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UT Knoxville STAT 201 - 9) sld_mediation_moderation

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- 24 depressed persons to receive either human or computer therapy- assess post-treatment depression & social inclusionMODERATION & MEDIATIONModeration & 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 theoryModeration-A moderator is a variable that affects the magnitude and/or direction of association between two other variablesin other words...-A moderator is a variable that interacts with another variableto alter the effect of the other variable on the DVHypothetical 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 moderatorMediation-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 mediatorsFour (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 effectTotal = 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) a*b = 0-direct effect is the total effect-indirect effect = 0The Barron & Kenny Approach…4th 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 test222222babasssasbaba = path a (estimated with B1 from Equation 2: M = B0 + B1X)sa = standard error of ab = 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 1.963 Versions of “Sobel” Test-The original Sobel Test: 2222basasbab-Barron & Kenny’s version: 222222babasssasbab-Goodman’s version: 222222babasssasbabFull & Partial Mediation-Full MediationSatisfy tests 1-4 and effect of X is no longer signifcant when M is controlled-Partial MediationSatisfy 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 controlledMethodological 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 bythe 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 inclusionNeed 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 controlledT1: Does Therapy Predict Depression?-human therapy reduced depression relative to computer therapy (B = -2.833), t(22) = -6.12, p = .0001T2: Does Therapy Predict Social Inclusion?- human therapy increased social inclusion relative to computer therapy (B = 3.25), t(22) = 7.38, p = .0001T3: 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:


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UT Knoxville STAT 201 - 9) sld_mediation_moderation

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