1. 1 Moderation Statements Treatment effects differ for males and females. Program effects on tobacco use were greater for persons who were more likely to believe the positive consequences of tobacco use at baseline. A program works for middle school students but not high school students. Program effects differ as a function of outcome variable use at baseline. Nicotine patch treatment differs depending on whether the person has a certain genetic disposition.

2. 2 Moderators  Moderators determine for whom the program is effective.  Mediation assumes no moderation effect: It is assumed that the relation from X to M and from M to Y are homogeneous across subgroups or other characteristics of participants in the study.

3. 3 Importance of Moderation in Prevention and Treatment Research Information on moderating variables can be used to identify the groups of persons who will benefit the most (and least) from a program. In some cases, important theoretical predictions can be tested. For example, if program effects depend on the level of risk.

4. 4 Mediator versus Moderator  Moderator is a variable that affects the strength or form of the relation between two variables. The variable is not intermediate in the causal sequence, so it is not a mediator.  Moderator is also an interaction, the relation between X and Y depends on a third variable. There are other more detailed definitions of a moderator.  Tested by including interaction effects in addition to main effects of X.

5. 5 Moderation Analysis 1 Group 1 Y 1 = i 1 + d 1 X + e 1 Group 2 Y 2 = i 2 + d 2 X + e 2 Combined Groups Y = i 1 + c 1 X + c 2 Z+ d 3 XZ+ e 2 d 3 = d 1 - d 2 and provides a general way to test moderator/interaction effects.

6. 6 Moderation Analysis 2 Centering is important in moderation analysis in order to reduce multicollinearity and interpretation of interaction effects. Centering consists of subtracting the mean from each observed score for X and Z (see Aiken & West, 1991). The combined model and test for d 3 is a general way to test moderator effects for both continuous and categorical moderators. In regression analysis, the interaction variable, XZ, is the product of the centered X variable and the centered Z variable. Power to detect moderator effects is often very low (Aiken & West, 1991) Plots are important for the interpretation of moderator effects.

7. 7 Models with Moderation and Mediation Moderated and Mediation may occur simultaneously in several different ways. Relation of X to M may differ across levels of X. Relation of M to Y may differ across levels of X. Both X to M and M to Y relations may differ.

8. 8 Moderated and Mediation X MY a1a1 b1b1 c1’c1’ Group 1 X MY a2a2 b2b2 c2’c2’ Group 2 Separate mediated effect in each group: a 1 b 1, a 2 b 2

9. 9 Mediation and Moderator Models Ho: a 1 - a 2 = 0 is a test of homogeneous action theory, called mediated moderation in Baron and Kenny (1986) Ho: b 1 - b 2 = 0 is a test of homogeneous conceptual theory, called moderated mediation in Baron and Kenny (1986). Ho: c 1 ’- c 2 ’ = 0 is a test of equal direct effect. Ho: a 1 b 1 – a 2 b 2 = 0 is a test of moderated mediation. A test of whether the mediated effect differs between groups. Extend to more than two groups by forming contrasts among mediated effects.

10. 10 Separate and Combined Group Moderation and Mediation Group 1 Y 1 = i 11 + c 11 ' X + b 11 M + e 11 M 1 = i 21 + a 11 X + e 11 Group 2 Y 2 = i 12 + c 12 ' X + b 12 M + e 12 M 2 = i 22 + a 12 X + e 22 Combined Groups Y = i 1 + c 1 ' X + c 2 ' Z+ c 3 ' XZ+ b 1 M + b 2 MZ + e 2 M = i 1 + a 1 X + a 2 Z+ a 3 XZ+ e 3

11. 11 Mediation and Moderator Models Ho: a 11 - a 12 = 0 is the same as Ho: a 3 = 0. Test of homogeneous action theory, called mediated moderation in Baron and Kenny (1986) Ho: b 11 - b 12 = 0 is the same as Ho: b 2 = 0. Test of homogeneous conceptual theory, called moderated mediation in Baron and Kenny (1986). Ho: c 11 ’- c 12 ’ = 0 is the same as Ho: c 3 `= 0. Test of equal direct effect.

12. 12 Mediation of Baseline by Treatment Interactions (MBTI) Program effects are often largest for persons lowest on the mediator at baseline. The mediation effect may differ at the levels of the baseline mediation variable. If the interaction is nonsignificant then assume constant mediation effect. If the interaction is significant then the size of the mediated effect depends on baseline values.

13. 13 MBTI (Morgan-Lopez, 2003) X 1 Y 1 X 1 M 1 Y 2 M 1 M 2 a 1 a 2 a 3 bc’ 1 c’ 2 c’ 3 c’ 4

14. 14 Summary Mediation and Moderation analyses address important questions in prevention and treatment research--How and for whom do programs work? Some research investigating mediation and moderation separately but still too few studies. Actual program effects may contain mediation and moderation simultaneously. Equations to test these models were described. Models with mediation and moderation reflect the complexity and richness of drug research.