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- 1. The Moderator-Mediator Variable Distinction in Social Psychologicl Research: Conceptual Strstegic, and Statistical Consideration Reuben Baron and David Kenny (1986) Journal of Personality and Social Psychology
- 2. Moderator-Mediator
- Distinction of the moderator and mediator
- The functions are discussed in three levels:
- 3. The Nature of Moderation
- A moderator is qualitative (e.g., gender, race, class) or quantitative (e.g. level of reward) variable that affects the direction and/or strength of the relation between an independent or predictor variable and a dependent or criterion variable.
- Specifically, within a correlational analysis framework, a moderator is a third variable that affects the zero-order between two other variables.
- 4. The Nature of Moderation
- A basic moderator can be represented as an interaction between a focal variable and a factor that specifies the appropriate conditions for its operation.
- 5. Framework for testing Moderation Predictor Moderator Outcome Variable
- 6. Framework for testing Moderation Predictor Moderator Predictor X Moderator Outcome Variable a b c
- 7. Framework for testing Moderation
- It is desirable that the moderator variable be uncorrelated with both the predictor and the criterion to provide a clearly interpretable interaction term
- The moderator variable always function as an independent variable.
- 8. Analytic procedure for testing moderation
- The statistical analysis must measure and test the differential effect of the independent variable on the dependent variable as a function of moderator.
- 9. Case 1: Moderator and IV are Categorical
- A dichotomous independent variables effect on the dependent variable varies as a function of another dichotomy.
- 2 x 2 ANOVA
- The moderation is indicated by the interaction
- 10. Case 2: Moderator is categorical and IV is continuous
- Correlate the independent with dependent separately for each category of the moderator.
- Ex. Action control is correlated with student participation for each level of achievement (high and low)
- 11. Case 2: Moderator is categorical and IV is continuous
- Deficiency: Assumes that the IV has equal variance at each level of the moderator
- The effect of IV on DV is tested using unstandardized regression coefficient. The regression coefficients are then tested for difference (see formula, Cohen & Cohen, 1983, p. 56)
- Reliabilities should be tested for the levels of moderation, and slopes should be disattenuated.
- 12. Case 3: Moderator is continuous and IV is categorical
- We must know a priori how the effect of the IV varies as a function of the moderator.
- (1) Linear function
- (2) Step function
- (3) Quadratic Function
- Example: IV: Rational vs. fear-arousing attitude change
- Moderator: Intelligence (IQ test)
- 13. Case 3: Moderator is continuous and IV is categorical
- Linear function : The moderator alters the effect of the IV on the DV.
- The effect of the IV changes linearly with respect to the moderator
- 14. Case 3: Moderator is continuous and IV is categorical
- Linear function
- Tested by adding the product of the moderator and the dichotomous IV to the regression equation
- Y = a + (X) + (Z) + (XZ)
- Moderation is indicated by XZ having a significant effect while X and Z are controlled.
- 15. Case 3: Moderator is continuous and IV is categorical
- Quadratic Function : The effect can be tested by dichotomizing the moderator at the point at which the function is presumed to accelerate.
- The effect of the IV should be greatest for those who are high on the moderator.
- 16. Case 3: Moderator is continuous and IV is categorical
- Quadratic function
- Can be tested using hierarchical regression
- Y = a + (X) + (Z) + (XZ) + (Z 2 ) + (XZ 2 )
- The test of quadratic moderation is given by the test XZ 2
- The interpretation is aided by graphing the predicted values for various values of X and Z.
- 17. Case 3: Moderator is continuous and IV is categorical
- Step function: dichotomizing the moderator at the point where the step is suppose to occur.
- 18. Case 4: Moderator and IV are continuous
- One can dichotomize the moderator at the point where the step tales place (step function)
- The measure of the effect of the IV is a regression coefficient.
- If the effect of the IV (X) on the DV (Y) varies linearly or quadratically with respect to the moderator (Z), the moderator squared is introduced.
- The XZ product term is tested by moderation
- 19. The Nature of Mediator Variables
- The effects of stimuli on behavior are mediated by various transformation procedures internal to the organism.
- The effect of IV on DV is mediated by another variable
- 20. Framework for testing Mediation Independent Variable Outcome Variable Mediator Variable a b c
- 21. Framework for testing Mediation
- A variable functions as a mediator when it meets the following conditions:
- (a) Variations in levels of the IV significantly account for variations in the presumed mediator (i.e., Path c)
- (b) Variations in the mediator significantly account for variations in the DV (i.e., Path b),
- (c) when Paths a and b are controlled, a previously significant relation between the IV and DV is no longer significant, with the strongest demonstration of mediation occurring when Path c is zero.
- 22. Framework for testing Mediation
- When Path c is reduced to zero, we have strong evidence for a single, dominant mediator.
- If the residual Path c is not zero, this indicates the operation of multiple mediating factors.
- 23. Analytic procedures for testing for mediation
- Conduct a series of regression models:
- 1. regressing the mediator on the independent variable;
- 2. regressing the dependent variable on the independent variable;
- 3. regressing the dependent variable on both the independent variable and on the mediator.
- 24. Analytic procedures for testing for mediation
- To establish mediation, the following conditions must hold:
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