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					                                 MKT 8543
                      Quantitative Marketing Seminar



    Mediators, Moderators, and
    Multi-Group Analysis


    March 24, 2009 Mediation

    March 31, 2009 Moderation and Multi-Group Analysis




Mississippi State University                             Nicole Ponder
 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, 1173-1182.

 The standard to cite when you are referring to the testing
  of mediation and/or moderation.
 Mediation

 A mediator explains or causes the relationship – the
  effects take place through the mediator. A mediator
  “comes between.”

                 Independent              Dependent
                  Construct               Construct




       Independent             Mediator               Dependent
        Construct                                     Construct
Mediation

 There can be partial mediation as well as full
     mediation, or direct as well as indirect effects


Independent             Mediator               Dependent         Indirect effect;
 Construct                                     Construct       complete mediation


              Independent          Mediator
               Construct                                    Both direct and indirect
                                                           effects; partial mediation

                                   Dependent
                                   Construct
    Testing for Mediation

                                             Mediator

                                a                              b
                 Independent                                       Dependent
                  Construct                                        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
Example of Mediation


                   H1         Interactive   H4
              γ = 0.576     Communication   β = 0.279
              t = 11.968                    t = 2.542


                                   H3
      Trust                                     Commitment
                               γ = -0.049
                               t = -0.562
                   H2
               γ = 0.554                    H5
               t = 10.922       Social
                                            β = 0.489
                              Interaction
                                            t = 7.071


 Model of the attorney-client relationship; n=308
 clients
Example of Mediation


Post-hoc analysis of trust and commitment in isolation:



                                  = 0.381
                                 t = 7.041
            Trust                                     Commitment
    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.
    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=7.04. 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
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=5.86. 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: http://davidakenny.net/cm/mediate.htm for
    more detailed information.
Moderation


• A moderator changes the relationship:


 Dependent      Model 2
 Construct       (hi)           Independent               Dependent
                                 Construct                Construct


                      Model 1
                       (lo)
                                              Moderator
                Independent
                 Construct
    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), 519-529.



    Attitude                               Attitude   Attitude                              Purchase
      Ad                                    Brand      Brand                                Intention




                     Motivation                                        Motivation




     H3: Higher levels of motivation decreases        H6: Higher levels of motivation increases the
     the strength of the relationship between          strength of the relationship between attitude
     attitude towards the ad and attitude towards      towards the brand and brand purchase intentions
     the brand
    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                     Purchase
        Brand                       Intention

                                                   H6: Higher levels of motivation increases the
                                                   strength of the relationship between attitude
                    Motivation                     towards the brand and brand purchase intentions
    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), 166-175.
        • 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),
          267-293.
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
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
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…



              Attitude
                         γ        Attitude
                Ad                 Brand
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)
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?)
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
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
    Multi-Group Analysis: An Example
    MacKenzie and Spreng (1992)




 Low motivation group versus high motivation group:

                         Attitude     γ               Attitude
                       towards the                  towards the
                            ad                         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
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

				
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