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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: