Structure Mediation Structural Equation Modeling

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

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

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

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

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

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)

How to test for structure: (1)Goal is to find best fitting model (2)You find best fitting model by looking at converging evidence of various criteria (3)Start with “confirmatory” analysis testing your hypothesis (4)Then move to “exploratory” analysis in which you first disconfirm rival hypotheses, and then test for new hypotheses (5)You have so many possible permutations of the variables that exploratory analysis is usually not comprehensive

Mediation: Terminology See my PsychWiki page 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

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)

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’

Mediation: Example 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. ProvocationAggression Anger

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 Identification Entitativity Retribution towards the Perpetrator Retribution towards the Group Anger composite.25**.45***.23*.20*.31***.56***

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 x 2 /df < 3 (3) Absolute fit: SRMR <.08 (4) Relative fit: CFI >.95

SEM: Example Overall model fit was excellent: X 2 =1.03, p =.794, x 2 /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 Identification Entitativity Retribution towards the Perpetrator Retribution towards the Group Anger composite.25**.45***.23*.20*.31***.56***