# moderator mediator

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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:

- Conceptual

- Strategic

- Statistical

- 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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