Mediation

1.Definition 2. Testing mediation using multiple regression Baron, 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, (over 7000 citations) 3. Testing mediation using bootstrapping Preacher, K. J., & Hayes, A. F. (2004). SPSS and SAS procedures for estimating indirect effects in simple mediation models. Behavior Research Methods, Instruments, & Computers, 36(4), SPSS and SAS procedures for estimating indirect effects in simple mediation models 4. Extensions (Moderated-Mediation and Mediated-Moderation)

Example IV: Helping context (Alone vs. W/others) DV: Help giving (1= no help, 7 = a lot of help) Finding: A person is more likely to provide help when alone  Why is it that people are more likely to help when they are alone? (MEDIATOR)  When will this effect become weaker/stronger/disappear? (MODERATOR)

Example IV: Stress (1-7 scale) DV: Depression (1-7 scale) Finding: Stressed people are more depressed  Why are stressed people more depressed? What is the mechanism that explains that? (MEDIATOR)  Under what conditions will the effect of stress on depression be weaker/stronger/disappear? (MODERATOR)

Definitions (Baron & Kenny, 1986)  Mediator – Answers the “why” question (gets at the process) - A variable that is caused by the IV, and in turn, causes the DV IV: Helping Context DV: Help Giving Mediator Responsibility

Definitions (Baron & Kenny, 1986)  Mediator – Answers the “why” question (gets at the process) - A variable that is caused by the IV, and in turn, causes the DV Helping contextHelp Responsibility

1. the IV predicts the DV (c = total effect) Predictor: Helping contexts, DV: Help giving 2. the IV predicts the MED (a) Predictor: Helping contexts, DV: Responsibility 3. the MED predicts the DV (controlling for the IV) (b) Predictors: Helping contexts, Responsibility, DV: Help giving 4. c is reduced (to zero/not) controlling for the MED (c’=direct effect) Same equation as # 3 IV: Helping context DV: Help giving Med: responsibility a c’ c’ b c Establishing Mediation using Multiple Regression

 Full Mediation – Controlling for the mediator, the IV no longer affects the DV. Hence, c’ = 0 (β is no longer sig different from zero) (e.g. if you “take out” responsibility you lose the effect of helping context on help giving)  Partial mediation – Controlling for the mediator, the effect of the IV on the DV (c’) is reduced, but still different from 0 (β is still sig) (e.g. if you “take out” responsibility you still get an effect of helping context on help giving) (OUTPUT) IV DV Mediator a b Full Mediation vs. Partial Mediation c’ c’ c

 Purpose: Test that a*b (or c-c’) is different from o.  Important to examine also when full mediation is obtained  Run a Sobel test: Z = a*b/ √(b²SEa² + a²SEb²)  Use Preacher’s website a c’ c’ b c Testing the Indirect effect IV: Helping context DV: Help giving Med: responsibility

Specification Error (do you have the right model?)  The mediator may be caused by the outcome Solutions: - Makes sense theoretically? - Design issues (temporal order: measure mediator before DV) - Test the alternative model (run the model with switching the Med with the DV and test mediation again)  Measurement error in mediator Solution: Measure with high reliability  Mediator and outcome are sharing variance due to method effect (self reports) Solution: Use different methods to measure mediator and DV  Omitted variable (causing both Med and DV) Solution: Specify, measure and control for it

 The a*b sampling distribution is assumed to be normal - but the distribution of products is usually positively skewed  The Sobel test runs the risk of violating assumptions of normality resulting in less power (less chance to find an effect that exists in the population)  Sobel’s test works best in large samples (N>200)  Solution: bootstrapping (for testing the indirect effect)  No distributional assumptions (a*b can be non-normally distributed)  Not a large-sample technique (can be applied to small samples with more confidence)  Preacher will do it for you (again!) (WEBSITE) a c’ c’ b c Limitation of Sobel test IV: Helping context DV: Help giving Med: responsibility

 Download the syntax command from preacher’s website  Run it in SPSS (highlight the entire text and click run)  Add a line at the end of the syntax file: SOBEL y=yvar / x = xvar / m = mvar / boot=z. yvar = the name of the dependent variable xvar = the name of the independent variable mvar = the name of the proposed mediating variable, z = specifies the number of bootstrap resamples desired (3000) a c’ c’ b c Bootstrapping IV: Helping context DV: Help giving Med: responsibility

Extensions

Moderator (Baron & Kenny, 1986)  Moderator – Answers the “when” question -A variable that affects the direction and/or strength of the relation between an IV and a DV. - A cause (IV) and not an Outcome (DV) – (ideally measured before IV and not correlated with it)  Establishing moderation: The moderator should interact with the predictor (IV) to cause the outcome (DV) IV: Helping context DV: Help giving Moderator: Target’s age

Mediated Moderation -Purpose: To examine possible reasons (mediators) for a particular interaction effect -Same logic as simple mediation, only here the effect to be explained involves an interaction (moderation) -In the mediation model, the IV is the interaction term (IV*Moderator). -Effect: When the target is a child people tend to help regardless of context. - Why? Helping Target’s Context * age Help Responsibility

Moderated Mediation  Purpose: Examine whether the mediation effect remains constant across different groups; Preacher, Rucker, & Hayes, 2007 for SPSS macro)  Conditional Indirect Effect -E.g., The mediation model doesn’t work for people who served at the Peace Corps Peace Corps Non-Peace Corps Helping Context Help Responsibility a c’ c’ b c Help Responsibility a c’ c’ b c Helping Context