A talk I gave at KCL (Health Psychology Section) in 2006, discussing logical fallacy of Baron & Kenny's paper on the analysis of mediation effects.

1. Mediation - only in moderation?
Thoughts on mediation analysis
Matthew Hankins, Department of Psychology (at Guy’s)

2. Introduction
• Mediation analysis is increasingly popular in
health psychology
• There is particular interest in identifying the
variables that mediate the relationship between
an intervention and an outcome
• I.e. the mechanism by which the intervention
works

3. Introduction
“If...theories are to contribute to understanding behaviour
change, then cognition-changing techniques need to be specified
and the mediation of behaviour change outcomes by theory-
specified cognition change must be demonstrated (Baron and
Kenny, 1986)”
• Michie & Abraham 2004

4. Baron & Kenny (1986)
• The most widely-used analytic strategy for
mediational analysis
• scholar.google.com located 2624 citations of
this paper
• This talk is an attempt to clarify the analytic
approach and to highlight some technical
problems
• E.g. the fact that it doesn’t actually work

5. Definitions
• “In general, a given variable may be said to
function as a mediator to the extent that it
accounts for the relation between the predictor
and the criterion”
• “Mediators explain how external physical events
take on internal psychological significance”
• “Mediators speak to how or why such effects
occur”
Baron & Kenny (1986)

6. Definitions
• “Mediation models explain “how” an effect
occurred by hypothesizing a causal sequence”
• “The basic mediation model is a causal
sequence”
MacKinnon (2000)
• To be clear: if an IV affects a DV then:
• any mediating variable (MV) is caused by the IV and
causes the DV

7. Example
MV DV
IV
causes Action plan causes Attendance
Intervention
formation for screening
• In this example, the formation of an action plan
mediates the effect of an intervention on
attendance for screening
• This is to say that:
>The intervention causes the formation of an action
plan;
>The formation of an action plan causes attendance
for screening

8. The Baron & Kenny approach
• The diagram
• Three (or four) conditions
• The analysis strategy
• The assumptions

9. The Baron & Kenny approach: outline
MV
IV DV
“A variable functions as a mediator when it meets the
following conditions”
(a) The IV and MV are correlated
(b) The MV and DV are correlated
(c) (1) The IV and DV are correlated, but (2) not if the
MV is controlled for

10. The analysis strategy: condition (a)
• (a) Linear regression with IV predicting MV
• The IV should predict the MV

11. The analysis strategy: condition (b)
• (b) Linear regression with MV predicting DV
• The MV should predict the DV

12. The analysis strategy: condition (c)
• (c1) Linear regression with IV predicting DV
• The IV should predict the DV
• (c2) Second regression with IV and MV predicting DV
• The IV should no longer predict the DV
• Or, at least, the effect size should reduce

13. Reasoning behind the strategy
• If a variable mediates between the IV and the DV, then:
• The IV must cause the MV: they should be correlated
= condition (a)
• The MV must cause the DV: they should be correlated
= condition (b)
• The IV can only affect the DV via the MV: when the MV
is controlled, the correlation between the IV and the DV
should disappear
= condition (c)

14. Direct and indirect effects
“This model assumes a three-variable system such that
there are two causal paths feeding into the outcome
variable:”

15. The direct effect
“the direct impact of the independent variable(Path c)”
i.e. the direct effect

16. The indirect effect
“and the impact of the mediator (Path b)” (p.1176)
i.e. the indirect effect

17. Single variable mediation
• If the association between the IV and the DV is zero
after controlling for the MV, this is “strong evidence” for
a “single, dominant mediator”
• I.e. a zero path (c) indicates no direct effect of the IV

18. Multiple variable mediation
• If the association between the IV and the DV is not zero
after controlling for the MV, this “indicates the operation
of multiple mediating factors”
• I.e. a non-zero path (c) indicates an indirect effect of the IV

19. Direct effects = indirect effects
• Hence, Baron & Kenny define the direct effect
as a mediated effect
• i.e. an indirect effect
• Similar confusion arises over full and partial
mediation (but not from B&K):
• Full mediation suggests single variable
mediation
• Partial mediation suggests multiple variable
mediation - not a ‘direct effect’

20. Example: theory of reasoned action
IV MV DV
Attitude causes Intention causes Behaviour
The TRA is the classic mediational model (though
rarely analysed as such)
Suppose we have cross-sectional data that show (by
regressions):
(a) Attitude and Intention are significantly correlated
(b) Intention and Behaviour are significantly correlated
(c) Attitude and Behaviour are significantly correlated, but not if
Intention is controlled for
The conditions are met: can we say that Intention is a
mediator?

21. No: correlations do not imply causation
• All we can say is that data are consistent with Intention
being a mediator
• Because what we have shown is:
MV
Intention
IV DV
Attitude Behaviour
• Rather than:
IV MV DV
Attitude Intention Behaviour
• We have no proof of causal direction

22. Alternative interpretations
• The results allow us to conclude that the data are
consistent with Intention being a mediator
• The results are, however, equally consistent with many
other interpretations:
Intention Attitude Behaviour
Behaviour Attitude Intention

23. Alternative interpretations: unmanipulated IV
Something
else
Intention Attitude Behaviour
• The large number of alternatives are due to the
measures being cross-sectional
• Even if the IV is manipulated, however, alternatives
exist

24. Alternative interpretations: manipulated IV
MV
Action plan
causes formation
IV
Intervention
causes
DV
Attendance

25. Alternative interpretations: manipulated IV
• Or:
MV
Action plan
causes formation
IV
Intervention
and later causes
DV
Attendance

26. Alternative interpretations: manipulated IV
• Or:
V
Action plan
causes formation
MV
IV
causes Something
Intervention
else causes
DV
Attendance

27. Alternative interpretations
• Alternative interpretations must be considered when
using this strategy in order to rule out the alternatives
• When the IV is manipulated, the number of alternative
models is limited
• If the IV is measured (not manipulated), then the
number of alternatives more than doubles
• But, even if the preferred mediational model can be
accepted,
• It is only consistent with a causal model
• Not proof of one

28. The bottom line
• To identify a mediating variable, we must be able to
determine causal directions
• The Baron & Kenny approach can only determine
causal directions if the assumptions of the analysis
strategy are correct
• The Baron & Kenny approach, therefore, cannot be
used to identify mediating variables...
• …unless you can prove that the assumptions of the
analysis strategy are correct

29. What are the assumptions?
• The assumptions of the approach are:
• (a) The IV causes the MV
• (b) The MV causes the DV
• (c) The IV causes the DV
• The Baron & Kenny method only works if these
assumptions are true
• I.e. in order to determine the causal directions, we
have to assume the causal directions

30. Can this be true?
• Baron & Kenny are quite explicit:
• “This model assumes a three-variable system such that
there are two causal paths feeding into the outcome
variable” (the IV and the MV)
• “the independent variable is assumed to cause the
mediator”
• So the assumptions of the model are:
MV
Intention
IV DV
Attitude Behaviour

31. The logical argument: modus ponens
• Baron & Kenny correctly assert:
IF the causal assumptions are TRUE
THEN conditions (a), (b) and (c) will obtain
• So that, if the causal model is correct, the conditions (a), (b)
and (c) are met
• Logical argument of the form modus ponens
• E.g. For TRA example, the correct argument is:
IF intention mediates between attitude & behaviour
THEN conditions (a), (b) and (c) will obtain

32. The logical fallacy: affirming the consequent
• Baron & Kenny correctly assert:
IF the causal assumptions are TRUE
THEN conditions (a), (b) and (c) will obtain
• But if the conditions (a), (b) and (c) are met, we cannot
conclude that the causal assumptions are true
• Logical fallacy of the form affirmation of the consequent
• E.g. For TRA example, the incorrect argument is:
IF conditions (a), (b) and (c) obtain
THEN intention mediates between attitude & behaviour

33. Examples of logical fallacy
• “To test this hypothesis, three preliminary regression
analyses were conducted to determine if the preconditions
for the proposed mediator model were met”
• I.e. conditions (a), (b) and (c) - Laubmeier & Zakowski 2004
• “(Baron & Kenny)…describe four steps that must be taken to
establish that a mediated relationship exists”
• evaluation of conditions (a), (b) and (c) - Miles & Shevlin 2001
• “Mediating effect established if…”
• conditions (a), (b) and (c) are met - Kim et al. 2001
• “For example, evidence that adherence mediates the
relationship between pessimism and viral load would be
obtained if…”
• conditions (a), (b) and (c) were met - Milam et al. 2004

34. Can’t confirm: disconfirm?
• Baron & Kenny’s approach cannot confirm that a
variable is a mediator
• Other assumptions or conditions must be shown to
be true
• But the approach can disconfirm a variable as a
mediator
• If one or more of the conditions are not met

35. The logical argument: modus tollens
• Baron & Kenny correctly assert:
IF the causal assumptions are TRUE
THEN conditions (a), (b) and (c) will obtain
• Therefore if the conditions (a), (b) and (c) are not met, the
causal assumptions cannot be true
• Logical argument of the form modus tollens
• E.g. For TRA example, the correct argument is:
IF conditions (a), (b) and (c) do not obtain
THEN intention does not mediate between attitude & behaviour

36. Can’t confirm: disconfirm?
• When ruling out a variable as a mediator, the statistical
power should be considered
• How likely are we to reject a hypothesised mediator in
error?

37. MacKinnon et al (2002)
• Monte carlo simulation of three methods of mediation
analysis, including Baron & Kenny
• Discovered wide variation in the Type I and Type II error
rates for the different approaches
• Concluded that Baron & Kenny approach had lower power
than the method suggested by MacKinnon et al 1995

38. Summary
• The Baron & Kenny approach cannot confirm that a variable
is a mediator
• It can be used to disconfirm that a variable is a mediator but
only if statistical power is adequate
• If the Baron & Kenny approach is used, additional
confirmation must be sought for an MV
• Through manipulated variables, for example
• Or argument based on the logical relationship between
variables
• Studies intending to examine mediational effects should be
adequately powered to do so

39. Further comments

40. Further comments
“The results indicated that the effects of hostility on lipids
were mediated by various factors such as body weight in
relation to body length (BMI), Socio-Economic Status (SES),
Left Ventricle Ejection Fraction (LVEF) and Age”
MVs
BMI
IV DV
causes SES causes
Hostility Lipids
LVEF
Age