Moderator mediator

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Moderator mediator

  1. 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. 2. Moderator-Mediator <ul><li>Distinction of the moderator and mediator </li></ul><ul><li>The functions are discussed in three levels: </li></ul><ul><ul><li>Conceptual </li></ul></ul><ul><ul><li>Strategic </li></ul></ul><ul><ul><li>Statistical </li></ul></ul>
  3. 3. The Nature of Moderation <ul><li>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. </li></ul><ul><li>Specifically, within a correlational analysis framework, a moderator is a third variable that affects the zero-order between two other variables. </li></ul>
  4. 4. The Nature of Moderation <ul><li>A basic moderator can be represented as an interaction between a focal variable and a factor that specifies the appropriate conditions for its operation. </li></ul>
  5. 5. Framework for testing Moderation Predictor Moderator Outcome Variable
  6. 6. Framework for testing Moderation Predictor Moderator Predictor X Moderator Outcome Variable a b c
  7. 7. Framework for testing Moderation <ul><li>It is desirable that the moderator variable be uncorrelated with both the predictor and the criterion to provide a clearly interpretable interaction term </li></ul><ul><li>The moderator variable always function as an independent variable. </li></ul>
  8. 8. Analytic procedure for testing moderation <ul><li>The statistical analysis must measure and test the differential effect of the independent variable on the dependent variable as a function of moderator. </li></ul>
  9. 9. Case 1: Moderator and IV are Categorical <ul><li>A dichotomous independent variable’s effect on the dependent variable varies as a function of another dichotomy. </li></ul><ul><li>2 x 2 ANOVA </li></ul><ul><li>The moderation is indicated by the interaction </li></ul>
  10. 10. Case 2: Moderator is categorical and IV is continuous <ul><li>Correlate the independent with dependent separately for each category of the moderator. </li></ul><ul><li>Ex. Action control is correlated with student participation for each level of achievement (high and low) </li></ul>
  11. 11. Case 2: Moderator is categorical and IV is continuous <ul><li>Deficiency: Assumes that the IV has equal variance at each level of the moderator </li></ul><ul><li>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) </li></ul><ul><li>Reliabilities should be tested for the levels of moderation, and slopes should be disattenuated. </li></ul>
  12. 12. Case 3: Moderator is continuous and IV is categorical <ul><li>We must know a priori how the effect of the IV varies as a function of the moderator. </li></ul><ul><li>(1) Linear function </li></ul><ul><li>(2) Step function </li></ul><ul><li>(3) Quadratic Function </li></ul><ul><li>Example: IV: Rational vs. fear-arousing attitude change </li></ul><ul><li>Moderator: Intelligence (IQ test) </li></ul>
  13. 13. Case 3: Moderator is continuous and IV is categorical <ul><li>Linear function : The moderator alters the effect of the IV on the DV. </li></ul><ul><li>The effect of the IV changes linearly with respect to the moderator </li></ul>
  14. 14. Case 3: Moderator is continuous and IV is categorical <ul><li>Linear function </li></ul><ul><li>Tested by adding the product of the moderator and the dichotomous IV to the regression equation </li></ul><ul><li>Y = a + β (X) + β (Z) + β (XZ) </li></ul><ul><li>Moderation is indicated by XZ having a significant effect while X and Z are controlled. </li></ul>
  15. 15. Case 3: Moderator is continuous and IV is categorical <ul><li>Quadratic Function : The effect can be tested by dichotomizing the moderator at the point at which the function is presumed to accelerate. </li></ul><ul><li>The effect of the IV should be greatest for those who are high on the moderator. </li></ul>
  16. 16. Case 3: Moderator is continuous and IV is categorical <ul><li>Quadratic function </li></ul><ul><li>Can be tested using hierarchical regression </li></ul><ul><li>Y = a + β (X) + β (Z) + β (XZ) + β (Z 2 ) + β (XZ 2 ) </li></ul><ul><li>The test of quadratic moderation is given by the test XZ 2 </li></ul><ul><li>The interpretation is aided by graphing the predicted values for various values of X and Z. </li></ul>
  17. 17. Case 3: Moderator is continuous and IV is categorical <ul><li>Step function: dichotomizing the moderator at the point where the step is suppose to occur. </li></ul>
  18. 18. Case 4: Moderator and IV are continuous <ul><li>One can dichotomize the moderator at the point where the step tales place (step function) </li></ul><ul><li>The measure of the effect of the IV is a regression coefficient. </li></ul><ul><li>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. </li></ul><ul><li>The XZ product term is tested by moderation </li></ul>
  19. 19. The Nature of Mediator Variables <ul><li>The effects of stimuli on behavior are mediated by various transformation procedures internal to the organism. </li></ul><ul><li>The effect of IV on DV is mediated by another variable </li></ul>
  20. 20. Framework for testing Mediation Independent Variable Outcome Variable Mediator Variable a b c
  21. 21. Framework for testing Mediation <ul><li>A variable functions as a mediator when it meets the following conditions: </li></ul><ul><li>(a) Variations in levels of the IV significantly account for variations in the presumed mediator (i.e., Path c) </li></ul><ul><li>(b) Variations in the mediator significantly account for variations in the DV (i.e., Path b), </li></ul><ul><li>(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. </li></ul>
  22. 22. Framework for testing Mediation <ul><li>When Path c is reduced to zero, we have strong evidence for a single, dominant mediator. </li></ul><ul><li>If the residual Path c is not zero, this indicates the operation of multiple mediating factors. </li></ul>
  23. 23. Analytic procedures for testing for mediation <ul><li>Conduct a series of regression models: </li></ul><ul><li>1. regressing the mediator on the independent variable; </li></ul><ul><li>2. regressing the dependent variable on the independent variable; </li></ul><ul><li>3. regressing the dependent variable on both the independent variable and on the mediator. </li></ul>
  24. 24. Analytic procedures for testing for mediation <ul><li>To establish mediation, the following conditions must hold: </li></ul><ul><li>1. the IV must affect the mediator in the first equation; </li></ul><ul><li>2. the IV must be shown to affect the DV in the second equation; </li></ul><ul><li>3. the mediator must affect the DV in the third equation. </li></ul><ul><li>4. the effect of the IV on the DV must be less in the third equation than in the second </li></ul><ul><li>5. Perfect mediation holds if the IV has no direct effect on the DV when the mediator is controlled. </li></ul>
  25. 25. Analytic procedures… <ul><li>Sobel (1982) provided an approximate significance test for the indirect effect of the independent variable on the dependent variable via the mediator (Sobel test). </li></ul><ul><li>a: IV to mediator, s a : standard error of a </li></ul><ul><li>b: Mediator to DV, s b : standard error of b </li></ul><ul><li>Indirect effect is estimated by: </li></ul>
  26. 26. Analytic procedures… <ul><li>Assumptions: </li></ul><ul><li>There must be no measurement error in the mediator and that the dependent variable not cause the mediator. </li></ul><ul><li>The presence of measurement error in the mediator tends to produce an underestimate of the effect of the mediator and an overestimate of the effect of the independent variable on the dependent variable when all coefficients are positive (Judd & Kenny, 1981 a). </li></ul>
  27. 27. Analytic procedures… <ul><li>Path analysis/Structural Equations Modeling are best used to estimate mediations in a model. </li></ul><ul><li>Multiple indicators can be used </li></ul><ul><li>The experimental context strengthens the SEM technique </li></ul><ul><li>All relevant paths are directly tested and none are ommitted </li></ul>
  28. 28. Analytic procedures… <ul><li>Feedback (source of bias): The use of multiple regression analysis presumes that the mediator is not caused by the dependent variable. </li></ul><ul><li>Smith’s (1982) method involves the manipulation of two variables, one presumed to cause only the mediator and not the dependent variable and the other presumed to cause the dependent variable and not the mediator. </li></ul><ul><li>Two-stage least square </li></ul>
  29. 29. Combining Mediation and Moderation

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