Structure

1. Structure Mediation Structural Equation Modeling

2. Research Questions:(from Tabachnick & Fidell, Chapter 2) • Degree of relationship amongst variables • Correlation • Linear Regression • Prediction of group membership • Logistic Regression • Structure • Mediation • Structural Equation Modeling (SEM) • Significance of group differences • 2 groups: t-test • 3+ groups: ANOVA

3. Research Questions:(from Tabachnick & Fidell, Chapter 2) • Degree of relationship amongst variables • Correlation • Linear Regression • Prediction of group membership • Logistic Regression • Structure • Mediation • Structural Equation Modeling (SEM) • Significance of group differences • 2 groups: t-test • 3+ groups: ANOVA

4. Overview of “Structure” • Defined: Testing interrelationships amongst variables • Variables: Variables are continuous and/or categorical (notice we are not talking about IVs and DVs) • Relationship: Structure amongst variables • Example: What is the relationship between provocation, anger, aggression, identifying with victim, perceiving outgroup as cohesive, etc • Assumptions: If linear: Normality. Linearity. Multicollinearity If categorical: Multicollinearity

5. Relationship to correlation/regression/logistic (CRL) • CRL involves: • 1 DV • 1+ IV IV 1 DV IV 2 IV 3

6. Relationship to correlation/regression/logistic (CRL) • CRL involves: • 1 DV • 1+ IV • Structure • 2+ variables Just a few of the permutations: (any variable can go in any position) IV 2 IV3 IV 1 IV4 IV 1 IV 2 IV 3 IV 4 IV2 IV 1 IV 3

7. Relationship to correlation/regression/logistic (CRL) • CRL involves: • 1 DV • 1+ IV • Structure • 2+ variables NOT CAUSATION(only correlation) PSEUDO CAUSATION(“true” causation is experiments)

8. How to test for structure: • Goal is to find best fitting model • You find best fitting model by looking at converging evidence of various criteria • Start with “confirmatory” analysis testing your hypothesis • Then move to “exploratory” analysis in which you first disconfirm rival hypotheses, and then test for new hypotheses • You have so many possible permutations of the variables that exploratory analysis is usually not comprehensive

9. Mediation: Terminology • See my PsychWiki page -- http://www.psychwiki.com/wiki/Mediation • Variables: • X is the predictor • Y is the outcome • M is the mediator • Paths • C is the total effect • C’ is the direct effect • A-to-B is the indirect

10. Mediation: Baron and Kenny • Most commonly used and most frequently cited test of mediation, but also the most flawed. • Four steps • X predicts Y (path c sig) • X predicts M (path a sig) • M predicts Y (path b sig) • X does NOT predict Y when controlling for M (path c’ NOT sig)

11. Mediation: Sobel test • The Sobel test is superior to the Baron & Kenny method in terms of all the limitations of the B&K method (e.g., power, Type I error, suppression effects, addressing the significance of the indirect effect). • Math is complicated, but basically the Sobel test tests the significance of the relationship between c and c’

12. Mediation: Example Anger • Baron and Kenny: • In the first step of the analysis, there was a significant relationship between Provocation and Aggression ( = .20, p = .05). • In the second step of analysis, there was a significant relationship between Provocation and Anger ( = .26, p = .01). • In the final step of the analysis, there was a significant relationship between Anger and Aggression ( = .26, p = .03), while the relationship between Provocation and Aggression became non-significant ( = .10, p = .31). • Sobel • There was a significant initial relationship between Provocation and Aggression ( = .20, p = .05) that was non-significant after controlling for the mediator ( = .14, p = .31) which indicates Anger mediates the relationship between Provocation and Aggression. Provocation Aggression

13. SEM: Terminology • Exogenous variable: not caused by another • Endogenous variable: caused by another • Coefficients: strength of relationship • Path model: see below • Model fit: see next page .45*** .25** Anger composite Identification Retribution towards the Perpetrator .23* .31*** .56*** Entitativity Retribution towards the Group .20*

14. SEM: Criteria • Theory: (1) Evaluating multiple fit indices simultaneously is recommended… (2) because different indices assess different aspects of goodness-of-fit… (3) and there is not always agreement on what constitutes good fit… (4) so satisfactory models should show consistently good-fitting results on many different indices. • Four recommended criteria: (1) Comparison:Chi-square: p < .05 (2) Parsimony:Ratio of x2/df< 3 (3) Absolute fit:SRMR < .08 (4) Relative fit:CFI> .95

15. SEM: Example • Overall model fit was excellent: X2=1.03, p =.794, x2/df =.34, SRMR =.03, CFI =1.00. • Alternative models achieved less satisfactory fit: (1) Other models didn’t reach criteria from hypothesized model (2) Nested models (subset of other) was sig chi-square test (3) Un-nested models had lower AIC value .45*** .25** Anger composite Identification Retribution towards the Perpetrator .23* .31*** .56*** Entitativity Retribution towards the Group .20*