Mediation Example David A. Kenny. 2 Example Dataset Morse et al. – J. of Community Psychology,...
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Transcript of Mediation Example David A. Kenny. 2 Example Dataset Morse et al. – J. of Community Psychology,...
Mediation ExampleDavid A. Kenny
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Example Dataset• Morse et al.
– J. of Community Psychology, 1994
– treatment housing contacts days of stable housing
– persons randomly assigned to treatment groups.
– 109 people
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Variables in the Example • Treatment — Randomized
– 1 = treated (intensive case management)– 0 = treatment as usual
• Housing Contacts: total number of contacts per during the 9 months after the intervention began
• Stable Housing– days per month with adequate housing
(0 to 30)– Averaged over 7 months from month 10
to month 16, after the intervention began
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Downloads
• Data • SPSS Syntax• SPSS Output
Step 1
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Model
Unstandardized Coefficients
Standardized Coefficients
t Sig.B Std. Error Beta1 (Constant) 12.784 1.607 7.955 .000
treatment 6.558 2.474 .248 2.651 .009a. Dependent Variable: stable_housing
REGRESSION /MISSING LISTWISE /STATISTICS COEFF /DEPENDENT stable_housing /METHOD=ENTER treatment.
Step 2
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REGRESSION /MISSING LISTWISE /STATISTICS COEFF /DEPENDENT hc9 /METHOD=ENTER treatment.
Model
Unstandardized Coefficients
Standardized Coefficients
t Sig.B Std. Error Beta1 (Constant) 8.063 1.417
5.689 .000
treatment 5.502 2.182 .237 2.522 .013
Steps 3 and 4
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REGRESSION /MISSING LISTWISE /STATISTICS COEFF /DEPENDENT stable_housing hc9 /METHOD=ENTER treatment.
ModelUnstandardized Coefficients
Standardized Coefficients
t Sig.B Std. Error Beta1 (Constant) 9.024 1.680
5.372 .000
treatment 3.992 2.332 .151 1.712 .090hc9 .466 .100 .410 4.646 .000
a. Dependent Variable: stable_housing
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Morse et al. Example
Step 1: X Y c = 6.558, p = .009
Step 2: X M a = 5.502, p = .013
Step 3: M (and X) Y b = 0.466, p < .001
Step 4: X (and M) Y c′ = 3.992, p = .090
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Decomposition of EffectsTotal Effect = Direct Effect + Indirect Effect
c = c′ + abExample:
6.558 ≈ 3.992 + 2.564 [(5.502)(0.466)]
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Estimating the Total Effect (c)
The total effect or c can be inferred from direct and indirect effect as c′ + ab.
Note that we can determine c or 6.558 from c′ + ab or 3.992 + 2.564 [(5.502)(0.466)]
Holds exactly (within the limits of rounding error) in this case.
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Percent of Total Effect Mediated
100[ab/c] or equivalently 100[1 - c′/c]Example:
100(2.564/6.558) = 39.1% of the total effect explained
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Strategies to Test ab = 0
• Joint significance of a and b
• Sobel test
• Bootstrapping
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Joint SignificanceTest of a: a = 5.502, p = .013
Test of b: b = 0.466, p < .001
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Sobel Test of MediationCompute the square root of a2sb
2 + b2sa2
which is denoted as sab Note that sa and sb are the standard
errors of a and b, respectively; ta = a/sa and tb = b/sb.
Divide ab by sab and treat that value as a Z.
So if ab/sab greater than 1.96 in absolute value, reject the null hypothesis that the indirect effect is zero.
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Resultsa = 5.502 and b = 0.466
sa = 2.182 and sb = 0.100
ab = 2.564; sab = 1.1512
Sobel test Z is 2.218, p = .027
We conclude that the indirect effect is statistically different from zero.
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http://quantpsy.org/sobel/sobel.htm
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BootstrappingStructural Equation Modeling programs
Hayes & Preacher macro called Indirectwww.afhayes.com/spss-sas-and-mplus-macros-and-code.html
Download
Run the macro indirect
Run this syntax
INDIRECT y = housing/x = treatment/m = hc9 /boot = 5000/normal 1/bc =1.
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Dependent, Independent, and Proposed Mediator Variables:DV = stable_h IV = treatmen MEDS = hc9Sample size 109IV to Mediators (a paths) Coeff se t phc9 5.5017 2.1819 2.5216 .0132Direct Effects of Mediators on DV (b paths) Coeff se t phc9 .4664 .1004 4.6462 .0000Total Effect of IV on DV (c path) Coeff se t ptreatmen 6.5580 2.4738 2.6510 .0092Direct Effect of IV on DV (c' path) Coeff se t ptreatmen 3.9922 2.3318 1.7121 .0898Model Summary for DV Model R-sq Adj R-sq F df1 df2 p .2204 .2057 14.9834 2.0000 106.0000 .0000
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NORMAL THEORY TESTS FOR INDIRECT EFFECTS
Indirect Effects of IV on DV through Proposed Mediators (ab paths) Effect se Z pTOTAL 2.5659 1.1512 2.2289 .0258hc9 2.5659 1.1512 2.2289 .0258
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BOOTSTRAP RESULTS FOR INDIRECT EFFECTS
Indirect Effects of IV on DV through Proposed Mediators (ab paths) Data Boot Bias SETOTAL 2.5659 2.6049 .0390 1.1357hc9 2.5659 2.6049 .0390 1.1357
Bias Corrected Confidence Intervals Lower UpperTOTAL .5150 5.0645hc9 .5150 5.0645
**********************************************************
Level of Confidence for Confidence Intervals: 95Number of Bootstrap Resamples: 5000
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Compare Two Mediators
INDIRECT y = stable_h/x = treatment/ m = hc9 ec9 / boot=5000/normal 1/ contrast 1 / bc =1.
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Indirect Effects of IV on DV through Proposed Mediators
Data Boot Bias SE
TOTAL 3.6696 3.6767 .0071 1.3457
hc9 2.3693 2.3991 .0297 1.0330
ec9 1.3003 1.2776 -.0226 .8814
C1 1.0690 1.1214 .0524 1.3701
Bias Corrected Confidence Intervals
Lower Upper
TOTAL 1.3170 6.6798
hc9 .5801 4.6410
ec9 -.0153 3.5945
C1 -1.6329 3.7939
INDIRECT EFFECT CONTRAST DEFINITIONS:
Ind_Eff1 MINUS Ind_Eff2
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Hayes’ Process: http://afhayes.com/spss-sas-and-mplus-macros-and-code.html
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Thank You!
• Thanks to Bob Calsyn for providing the data.
• Sensitivity Analyses