Moderation Statements

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
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
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
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
Moderation Analysis 1

• Group 1
• Y1 i1 d1 X e1
• Group 2
• Y2 i2 d2 X e2
• Combined Groups
• Y i1 c1 X c2 Z d3 XZ e2
• d3 d1 - d2 and provides a general way to test
  moderator/interaction effects.

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 d3 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
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
Moderated and Mediation
c1
a1
b1
Group 1
X
M
Y
a2
b2
Group 2
X
M
Y
c2
Separate mediated effect in each group a1b1, a2b2
9
Mediation and Moderator Models

• Ho a1- a2 0 is a test of homogeneous action
  theory, called mediated moderation in Baron and
  Kenny (1986)
• Ho b1- b2 0 is a test of homogeneous
  conceptual theory, called moderated mediation in
  Baron and Kenny (1986).
• Ho c1- c2 0 is a test of equal direct
  effect.
• Ho a1b1 a2b2 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
Separate and Combined Group Moderation and
Mediation

• Group 1
• Y1 i11 c11' X b11 M e11
• M1 i21 a11 X e11
• Group 2
• Y2 i12 c12' X b12 M e12
• M2 i22 a12 X e22
• Combined Groups
• Y i1 c1' X c2' Z c3' XZ b1 M b2 MZ
  e2
• M i1 a1 X a2 Z a3 XZ e3

11
Mediation and Moderator Models

• Ho a11- a12 0 is the same as Ho a3 0. Test
  of homogeneous action theory, called mediated
  moderation in Baron and Kenny (1986)
• Ho b11- b12 0 is the same as Ho b2 0. Test
  of homogeneous conceptual theory, called
  moderated mediation in Baron and Kenny (1986).
• Ho c11- c12 0 is the same as Ho c3 0.
  Test of equal direct effect.

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
MBTI (Morgan-Lopez, 2003)
a
1
X
M
1
2
a
2
a
3
M
1
b
c

1
c

2
X
M
1
1
c

3
c

Y
4
Y
2
1
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.