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UT Knoxville STAT 201 - 9) mediation_moderation

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Course Mult Regression Topic Moderation and Mediation 1 Moderation and Mediation When developing and testing theory it is important to fully and clearly articulate the hypothesized function of relevant variables Two important functions potentially served by a variable are the moderator and mediator functions In the current lecture we will distinguish between the moderator and mediator function and examine how mediation can be tested using ordinary least squared regression as you will discover we already covered moderation in depth THE MODERATOR FUNCTION A moderator variable 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 dependent variable A moderator can be quantitative or nominal For example group identification might moderate the effect of self esteem on liking for the group such that liking and self esteem are positively related at high levels of identification and unrelated at lower levels of identification Likewise sex might moderate the effect of exposure to parental violence on the perpetration of spousal abuse such that exposure and abuse are positively associated for females and unrelated for males We can test with regression whether a given variable operates as a moderator by testing whether the variable interacts with the other variable In the identification example we could test whether identification moderates the effect of self esteem on liking by testing whether selfesteem and identification interact in the prediction of liking For example the following diagram provides a graphical representation of moderation Self Esteem predictor a Group Identification moderator Self Esteem x Identification b Liking for the group DV c Path c represents the moderating effect of identification Identification can be deemed a moderator if path C is statistically significant regardless of whether paths a or b are significant THE MEDIATOR FUNCTION The methodological literature exploring quantitative techniques for testing mediation is in a state of rapid growth In this lecture we will examine four techniques that can be employed in SAS and SPSS for testing mediation a Barron Kenny Causal Sequence Technique b Z pronounced Z Prime c PRODCLIN or Distribution of the Product Confidence Limits for the Indirect Effect and d Bootstrapping of the Indirect Effect the latter two techniques require downloading additional but free programs to be used with SAS or SPSS Those techniques are discussed in the following articles Course Mult Regression Topic Moderation and Mediation 2 Barron R M Kenny D A 1986 The moderator mediator variable distinction in social psychological research Conceptual strategic and statistical considerations Journal of Personality and Social Psychology 51 11731182 MacKinnon D P Lockwood C M Hoffman J M West S G Sheets B 2002 A comparison of methods to test mediation and other intervening variable effects Psychological Methods 7 83 104 MacKinnon D P Fritz M S Williams J Lockwood C M 2007 Distribution of the product confidence limits for the indirect effect Program PRODCLIN Behavior Research Methods 39 384 389 Preacher K J Hayes A F 2008 Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models Behavior Research Methods 40 879 891 Other articles that will be of interest are Bauer D J Preacher K J Gil K M 2006 Conceptualizing and testing random indirect effects and moderated mediation in multilevel models New procedures and recommendations Psychological Methods 11 142 163 Muller D Judd C M Yzerbyt V Y 2005 When moderation is mediated and mediation is moderated Journal of Personality and Social Psychology 89 852 863 Preacher K J Rucker D D Hayes A F 2007 Addressing moderated mediation hypotheses Theory methods and prescriptions Multivariate Behavioral Research 42 185 227 Spencer S J Zanna M P Fong G T 2005 Establishing a causal chain Why experiments are often more effective than mediational analyses in examining psychological processes Journal of Personality and Social Psychology 89 845 851 Zhang Z Zypur M J Preacher K J 2009 Testing multilevel mediation using hierarchical linear models Problems and solutions Organizational Research Methods 12 695 719 Mediation A mediator is a variable through which another variable affects the dependent variable The following diagrams provide a graphical representation of mediation X Y c M b a X c Y Course Mult Regression Topic Moderation and Mediation 3 The top diagram reveals that variable X affects variable Y i e path c The bottom diagram reveals the manner in which X affects Y In particular variable X affects variable M path a which in turn affects variable Y path b In the above diagram variable M is a mediator and is said to mediate the effect of X on Y because X produces changes in Y through M Variable M may either fully mediate or partially mediate the effect of X on Y Full mediation occurs when the totality of X s effect on Y is through M i e path c is 0 and smaller than path c Partial mediation occurs when only a portion of the effect of X on Y occurs through M i e path c is non zero but smaller than path c In partial mediation X might directly affect Y in addition to affecting Y through M and or there might additional partial mediators e g variables N O P through which X affects Y An example of mediation comes from Markus Kitayama s 1991 explanation of cultural differences in self enhancement i e motivation to maintain and enhance a positive selfview Some research suggests that self enhancement occurs more strongly if not exclusively among members of individualistic than collectivistic cultures According to Markus and Kitayama individualistic cultures promote a self conception valuing independence uniqueness and individual achievement and collectivistic cultures on the other hand promote a selfconception valuing relationships and fitting in Because self enhancement is irrelevant to the interdependent nature of the self that is fostered in collectivistic culture self enhancement functions less strongly in collectivistic than individualistic cultures In such a framework the self concept mediates the effect of culture on self enhancement tendencies culture affects the self concept which in turn affects self enhancement There are numerous procedures for testing mediation MacKinnon et al 2002 review 14


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UT Knoxville STAT 201 - 9) mediation_moderation

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