Moderated Mediation: Annotated SAS Output
proc contents; run;
proc means data=protest; run;
The SAS System
The CONTENTS Procedure
Data Set Name WORK.PROTEST2 Observations 129
Alphabetic List of Variables and Attributes
# Variable
Type Len Format
Label
6 LikingZ
Num
8
7 RespapprZ Num
8
5 SexismZ
Num
8
2 liking
Num
8 F8.2
4 protest
Num
8 PROTEST. PROTEST: experimental condition (0 = no protest, 1 = protest)
3 respappr
Num
8 F8.2
RESPAPPR: appropriateness of response
1 sexism
Num
8 F8.2
SEXISM: perceived pervasiveness of sex discrimination
LIKING: liking of the target
The MEANS Procedure
Variable
Label
sexism
SEXISM: perceived
pervasiveness of sex
discrimination
liking
respappr
protest
LIKING: liking of the target
RESPAPPR:
appropriateness of
response
PROTEST: experimental
condition (0 = no protest, 1
= protest)
data protest2; set protest;
SexismZ=(sexism-5.1169767)/0.7837616;
LikingZ=(liking-5.6367442)/1.0496973;
RespapprZ=(respappr-4.8662791)/1.3481203; run;
Proc Means; run;
N
Mean
Std Dev
Minimum
Maximum
129 5.1169767
0.7837616 2.8700000
7.0000000
129 5.6367442
1.0496973 1.0000000
7.0000000
129 4.8662791 1.3481203 1.5000000
7.0000000
129 0.6821705
1.0000000
0.4674481
0
The MEANS Procedure
Variable
Label
sexism
SEXISM: perceived
pervasiveness of sex
discrimination
liking
respappr
protest
SexismZ
LikingZ
RespapprZ
LIKING: liking of the
target
RESPAPPR:
appropriateness of
response
PROTEST:
experimental
condition (0 = no
protest, 1 = protest)
N
Mean
Std Dev
Minimum
Maximum
129
5.1169767
0.7837616
2.8700000
7.0000000
129
5.6367442
1.0496973
1.0000000
7.0000000
129
4.8662791
1.3481203
1.5000000
7.0000000
129
0.6821705
0.4674481
0
1.0000000
129 5.6376896E-8 1.0000000 -2.8669135
2.4025460
129
-1.329287E-8 1.0000000 -4.4172203
1.2987133
129
-2.242571E-8 1.0000000 -2.4970168
1.5827378
Simple Mediation Analysis
%process (data=protest2, vars=protest RespapprZ LikingZ,y=LikingZ,x=protest,m=RespapprZ,boot=10000,model=4);
Model and Variables
Model = 4
Y=
LIKINGZ
X=
PROTEST
M=
RESPAPPRZ
Sample size:
129
Outcome: RESPAPPRZ
Model Summary
R
R-sq
F
df1
df2
p
0.4992 0.2492 42.1550 1.0000 127.0000 0.0000
Model
coeff
se
t
p
LLCI
ULCI
Constant -0.7285 0.1359 -5.3625 0.0000 -0.9973 -0.4597
PROTEST 1.0679 0.1645 6.4927 0.0000 0.7425 1.3934
If you were to conduct an independent samples t-test comparing the two groups on perceived response
appropriateness, you would get the t and p reported here. Mean standardized perceived appropriateness was
1.068 higher when the attorney protested than when she did not.
Outcome: LIKINGZ
Model Summary
R
R-sq
F
df1
df2
p
0.4959 0.2459 20.5483 2.0000 126.0000 0.0000
Model
coeff
constant
se
t
p
LLCI
ULCI
0.0655 0.1514 0.4324 0.6662 -0.2341 0.3650
RESPAPPRZ 0.5168 0.0893 5.7884 0.0000 0.3401 0.6935
PROTEST
-0.0959 0.1910 -0.5023 0.6163 -0.4739 0.2820
This is an ANCOV. If you were to conduct an independent samples t-test comparing the groups on how
much the respondent liked the attorney, you would find a significant difference, with them liking her better when
she protested, d = .465. Here we have held constant the effect of response appropriateness, and the adjusted
means no longer differ significantly.
****************************** DIRECT AND INDIRECT EFFECTS *******************************
Direct effect of X on Y
Effect
SE
t
p
LLCI
ULCI
-0.0959 0.1910 -0.5023 0.6163 -0.4739 0.2820
Indirect effect of X on Y
Effect Boot SE BootLLCI BootULCI
RESPAPPRZ 0.5519
0.1436
0.3115
0.8775
The indirect effect here is the product of the coefficients, 1.0679(.5168) = .5519.
Simple Moderation Analysis
%process (data=protest2, vars=protest RespapprZ
SexismZ,y=RespapprZ,x=protest,m=SexismZ,quantile=1,model=1);
Model and Variables
Model = 1
Y=
RESPAPPRZ
X=
PROTEST
M=
SEXISMZ
Outcome: RESPAPPRZ
Model Summary
R
R-sq
F
df1
df2
p
0.5442 0.2962 17.5340 3.0000 125.0000 0.0000
Model
coeff
constant
se
t
p
LLCI
ULCI
-0.7466 0.1328 -5.6206 0.0000 -1.0095 -0.4837
SEXISMZ -0.3075 0.1371 -2.2426 0.0267 -0.5790 -0.0361
PROTEST 1.0815 0.1607 6.7282 0.0000 0.7634 1.3997
INT_1
0.4709 0.1639 2.8732 0.0048 0.1465 0.7953
Back to the future.
Interactions:
INT_1 PROTEST X SEXISMZ
R-square increase due to interaction(s):
R2-chng
INT_1
F
df1
df2
p
0.0465 8.2551 1.0000 125.0000 0.0048
Conditional effect of X on Y at values of the moderator(s)
SEXISMZ Effect
se
t
p
LLCI
ULCI
-1.2720 0.4825 0.2590 1.8633 0.0648 -0.0300 0.9950
-0.7872 0.7108 0.2027 3.5065 0.0006 0.3096 1.1120
0.0039 1.0833 0.1608 6.7386 0.0000 0.7652 1.4015
0.6418 1.3838 0.1950 7.0950 0.0000 0.9978 1.7698
1.2798 1.6842 0.2685 6.2724 0.0000 1.1528 2.2156
Values for quantitative moderators are the 10th, 25th, 50th, 75th, and 90th percentiles.
Values for dichotomous moderators are the two values of the moderator.
Perceived prevalence of sexism significantly moderates the effect of protesting on perceived response
appropriateness. As perceived prevalence of sexism increases, the difference between the two groups gets
larger.
Moderation Analysis With Covariate
%process (data=protest2, vars=protest RespapprZ SexismZ
LikingZ,y=LikingZ,x=protest,m=SexismZ,quantile=1,model=1);
Here we have identified Response Appropriateness as a covariate.
Model = 1
Y=
LIKINGZ
X=
PROTEST
M=
SEXISMZ
Statistical controls:
RESPAPPRZ
Sample size:
129
Outcome: LIKINGZ
Model Summary
R
R-sq
F
df1
df2
p
0.5323 0.2833 12.2551 4.0000 124.0000 0.0000
Model
coeff
se
t
p
LLCI
ULCI
constant
0.0127 0.1506 0.0844 0.9329 -0.2854 0.3108
SEXISMZ
-0.2109 0.1417 -1.4882 0.1392 -0.4914 0.0696
PROTEST
-0.0297 0.1901 -0.1563 0.8760 -0.4059 0.3465
INT_1
0.4051 0.1714 2.3628 0.0197 0.0658 0.7444
RESPAPPRZ 0.4614 0.0906 5.0916 0.0000 0.2820 0.6408
Back to the future.
Interactions:
INT_1 PROTEST X SEXISMZ
R-square increase due to interaction(s):
R2-chng
INT_1
F
df1
df2
p
0.0323 5.5830 1.0000 124.0000 0.0197
*****************************************************************************************
Conditional effect of X on Y at values of the moderator(s)
SEXISMZ
Effect
se
t
p
LLCI
ULCI
-1.2720 -0.5450 0.2660 -2.0491 0.0426 -1.0715 -0.0186
-0.7872 -0.3486 0.2152 -1.6196 0.1079 -0.7746 0.0774
0.0039 -0.0282 0.1902 -0.1480 0.8826 -0.4046 0.3483
0.6418 0.2303 0.2340 0.9840 0.3270 -0.2329 0.6935
1.2798 0.4887 0.3119 1.5668 0.1197 -0.1287 1.1061
Back to the future.
Values for quantitative moderators are the 10th, 25th, 50th, 75th, and 90th percentiles.
Values for dichotomous moderators are the two values of the moderator.
Since we have held constant the effect of the mediator, these effects are the conditional direct effects of
protesting on liking. Those low in perceived pervasiveness of sexism actually like the attorney better when she did not
protest.
Moderated Mediation Analysis
%process (data=protest2, vars=protest RespapprZ SexismZ LikingZ,y=LikingZ,x=protest,w=SexismZ,
m=RespapprZ,quantile=1,model=8, boot=10000);
Model and Variables
Model = 8
Y=
LIKINGZ
X=
PROTEST
M=
RESPAPPRZ
Model and Variables
W=
SEXISMZ
Sample size:
129
Outcome: RESPAPPRZ
Model Summary
R
R-sq
F
df1
df2
p
0.5442 0.2962 17.5340 3.0000 125.0000 0.0000
Model
coeff
se
t
p
LLCI
ULCI
Constant -0.7466 0.1328 -5.6206 0.0000 -1.0095 -0.4837
PROTEST 1.0815 0.1607 6.7282 0.0000 0.7634 1.3997
SEXISMZ -0.3075 0.1371 -2.2426 0.0267 -0.5790 -0.0361
INT_1
0.4709 0.1639 2.8732 0.0048 0.1465 0.7953
Interactions:
INT_1 PROTEST X SEXISMZ
We have seen this interaction earlier
Outcome: LIKINGZ
Model Summary
R
R-sq
F
df1
df2
p
0.5323 0.2833 12.2551 4.0000 124.0000 0.0000
Model
coeff
constant
se
t
p
LLCI
ULCI
0.0127 0.1506 0.0844 0.9329 -0.2854 0.3108
RESPAPPRZ 0.4614 0.0906 5.0916 0.0000 0.2820 0.6408
PROTEST
-0.0297 0.1901 -0.1563 0.8760 -0.4059 0.3465
SEXISMZ
-0.2109 0.1417 -1.4882 0.1392 -0.4914 0.0696
INT_2
0.4051 0.1714 2.3628 0.0197 0.0658 0.7444
Interactions:
Interactions:
INT_2 PROTEST X SEXISMZ
We have seen this interaction earlier.
DIRECT AND INDIRECT EFFECTS We have seen these conditional direct effects earlier.
Conditional direct effect(s) of X on Y at values of the moderator(s)
SEXISMZ
Effect
SE
t
p
LLCI
ULCI
-1.2720 -0.5450 0.2660 -2.0491 0.0426 -1.0715 -0.0186
-0.7872 -0.3486 0.2152 -1.6196 0.1079 -0.7746
0.0774
0.0039 -0.0282 0.1902 -0.1480 0.8826 -0.4046
0.3483
0.6418
0.2303 0.2340
0.9840 0.3270 -0.2329
0.6935
1.2798
0.4887 0.3119
1.5668 0.1197 -0.1287
1.1061
Conditional indirect effect(s) of X on Y at values of the moderator(s)
SEXISMZ Effect Boot SE BootLLCI BootULCI
RESPAPPRZ
-1.2720 0.2226
0.1402
-0.0134
0.5549
RESPAPPRZ
-0.7872 0.3280
0.1186
0.1397
0.6199
RESPAPPRZ
0.0039 0.4998
0.1258
0.2915
0.7829
RESPAPPRZ
0.6418 0.6385
0.1646
0.3542
1.0008
RESPAPPRZ
1.2798 0.7771
0.2172
0.3971
1.2584
As the value of perceived pervasiveness of sexism increases, the magnitude of the indirect effect of protest on
liking through response appropriateness increases.
Values for quantitative moderators are the 10th, 25th, 50th, 75th, and 90th percentiles.
Indirect effect of highest order interaction
Effect Boot SE BootLLCI BootULCI
RESPAPPRZ 0.2173
0.1040
0.0323
0.4462
(Protest x SexismResponse Appropriateness)(Response AppropriatenessLiking)
.4709(.4614) = .2173.
proc sgplot;
series x=SexismZ y=direct/curvelabel = 'Direct Effect' lineattrs=(color=blue pattern=ShortDash);
series x=SexismZ y=indirect/curvelabel = 'Indirect Effect' lineattrs=(color=red pattern=Solid);
xaxis label = 'Perceived Pervasiveness of Sexism';
yaxis label = 'Conditional Effect of Protest';
refline 0/axis=y lineattrs=(color=gray pattern=ShortDash);
run;