Mediation - only in moderation?Mediation - only in moderation? Thoughts on mediation analysisThoughts on mediation analysis

Matthew Hankins, Department of Psychology (at Guy’s)Matthew Hankins, Department of Psychology (at Guy’s)

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

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

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

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)

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

Example

• 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

IVIntervention causes

MVAction planformation

causesDV

Attendancefor screening

The Baron & Kenny approach

• The diagram

• Three (or four) conditions

• The analysis strategy

• The assumptions

The Baron & Kenny approach: outline

“A variable functions as a mediator when it meets the following conditions”

DVMV

IV

(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

The analysis strategy: condition (a)

• (a) Linear regression with IV predicting MV

• The IV should predict the MV

The analysis strategy: condition (b)

• (b) Linear regression with MV predicting DV

• The MV should predict the DV

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

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)

Direct and indirect effects

“This model assumes a three-variable system such that there are two causal paths feeding into the outcome variable:”

The direct effect

“the direct impact of the independent variable(Path c)”

i.e. the direct effect

The indirect effect

“and the impact of the mediator (Path b)” (p.1176)

i.e. the indirect effect

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

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

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’

Example: theory of reasoned action

The TRA is the classic mediational model (though rarely analysed as such)

(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

IVAttitude causes

MVIntention causes

DVBehaviour

Suppose we have cross-sectional data that show (by regressions):

The conditions are met: can we say that Intention is a mediator?

No: correlations do not imply causation

• All we can say is that data are consistent with Intention being a mediator

• Rather than:

• Because what we have shown is:

IVAttitude

MVIntention

DVBehaviour

IVAttitude

MVIntention

DVBehaviour

• We have no proof of causal direction

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

Alternative interpretations: unmanipulated IV

Intention Attitude Behaviour

Somethingelse

• The large number of alternatives are due to the measures being cross-sectional

• Even if the IV is manipulated, however, alternatives exist

Alternative interpretations: manipulated IV

IVIntervention

causes

MVAction planformation

causesDV

Attendance

Alternative interpretations: manipulated IV• Or:

IVIntervention

causes

MVAction planformation

and later causesDV

Attendance

Alternative interpretations: manipulated IV• Or:

VAction planformation

IVIntervention causes

MVSomething

else

IVIntervention causes

MVSomething

else

IVIntervention causes

MVSomething

else causesDV

Attendance

causes

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

The bottom line

• The Baron & Kenny approach can only determine causal directions if the assumptions of the analysis strategy are correct

• To identify a mediating variable, we must be able to determine causal directions

• 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

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

• I.e. in order to determine the causal directions, we have to assume the causal directions

• The Baron & Kenny method only works if these assumptions are true

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”

IVAttitude

MVIntention

DVBehaviour

• So the assumptions of the model are:

The logical argument: modus ponens• Baron & Kenny correctly assert:

IF the causal assumptions are TRUE

THEN conditions (a), (b) and (c) will obtain

• E.g. For TRA example, the correct argument is:

IF intention mediates between attitude & behaviour

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

The logical fallacy: affirming the consequent• Baron & Kenny correctly assert:

IF the causal assumptions are TRUE

THEN conditions (a), (b) and (c) will obtain

• E.g. For TRA example, the incorrect argument is:

IF conditions (a), (b) and (c) obtain

THEN intention mediates between attitude & behaviour

• 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

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

• “Mediating effect established if…”

• conditions (a), (b) and (c) are met - Kim et al. 2001

• “(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

• “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

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

The logical argument: modus tollens• Baron & Kenny correctly assert:

IF the causal assumptions are TRUE

THEN conditions (a), (b) and (c) will obtain

• 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

• Therefore if the conditions (a), (b) and (c) are not met, the causal assumptions cannot be true

• Logical argument of the form modus tollens

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?

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

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

Further comments

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”

IVHostility causes

MVsBMISES

LVEFAge

causesDV

Lipids