MODERATION MEDIATION Moderation Mediation When developing and testing theory it is important to fully articulate the function of relevant variables Moderation and Mediation are two functions important to theory Moderation A moderator is a variable that affects the magnitude and or direction of association between two other variables in other words A moderator is a variable that interacts with another variable to alter the effect of the other variable on the DV Hypothetical Examples of Moderation If liking for a group and self esteem are positively related for persons who strongly identify with the group and unrelated for persons who weakly identify with the group group identification can be considered a moderator If the association between exposure to parental violence and the perpetration of relationship abuse is stronger for females than males sex or gender can be considered a moderator Testing For Moderation Can use regression to test for moderation by testing whether the hypothesized moderator significantly interacts with the other variable If the Esteem x Identification interaction path c is significant identification can be deemed a moderator Mediation A mediator is a variable through which another variable affects the dependent variable X affects M which in turn affects Y M mediates the effect of X on Y Full and Partial Mediation Full Mediation When the totality of X s effect on Y occurs through M Path c 0 and is less different than path c Partial Mediation When a portion of X s effect on Y occurs through M Path c 0 and is less different than path c Some of X s effect occurs directly on Y or there are other partial mediators Four of many Tests of Mediation Barron Kenny s 1986 Causal Sequence Approach formerly most popular approach in the psychological literature MacKinnon s Z Prime Z MacKinnon s PRODCLIN Distribution of the Product Confidence Limits Bootstrapping via Preacher Hayes 2008 Logic of the Approaches Total effect direct effect indirect effect path c is the total effect of X on Y Indirect effect is effect of a variable via other variables Indirect for X reg parameter for path a reg parameter for path b Direct effect is effect of a variable NOT via other variables direct for X reg parameter for c i e reg of Y on X controlling M Logic of the Approaches Total effect direct effect indirect effect Total c a b If mediation c c which is same as a b 0 direct effect should be smaller than total effect indirect effect contributes to total effect note c c a b If no mediation c c which is same as direct effect is the total effect indirect effect 0 a b 0 The Barron Kenny Approach th 4 Test Sobel Test Test of whether effect of predictor is significantly reduced when the moderator is controlled c c which is same as testing whether the indirect effect is zero a b 0 is performed with modified Sobel s test ab b 2 sa2 a 2 sb2 sa2 sb2 a path a estimated with B1 from Equation 2 M B0 B1X sa standard error of a b path b estimated with B2 from Equation 3 Y B0 B1X B2M sb standard error of b Numerator is equivalent to difference between path c and path c Denominator is standard error of difference Distributed as a Z statistic and is significant at the 05 level when absolute value exceeds 1 96 3 Versions of Sobel Test The original Sobel Test ab b s a 2 sb2 2 2 a Barron Kenny s version Goodman s version ab b s a 2 sb2 sa2 sb2 2 2 a ab b s a 2 sb2 sa2 sb2 2 2 a Full Partial Mediation Full Mediation Satisfy tests 1 4 and effect of X is no longer signifcant when M is controlled Partial Mediation Satisfy tests 1 4 and effect of X remains signifcant when M is controlled A significant Sobel Test is necessary for Full and Partial Collinearity between X M increases SE of X in Eq 3 and increased SE can result in non sig X Test of X in Eq 3 might be less powerful than in Eq 1 due to loss of df associated with the inclusion of M in the model Sobel test establishes whether effect of X is reduced when M is controlled Methodological Issues Assumed that variables are measured with out error An unreliable measure of the mediator makes detection of mediation difficult because the effect of the mediator can not be fully removed from the predictor in the 3rd equation Assumed that direction of causation follows that specifed by the mediational model Mediational analysis is only suggestive with an observational design Collinearity can be problematic mediation requires relations b w X M high correlation can introduce collinearity in Equation 3 which increases standard errors An Example In human therapy the patient discusses problems with a therapist In computer therapy the patient interacts with a computer program Research suggests that human therapy is more effective at reducing depression than is computer therapy Perhaps meaningful discussion with human therapist fosters a sense of social inclusion which in turn reduces depression Does social inclusion mediate the effect of human relative to computer therapy on depression An Example 24 depressed persons to receive either human or computer therapy assess post treatment depression social inclusion Need to Dummy code therapy computer 0 human 1 Test if 1 human therapy results in less depression than does computer therapy 2 human therapy results in greater inclusion than does computer therapy 3 depression is associated with inclusion when therapy is controlled 4 the difference between human therapy and computer therapy in depression is significantly reduced when social inclusion is controlled T1 Does Therapy Predict Depression human therapy reduced depression relative to computer therapy B 2 833 t 22 6 12 p 0001 T2 Does Therapy Predict Social Inclusion human therapy increased social inclusion relative to computer therapy B 3 25 t 22 7 38 p 0001 T3 Does Inclusion Uniquely Predict Depression depression was neg related to inclusion B 469 t 21 2 28 p 0330 human and computer therapy did not differ when inclusion was controlled B 1 309 t 21 1 65 p 1131 T4 Was Effect of Therapy Smaller When Inclusion was Controlled i e is c c or a b 0 T4 Barron Kenny s Sobel Test ab 2 2 a b s a 2 sb2 sa2 sb2 Z 3 25 0 469 0 469 2 0 440 2 3 25 2 0 206 2 0 440 2 0 206 2 2 16 Effect of therapy was significantly smaller when inclusion was controlled Z 2 16 p 05 Conclusion w Barron Kenny 1 Therapy significantly predicted depression 2 Therapy signifciantly predicted social inclusion 3 Inclusion uniquely and significantly predicted depression when therapy was controlled 4 Effect of therapy was
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