Can Mediation be Tested
with Cross-sectional
Studies?
Mediation
Mediation occurs when a variable (IV)
affects another variable (DV) wholly or
partly via its effect on another variable
(MV)
1
Mediation
There is an element of Oh, so that’s why A
affects B! The total effect of the IV on the DV:
is revealed to be wholly or partly due to its
effect on an in-between mediating variable:
Mediation: Analysis
The goal of mediation analysis is to decompose a
total effect (c)
into the component parts of direct (c) and indirect
(a*b) effect.
2
Mediation Analysis: Some important
points
Mediation is seen
as causal
The IV must precede the MV and the MV must
precede the DV
Mediation is always longitudinal
The one-headed arrows indicate causality
The Baron & Kenny steps (1)
(adapted from David Kenny’s web page
http://davidakenny.net/cm/mediate.htm#BK)
Step 1: Show that the IV is correlated with the DV. Use
the DV as the criterion variable in a regression equation
and the IV as a predictor (estimate and test path c). This
step establishes that there is an effect that may be
mediated.
3
The Baron & Kenny steps (2)
(adapted from David Kenny’s web page
http://davidakenny.net/cm/mediate.htm#BK)
Step 2: Show that the IV is correlated with the MV. Use
MV as the criterion variable in the regression equation
and the IV as a predictor (estimate and test path a).
The Baron & Kenny steps (3)
(adapted from David Kenny’s web page
http://davidakenny.net/cm/mediate.htm#BK)
Step 3: Show that the MV affects the DV. Use the DV
as the criterion variable in a regression equation and
the IV and MV as predictors (estimate and test path b).
4
The Baron & Kenny steps (4)
(adapted from David Kenny’s web page
http://davidakenny.net/cm/mediate.htm#BK)
Step 4: To establish that the MV completely
mediates the IV-DV relationship, the effect of the
IV on the DV controlling for the MV should be zero
(estimate and test path c’). The effects in both
Steps 3 and 4 are estimated in the same equation.
An Example
Based on data and hypotheses supplied by Ron Rapee
Anxiety Î Bullying Î Depression
5
Example: B & K Step 1
N = 666 (complete cases only)
Example: B & K Steps 2, 3 & 4
Indirect effect = .48 * .42 = .202, p = .003
6
Can we test mediation with cross-sectional data?
Journal of Abnormal Psychology, 2003, 112, 23-44
Can we test mediation with cross-sectional data?
Psychological Methods, 2007,12, 2007
7
Cross-sectional and longitudinal studies
Cross-sectional: X1 Î M1 Î Y1, or X2 Î M2 Î Y2, etc
Longitudinal: X1 Î M2 Î Y3
Half longitudinal: X1 Î M2 Î Y2 or
X1 Î M1 Î Y2
Cole & Maxwell, 2003:
1. The results of analyses based on cross-sectional data
are unlikely to accurately reflect longitudinal mediation
effects.
2. If M2 is not adjusted for M1, and/or Y3 is not adjusted for
Y2, estimates of causal paths may be spuriously inflated.
3. Half-longitudinal designs do not allow control of both M1
and Y2 (but see p. 562 for a possible solution, given the
assumption of stationarity).
4. The timing of measurements is critical – pilot tests are
needed.
5. Retrospective measures will tend to be biased.
8
Back to the data ….
Longitudinal data without adjustment for previous values
Indirect effect: .102, p = .005
9
Longitudinal data with adjustment for M1 and Y2
Bold lines are
those for which the
path coefficients are
significant.
Can we test mediation with cross-sectional data?
Suggestions of Cole & Maxwell
Do not test mediation hypotheses unless you have
longitudinal data (spaced appropriately) for at least
two time points, preferably three.
Include the T – 1 measures of the proposed mediator, and
of the dependent variable, in the analyses as covariates.
Use a SEM program, and represent the measures by latent
variables where possible.
10
C & M’s Steps in Testing a Longitudinal Model
The hypothesised model
C & M’s Steps in Testing a Longitudinal Model
1. Test of the Measurement Model – all latent variables allowed
to covary
11
C & M’s Steps in Testing a Longitudinal Model
1. Test of the Measurement Model – all latent variables allowed
to covary, and
errors of
observed
variables allowed
to covary over
time.
C & M’s Steps in Testing a Longitudinal Model
2a. Tests of Equivalence
– loadings of
equivalent
observed
variables
constrained to
be equal over time.
Note ga = ga = ga,
ba = ba = ba, etc.
12
C & M’s Steps in Testing a Longitudinal Model
2b. Tests of Equivalence
– variances and
covariances
of latent variables
constrained to be
equal over time.
Note abcv = abcv = abcv,
av = av = av, etc
C & M’s Steps in Testing a Longitudinal Model
3. Test of Added
Components – Full
Model: all upstream
variables Î downstream, exogenous
latent variables
allowed to correlate,
residuals of
latent variables
allowed to
correlate within
waves.
13
C & M’s Steps in Testing a Longitudinal Model
3. Test of Added
Components – Test
Model: correlations
of upstream
latent variables
set to zero.
If model doesn’t fit,
some variation not
explained by the
exogenous variables.
C & M’s Steps in Testing a Longitudinal Model
4. Test of Omitted
Paths – Full Model:
all upstream variables
Îall downstream
variables.
14
C & M’s Steps in Testing a Longitudinal Model
4. Test of Omitted
Paths – Test Model:
Only the paths in
the hypothesised
model are
estimated.
C & M’s Steps in Testing a Longitudinal Model
4. Test of Omitted
Paths – Extra paths
added.
This is the model
with which the
mediation model
is tested.
15
C & M’s Steps in Testing a Longitudinal Model
5. Testing
Mediational Effects
- Total Effects
C & M’s Steps in Testing a Longitudinal Model
The setup:
16
C & M’s Steps in Testing a Longitudinal Model
Overall Total Effect:
Overall Indirect Effect:
C & M’s Steps in Testing a Longitudinal Model
Overall Effect of the IV on the MV:
Overall Direct Effect:
17
Summary
There is no evidence that the relationship between anxiety
and depression is mediated by bullying.
Anxiety is not related to bullying T1 Î T2 (but see next slide).
Anxiety has a direct relationship with depression.
Significant Paths in the Final Model
Bullied T1 Î Anxiety T2,
Depression T2
Anxiety T2 Î Bullied T3
(cf T1 Î T2)
Bullied T2 Î Anxiety T3,
Depression T3
18
Significant Paths in the Final Model
Total Effects in the Final Model
Postscript – A Two-wave Model
19
Can Mediation be
Tested
with Crosssectional Studies?
20