Mediation: Assumptions David A. Kenny davidakenny.net

2 The Mediational Model

3 Assumptions: Multiple Regression Linearity Normal Distribution of Errors –Interval level of measurement of M and Y Equal Error Variance Independence –No clustering 3

4 No XM Interaction: Linear Mediation Called “Moderation” in Baron & Kenny Some approaches refer to this as nonlinear mediation. Add XM (and possibly other interaction terms, e.g., X 2 M) when explaining Y.

5 Causal Assumptions Mediation analysis as causal analysis. The “Steps” papers did emphasize enough the causal assumptions underlying mediational analysis. Practitioners hardly ever discuss the causal assumptions. Early critics of mediational analysis argued that assumptions were hardly ever justified. 5

6 Causal Assumptions (Guaranteed if X is manipulated.) Perfect Reliability –for M and X No Reverse Causal Effects –Y may not cause M – M and Y not cause X No Omitted Variables (Confounders) –all common causes of M and Y, X and M, and X and Y measured and controlled 6

7 Basic Mediational Causal Model Note that U1 and U2 are theoretical variables and not “errors” from a regression equation.

8 Mediation: The Full Model

9 Mediation: The Full Model – X Manipulated

10 Limitation This webinar does not discuss solutions to these three problems. See Solutions to the Violations of Assumptions webinar.

11 Unreliability Usually safe to assume that X is perfectly reliable when manipulated. Measurement error in Y does not bias unstandardized regression coefficients. Measurement error in M is problematic.

12 Unreliability in M

13 Effect of Unreliability in M b is attenuated (closer to zero) c′ is inflated (given consistent mediation) –more as a increases –more as b increases (Note that the bigger the indirect effect, the greater the bias in c′.) –more as unreliability increases.

14 Reverse Causation

15 Effect of Reverse Causation Typically, b and g have the same sign, which likely makes the value of b inflated and the value of c′ deflated if g is mistaken presumed to be zero.

16 Omitted Variables

17 What is the Effect of Omitted Variables? Usually, but not always, the sign of ef is the same as b. –Inflating the estimate of b –Deflates the estimate of c′ (could produce inconsistent mediation).

18 Effect of Vitamin A Supplements in Northern Sumatra 18 Sommer et al. (1986) in Lancet (N = 25,939)

19 “Standard” Results 19

20 Additional Webinars Solutions to Violation of Assumptions Sensitivity Analyses Causal Inference Approach