statistics

1. Custom mediation models using Process macro with SPSS: An introduction
Mike Crowson, Ph.D.
August 2023
Video link: https://youtu.be/A4Sg5FjvpOA

2. A couple of suggestions:
1. Draw out your conceptual model. It may also help you to draw out the components of the statistical
model that are used to estimate your model parameters.
2. My recommendation is as part of your reporting ‘fill in’ the regression parameters (either unstandardized
or standardized) into the conceptual model diagram. This is along the lines of what you would see with a
path diagram when using a structural equation modeling program. This makes it easier to communicate
your results to your reader.
For more details on custom Process models, see Appendix B in Hayes (2022) book, Introduction to mediation,
moderation, and conditional process analysis (3rd Ed.).

3. The examples provided in this presentation are based on data from the article below. Nevertheless, the
examples are not intended as replications of what the authors did in their analyses.
Keshtidar M., Behzadnia, B. (2017). Prediction of intention to continue sport in athlete students: A self-determination
theory approach. PLoS ONE, 12(2): e0171673. doi:10.1371/journal.
pone.0171673
Link to SPSS data: https://drive.google.com/file/d/1x8IC8Iup1RQqh-nnNj2v5VydUN2eq0Br/view

4. Conceptual model

5. Task
orientation
Autonomous
motivation
Controlled
motivation
Intention to
continue
Process syntax to generate results for this model.
y=consequent variable
x=antecedent variable
m=mediator(s)
conf=confidence interval (here set at 95%)
stand=1 (requests fully standardized regression coefficients)
seed=12345 (This use important for generate the same bootstrap confidence intervals upon re-analysis of the same data with
same model specifications; the seed # you use is optional; I simply used 12345)
model=4 (model number of our mediation analysis)

6. The specification using syntax is the same as this via the dropdown menu
One downside of the dropdown menu is you cannot set a seed value. Thus, if you run your analysis more than once, the
lower and upper bounds of the bootstrap confidence intervals will vary somewhat over analyses. The syntax option allows
you to use a constant seed number across analyses that will result in the same lower and upper bound values.

7. task auton
1.5144
1.5144

8. task control
.2166
1.5144
.2166
The estimates I focus on throughout this Powerpoint will mainly be unstandardized regression coefficients from the
component regression models. These are what I am showing in the diagrams above (and throughout the Powerpoint).
However, you can easily use the standardized coefficients when making your own diagrams (if you would rather focus
on those).

9. 1.5144
.2166
task
intention
auton
control
.0982
.0982
.1289
.1289
.0143
.0143

10. Unstandardized indirect effects of task orientation (X) on intention to
continue (Y) via each proposed mediator. These are computed using the
unstandardized regression coefficients from the previous models. The specific
indirect effect of autonomous motivation is .1952. The specific indirect effect
of controlled motivation is .0031. The total indirect (see TOTAL) is computed
as the sum of the two specific indirect effects: .1952 + .0031 = .1983
These effects are tested using the bootstrap 95% confidence intervals. If 0
(the null) falls between the lower and upper bound of an interval, that
particular indirect effect is non-significant. If 0 falls outside the lower and
upper bound for an interval, then the indirect effect is considered significant.
We see here that the specific indirect effect of task orientation on intention to
continue via autonomous motivation (IE=.1952) is significant [bootstrap 95%
CI = (.1144,.2928)], whereas the specific indirect effect (IE=.0031) of task
orientation via controlled motivation is not significant [bootstrap 95% CI = (-
.0104,.0237)]. The total indirect effect (IE=.1983) on intention to continue via
the two mediators is significant [bootstrap 95% CI = (.1140,.3002).

11. Completely standardized specific indirect effects of task
orientation (X) on intention to continue (Y) via each proposed
mediator. These are computed using the standardized
regression coefficients from the previous models.

12. To be able to generate custom mediation models, we must create a bmatrix. This essentially is a matrix that specifies which
regression parameters in your model are estimated and which are fixed to 0. My recommendation is to begin this process
by (1) drawing out your model (if you have not already done so) and then (2) creating a k X k matrix (where k=number of
variables in your analysis. Each column is headed by a variable that potentially points away from one variable in the model
to another. Think of these variables as ‘upstream’. Each row represents a variable ‘downstream’ being pointed to by an
upstream variable. Since a variable cannot predict itself, I have indicated that with a dash (-) in the matrix below for cells
M1-M1 and M2-M2. Since cell M1-M2 (row 2, col 1) is open for specification, we are not allowed to leave cell M2-M1 (row
1, col 2) open for specification.
- -
-
X
M1
M2
M1
M2
Y
Upstream variables with arrows pointing FROM them
Downstream variables
with arrows pointing
TO them

13. Next, we designate parameters that are freely estimated with a 1 and parameters that are not estimated with a 0.
1 - -
1 0 -
1 1 1
X
M1
M2
M1
M2
Y
In the Process syntax, the bmatrix option will collect the 1’s and 0’s row by row in this matrix:
bmatrix=1,1,0,1,1,1
The first 1 is in row 1. The 1 followed by 0 is in row 2. The 1, 1, and 1 are found in row 3.
Upstream variables with arrows pointing FROM them
Downstream variables
with arrows pointing
TO them

14. In the Process syntax, the bmatrix option will collect the 1’s and 0’s row by row in this matrix:
bmatrix=1,1,0,1,1,1
The first 1 is in row 1. The 1 followed by 0 is in row 2. The 1, 1, and 1 are found in row 3.
1 - -
1 0 -
1 1 1
task
autonomous
controlled
intention
controlled
autonomous
Same as previous…
The syntax in Process…

15. To test this model, we need to remove the direct effect of task orientation (X) to intention to continue (Y).
1 - -
1 0 -
0 1 1
task
autonomous
controlled
intention
controlled
autonomous
Going back to our matrix, we set the parameter in row 3, column 1 to 0 (bolded below).
Process syntax…

16. Same results as before

17. intention
auton
control
.1402
.0138
1.5144
.2166
.1402
.0138
In this model, the direct effects of autonomous motivation and controlled motivation are not controlling for task
orientation (as had occurred in our previous analysis).

19. This model includes serial mediation, where one mediator has a direct effect on another mediator. To test this model,
we need to remove the direct effect of task orientation (X) to intention to continue (Y) – as before – and add the direct
effect of autonomous motivation on controlled motivation.
1 - -
1 1 -
0 1 1
task
autonomous
controlled
intention
controlled
autonomous
Going back to our matrix, we (again) set the parameter in row 3, column 1 to 0 (bolded below). Now, however, we
change the former 0 (in row 2, column 2) to 1 (bolded below).
Process syntax…

20. Important: If you have mediators that follow a particular sequence (ordering), you need to set m=<first mediator in
sequence> <second mediator in sequence> within the Process syntax. This also dictates the layout of the bmatrix.
First
mediator
Second
mediator

21. Output for the first regression model is the same as before
The second regression model output reflects both task-
orientation and autonomous motivation as predictors
of controlled motivation.
1.5144
-.2704
.3216

22. 1.5144
-.2704
.3216
.1402
.0138

23. The specific and total indirect effects here are still products of the
paths that trace from X to Y.
Ind1 = 1.5144 * .1402 = .2123
Ind2 = -.2704 * .0138 = -.0037
Ind3 = 1.5144 * .3216 * .0138 = .0067
This is a key for which tracings from X to Y are associated
with the indirect effects displayed in the table(s) above.
1.5144
-.2704
.3216
.1402
.0138

24. What if we want to change the specified direction of influence, where we have a direct effect of controlled motivation on
autonomous motivation? To ensure the sequencing is correct, we need to reverse the order of the mediators (in our
table below) and in the Process syntax.
1 - -
1 1 -
0 1 1
task
controlled
autonomous
intention
autonomous
controlled
Order reversed from
previous example

25. Unlike the previous example (see right), the
first mediator here is controlled motivation.

26. .2166
1.4991
.0705

27. .2166
1.4991
.0705
.1402
.0138

29. Final note:
I am sometimes asked whether it is possible to include multiple antecedent (X) variables in Process models. I have found
there is no straightforward way to do this. It is possible to include other antecedents (X’s) as covariates [using the ‘cov=‘
option] using Process syntax. However, when these variables are included in this way, their effects will be registered on all
variables ‘downstream’. In other words, these antecedents/covariates will be included as regressors in each regression
model predicting the downstream variables. To my knowledge, there is no direct way of fixing some of those effects to 0
[when you do not wish to include them in a model]. If this is a problem for you, the only thing I can suggest is to test your
model as a path model using an SEM program.

30. References
Hayes, A. F. (2022). Introduction to mediation, moderation, and conditional process analysis (3rd Ed.). New York: The
Guilford Press.
Keshtidar M., Behzadnia, B. (2017). Prediction of intention to continue sport in athlete students: A self-determination
theory approach. PLoS ONE, 12(2): e0171673. doi:10.1371/journal.
pone.0171673