Presentation on theme: "Quantitative Marketing Seminar"— Presentation transcript:
1Quantitative Marketing Seminar MKT 8543Quantitative Marketing SeminarMediators, Moderators, and Multi-Group Analysis March 24, Mediation March 31, Moderation and Multi-Group AnalysisMississippi State UniversityNicole Ponder
2Helpful, Key ArticleBaron, 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.
3MediationA mediator explains or causes the relationship – the effects take place through the mediator. A mediator “comes between.”IndependentConstructDependentConstructIndependentConstructMediatorDependentConstruct
4Both direct and indirect effects; partial mediation There can be partial mediation as well as full mediation, or direct as well as indirect effectsIndirect effect;complete mediationIndependentConstructDependentConstructMediatorIndependentConstructMediatorBoth direct and indirect effects; partial mediationDependentConstruct
5Testing for Mediation a b c MediatorabIndependentConstructDependentConstructcDirect effects: if c is significant when the mediator is omitted from the model, then the independent construct directly affects the dependent constructIndirect effects: can be either full mediation or partial mediationFull 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. constructsa*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
6Example of MediationH4β = 0.279t = 2.542H1γ = 0.576t =InteractiveCommunicationH3γ =t =TrustCommitmentH2γ = 0.554t =H5β = 0.489t = 7.071SocialInteractionModel of the attorney-client relationship; n=308 clients
7Example of MediationPost-hoc analysis of trust and commitment in isolation: = 0.381t = 7.041TrustCommitment
8Testing for MediationDissertation 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.
9Testing for MediationApplying 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=12.00Path from trust to social bonds is 0.55; t-value=10.83
10Testing for MediationStep 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=2.26Path from social bonds to commitment is 0.49; t-value=6.77Step 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=-0.44Indirect 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.
11Moderation A moderator changes the relationship: Model 2 (hi) DependentConstructIndependentConstructDependentConstructModel 1 (lo)ModeratorIndependentConstruct
12ModerationExample 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),AttitudeAdAttitudeBrandAttitudeBrandPurchaseIntentionMotivationMotivationH3: Higher levels of motivation decreases the strength of the relationship between attitude towards the ad and attitude towards the brandH6: Higher levels of motivation increases the strength of the relationship between attitude towards the brand and brand purchase intentions
13ModerationLow 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 accordinglyHigh 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 intentionsAttitudeBrandPurchaseIntentionH6: Higher levels of motivation increases the strength of the relationship between attitude towards the brand and brand purchase intentionsMotivation
14Moderator AnalysisModerators 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 LISRELfor 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),
15Moderator AnalysisThe easier thing to do…create groups based on the values of the continuous moderator and do a multi-group analysisEx: group 1=low motivation, group 2=high motivationThis is a less powerful test than the continuous interaction analysisEsp. if the independent variable and the moderator are correlated – this analysis can be misleadingYou do need large samples to detect whether the moderator is significant
16Testing for Moderator Effects Using Multi-Group Analysis Multi-group analysis tests whether relationships between constructs are different depending on the value of the moderating variableYou can analyze your model for separate groups (2 or more) and see what’s differentDo 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
17Testing 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…γAttitudeAdAttitudeBrand
18Testing 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 invarianceMust use same items across groups (p. 79)Must set reference variables, same item must be used as reference across all groupsMust use covariance matrix, not correlation matrix (p. 82)
19Types 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?)
20Types 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
21Running Multi-Group Analyses New LISREL abbreviations:NG = 2 number of groups equals 2matrix = IN means matrix is invariant; same as the previous groupmatrix = PS means same pattern matrix and start values as previous groupMust 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
22Multi-Group Analysis: An Example MacKenzie and Spreng (1992) Low motivation group versus high motivation group:γAttitude towards the adAttitude towards the branda1a2a3b1b2b3H3: 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 attitudeIn other words, for those highly motivated to purchase, the gamma parameter estimate will be weaker than for those who are low in motivation
23Multi-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 invarianceDifference in chi-square values between the restricted and unrestricted analyses tests the significance of the equality constraints