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This page uses code by Kristopher J. Preacher of the University of Kansas and Andrew F. Hayes of Ohio State University. The code can be found on the webpage accompanying their paper:
Preacher, K. J., & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40, 879-891.
To use the Preacher and Hayes's script, first download the .sbs file found here. Then open it in SPSS and run it by clicking on the green arrow or choosing "Run" from the Macro menu. This will open an SPSS dialog window.
For this example, we will use the hsb2 dataset with science as the dependent variable, math as the independent variable and read and write as the two mediator variables. The paths in such a model are depicted below. In our analysis, we are interested in finding these paths to calculate the direct and indirect effects of our variables.
To begin, we indicate which of our variables are the dependent, independent, and mediator variables in the dialog window.
This generates the output below.
Run MATRIX procedure:
Dependent, Independent, and Proposed Mediator Variables:
DV = science
IV = math
MEDS = read
write
Sample size
200
IV to Mediators (a paths)
Coeff se t p
read .7248 .0583 12.4378 .0000
write .6247 .0566 11.0452 .0000
Direct Effects of Mediators on DV (b paths)
Coeff se t p
read .3015 .0687 4.3903 .0000
write .2065 .0708 2.9185 .0039
Total Effect of IV on DV (c path)
Coeff se t p
math .6666 .0583 11.4371 .0000
Direct Effect of IV on DV (c-prime path)
Coeff se t p
math .3190 .0767 4.1605 .0000
Model Summary for DV Model
R-sq Adj R-sq F df1 df2 p
.4999 .4923 65.3187 3.0000 196.0000 .0000
******************************************************************
NORMAL THEORY TESTS FOR INDIRECT EFFECTS
Indirect Effects of IV on DV through Proposed Mediators (ab paths)
Effect se Z p
TOTAL .3476 .0596 5.8277 .0000
read .2186 .0524 4.1692 .0000
write .1290 .0454 2.8422 .0045
*****************************************************************
BOOTSTRAP RESULTS FOR INDIRECT EFFECTS
Indirect Effects of IV on DV through Proposed Mediators (ab paths)
Data boot Bias SE
TOTAL .3476 .3449 -.0027 .0645
read .2186 .2164 -.0022 .0537
write .1290 .1285 -.0005 .0496
Bias Corrected and Accelerated Confidence Intervals
Lower Upper
TOTAL .2230 .4700
read .1125 .3245
write .0294 .2235
*****************************************************************
Level of Confidence for Confidence Intervals:
95
Number of Bootstrap Resamples:
1000
------ END MATRIX -----
The results above assuming normality suggest that each of the separate indirect effects as well as the total indirect effect are significant. From the above results it is also possible to compute the ratio of indirect to direct effect (.3476/.3190 = 1.09) and the proportion of the total effect due to the indirect effect (.3476/(.3476 + .3190) = .52).
The normal theory tests for indirect effects compute the standard errors using the delta method which assumes that the estimates of the indirect effect are normally distributed. For many situations this is acceptable, but it does not work well for the indirect effects which are usually positively skewed and kurtotic. Thus the z-test and p-values for these indirect effects generally cannot be trusted. Therefore, it is recommended that bootstrap standard errors and confidence intervals be used. Additionally, if your outcome is binary, a proportion, or a percent, bootstrap estimates should be used. These can be found in the next block of output. These standard errors are slightly larger than those calculated assuming normality and the overall interpretation remains the same.
What do you do if you also have control variables? You add them as covariates to the model. Let's say that socst is a covariate. We can see the new results below.
Run MATRIX procedure: Dependent, Independent, and Proposed Mediator Variables: DV = science IV = math MEDS = read write Statistical Controls: CONTROL= socst Sample size 200 IV to Mediators (a paths) Coeff se t p read .5038 .0634 7.9512 .0000 write .4144 .0617 6.7112 .0000 Direct Effects of Mediators on DV (b paths) Coeff se t p read .3100 .0729 4.2517 .0000 write .2149 .0748 2.8723 .0045 Total Effect of IV on DV (c path) Coeff se t p math .5671 .0684 8.2863 .0000 Direct Effect of IV on DV (c-prime path) Coeff se t p math .3218 .0773 4.1654 .0000 Partial Effect of Control Variables on DV Coeff se t p socst -.0227 .0645 -.3519 .7253 Model Summary for DV Model R-sq Adj R-sq F df1 df2 p .5003 .4900 48.8010 4.0000 195.0000 .0000 ***************************************************************** BOOTSTRAP RESULTS FOR INDIRECT EFFECTS Indirect Effects of IV on DV through Proposed Mediators (ab paths) Data boot Bias SE TOTAL .2452 .2439 -.0014 .0478 read .1562 .1539 -.0023 .0413 write .0891 .0900 .0009 .0342 Bias Corrected and Accelerated Confidence Intervals Lower Upper TOTAL .1597 .3522 read .0863 .2476 write .0311 .1671 ***************************************************************** Level of Confidence for Confidence Intervals: 95 Number of Bootstrap Resamples: 1000 ------ END MATRIX -----
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