γ =
t =
Trust
Commitment H2
γ = 0.554
t = H5
β = 0.489
t = 7.071
Social
Interaction
Model of the attorney-client relationship; n=308 clients

7. Example of Mediation
Post-hoc analysis of trust and commitment in isolation:
 = 0.381
t = 7.041
Trust
Commitment

8. Testing for Mediation
Dissertation example was a very simple one. Testing for mediation actually has four step (Baron and Kenny 1986):
Step 1:  Show that the indep. variable is correlated with the dep. variable.  Run a structural model with just the indep. and dep. constructs (estimate and test path c). This step establishes that there is an effect that may be mediated.
Step 2: Show that the indep. construct is correlated with the mediator.  Examine the direct effect of indep. construct on the mediator (test path a).  This step essentially involves treating the mediator as if it were an outcome variable.
Step 3:  Show that the mediator affects the outcome variable.  Examine the direct effect of the mediator on the dep. construct (test path b). 
Step 4:  The initially significant relationship between the indep. and dep. constructs becomes nonsignificant when the mediator is accounted for in the model. (Run the full structural model, with all constructs included.) This is full mediation. If the path between the indep. and dep. constructs is still significant, but weaker than the path in Step 1, then partial mediation exists.

9. Testing for Mediation
Applying these steps to a model of real estate agent-client relationships:
Step 1:  Run a structural model with just the indep. and dep. constructs (estimate and test path c). This step establishes that there is an effect that may be mediated.
The path from trust to commitment is 0.38; t-value= Thus, there is a significant direct effect of trust on commitment.
Step 2: Examine the direct effect of indep. construct on the mediator. 
Path from trust to communication is 0.58; t-value=12.00
Path from trust to social bonds is 0.55; t-value=10.83

10. Testing for Mediation
Step 3:  Show that the mediator affects the outcome variable.  Examine the direct effect of the mediator on the dep. construct (test path b). 
Path from communication to commitment is 0.26; t-value=2.26
Path from social bonds to commitment is 0.49; t-value=6.77
Step 4:  The initially significant relationship between the indep. and dep. constructs becomes nonsignificant when the mediator is accounted for in the model. (Run the full structural model, with all constructs included.) This is full mediation. If the path between the indep. and dep. constructs is still significant, but weaker than the path in Step 1, then partial mediation exists.
Path from trust to commitment is -0.04; t-value=-0.44
Indirect effects of trust on commitment is 0.42; t-value= These are the total indirect effects. To calculate specific indirect effects if you have multiple mediators, you need to conduct the Sobel test.
See David Kenny’s website: for more detailed information.

11. Moderation A moderator changes the relationship: Model 2 (hi)
Dependent
Construct
Independent
Construct
Dependent
Construct
Model 1 (lo)
Moderator
Independent
Construct

12. Moderation
Example of moderation: Mackenzie, Scott B. and Richard A. Spreng (1992), “How Does Motivation Moderate the Impact of Central and Peripheral Processing on Brand Attitudes and Intentions?,” Journal of Consumer Research, 18 (March),
Attitude Ad
Attitude
Brand
Attitude
Brand
Purchase
Intention
Motivation
Motivation
H3: Higher levels of motivation decreases the strength of the relationship between attitude towards the ad and attitude towards the brand
H6: Higher levels of motivation increases the strength of the relationship between attitude towards the brand and brand purchase intentions

13. Moderation
Low motivation group: not really in the market to buy a wristwatch, so even if you really like the ad, your purchase intentions do not increase accordingly
High motivation group: you are highly motivated to engage in the information search process for a new watch; if you develop a favorable attitude towards the brand, this could greatly increase purchase intentions
Attitude
Brand
Purchase
Intention
H6: Higher levels of motivation increases the strength of the relationship between attitude towards the brand and brand purchase intentions
Motivation

14. Moderator Analysis
Moderators may be continuous variables (e.g., religiosity) or categorical variables (e.g., gender, country of origin)
For continuous interactions…
ideally, should be tested as y = f(x, z, and x*z)
unfortunately, continuous interactions are difficult to model in LISREL
for more info, see Ping Jr., Robert A. (1996), “Latent Variable Interaction and Quadratic Effect Estimation: A Two-Step Technique Using Structural Equation Analysis,” Psychological Bulletin, 119 (1),
Li et.al. (1998), “Approaches to Testing Interaction Effects Using Structural Equation Modeling Methodology,” Multivariate Behavioral Research, 33 (1), 1-39.
Bollen, Kenneth A. and Pamela Paxton (1998), “Interactions of Latent Variables in Structural Equation Models,” Structural Equation Modeling, 5 (3),

15. Moderator Analysis
The easier thing to do…create groups based on the values of the continuous moderator and do a multi-group analysis
Ex: group 1=low motivation, group 2=high motivation
This is a less powerful test than the continuous interaction analysis
Esp. if the independent variable and the moderator are correlated – this analysis can be misleading
You do need large samples to detect whether the moderator is significant

16. Testing for Moderator Effects Using Multi-Group Analysis
Multi-group analysis tests whether relationships between constructs are different depending on the value of the moderating variable
You can analyze your model for separate groups (2 or more) and see what’s different
Do your parameter estimates change from one group to another? How about the overall fit for group 1 versus group 2?
LISREL can do this in one run and provide info to give you the desired significance tests

17. Testing for Moderator Effects Using Multi-Group Analysis
Is the relationship here (the gamma parameter estimate) different between highly motivated and low-motivation consumers? Hint of example to come… γ
Attitude Ad
Attitude
Brand

18. Testing for Moderator Effects Using Multi-Group Analysis
Steenkamp and Baumgartner (1998):
Multigroup CFA model represents the most powerful and versatile approach for testing cross-national measurement invariance
Must use same items across groups (p. 79)
Must set reference variables, same item must be used as reference across all groups
Must use covariance matrix, not correlation matrix (p. 82)

19. Types of Invariance in Multi-Group Analysis Steenkamp and Baumgartner (1998)
Configural invariance: are the models the same across different groups? (also see J&S p. 281: testing equality of factor structures)
Metric invariance (or measurement invariance): are lambda-x and lambda-y equal across different groups?
Scalar invariance: are the construct means equal across different groups?, an additional constraint on the model of metric invariance (see J&S Chapter 10: LISREL with mean structures for more information)
Other forms of invariance: factor covariance invariance and factor variance invariance (is phi equal across groups?; see J&S p. 285 as an example); error variance invariance (are the deltas equal across groups?)

20. Types of Invariance in Multi-Group Analysis
Steenkamp and Baumgartner (1998):
The authors also distinguish between full invariance and partial invariance (p. 81)
If full metric invariance is not achieved, the researcher may begin relaxing invariance constraints one by one to see what model fits the data the best (p. 85)
Constraints are relaxed according to the modification indices

21. Running Multi-Group Analyses
New LISREL abbreviations:
NG = 2 number of groups equals 2
matrix = IN means matrix is invariant; same as the previous group
matrix = PS means same pattern matrix and start values as previous group
Must use covariance matrix and set reference variables (instead of analyzing as a correlation matrix and standardizing phi)
On the MO line, the number of variables and the form of each matrix (LY, LX, etc.) is set for group 1 and must be the same for all other groups

22. Multi-Group Analysis: An Example MacKenzie and Spreng (1992)
Low motivation group versus high motivation group: γ
Attitude towards the ad
Attitude towards the brand a1 a2 a3 b1 b2 b3
H3: Motivation decreases the impact of attitude towards the ad on brand attitude by decreasing the strength of the relationship between attitude toward the ad and brand attitude
In other words, for those highly motivated to purchase, the gamma parameter estimate will be weaker than for those who are low in motivation

23. Multi-Group Analysis: An Example
Less restricted model: parameter estimates associated with the measurement equations are restricted to be the same (lx, ly, td, te, and ps are set to invariance)
More restricted model: addition of ga=in (gamma is invariant): the structural relationship in group 1 and group 2 is restricted to be the same; all of the other model parameters are also set to invariance
Difference in chi-square values between the restricted and unrestricted analyses tests the significance of the equality constraints