Potthoff Analysis Using Process Hayes

Potthoff Analysis Using Process Hayes

%process (data=kevin,vars=ar misanth idealism,y=ar,x=idealism,m=misanth,

model=1,jn=1,plot=1);

Notice that the focal predictor is idealism (a dichotomous variable) and the moderator is misanthropy. We are interested in how the difference between groups changes across levels of the moderator.

************************* PROCESS Procedure for SAS Release 2.10 ************************
Written by Andrew F. Hayes, Ph.D. http://www.afhayes.com
Documentation available in Hayes (2013). www.guilford.com/p/hayes3
*******************************************************************************************************
Model and Variables /
Model = / 1
Y = / AR
X = / IDEALISM
M = / MISANTH
Sample size: /
154
*****************************************************************************************
Outcome: / AR
Model Summary /
R / R-sq / F / df1 / df2 / p /
0.3042 / 0.0925 / 5.0987 / 3.0000 / 150.0000 / 0.0022
Model /
/ coeff / se / t / p / LLCI / ULCI /
constant / 1.6258 / 0.1989 / 8.1726 / 0.0000 / 1.2327 / 2.0189
MISANTH / 0.3001 / 0.0806 / 3.7230 / 0.0003 / 0.1408 / 0.4593
IDEALISM / 0.7787 / 0.3024 / 2.5753 / 0.0110 / 0.1812 / 1.3761
INT_1 / -0.2847 / 0.1264 / -2.2523 / 0.0258 / -0.5345 / -0.0349
Interactions: /
INT_1 / IDEALISM / X / MISANTH
R-square increase due to interaction(s): /
/ R2-chng / F / df1 / df2 / p /
INT_1 / 0.0307 / 5.0730 / 1.0000 / 150.0000 / 0.0258
*****************************************************************************************
Conditional effect of X on Y at values of the moderator(s) /
/ MISANTH / Effect / se / t / p / LLCI / ULCI /
1.6473 / 0.3097 / 0.1179 / 2.6256 / 0.0095 / 0.0766 / 0.5427
2.3208 / 0.1179 / 0.0848 / 1.3900 / 0.1666 / -0.0497 / 0.2855
2.9942 / -0.0738 / 0.1224 / -0.6033 / 0.5472 / -0.3157 / 0.1680

When misanthropy is low (one standard deviation below the mean), AR is significantly higher (by .3097) in the idealistic group than it is in the nonidealistic group.

When misanthropy is at its mean level, or one standard deviation above its mean, the difference between the groups falls short of statistical significance.

Values for quantitative moderators are the mean and plus/minus one SD from mean.
Values for dichotomous moderators are the two values of the moderator.
******************************** JOHNSON-NEYMAN TECHNIQUE ********************************
Moderator values(s) defining Johnson-Neyman
significance region(s) /
Value / % below / % above /
2.1286 / 39.6104 / 60.3896
Conditional effect of X on Y at values of the moderator (M) /
/ MISANTH / Effect / se / t / p / LLCI / ULCI /
1.0000 / 0.4940 / 0.1845 / 2.6779 / 0.0082 / 0.1295 / 0.8584
1.1500 / 0.4513 / 0.1678 / 2.6886 / 0.0080 / 0.1196 / 0.7829
1.3000 / 0.4086 / 0.1518 / 2.6917 / 0.0079 / 0.1086 / 0.7085
1.4500 / 0.3658 / 0.1365 / 2.6809 / 0.0082 / 0.0962 / 0.6355
1.6000 / 0.3231 / 0.1222 / 2.6449 / 0.0090 / 0.0817 / 0.5645
1.7500 / 0.2804 / 0.1093 / 2.5654 / 0.0113 / 0.0644 / 0.4964
1.9000 / 0.2377 / 0.0984 / 2.4147 / 0.0170 / 0.0432 / 0.4322
2.0500 / 0.1950 / 0.0903 / 2.1597 / 0.0324 / 0.0166 / 0.3734
2.1286 / 0.1726 / 0.0874 / 1.9759 / 0.0500 / 0.0000 / 0.3453
2.2000 / 0.1523 / 0.0856 / 1.7785 / 0.0773 / -0.0169 / 0.3215
2.3500 / 0.1096 / 0.0850 / 1.2887 / 0.1995 / -0.0584 / 0.2776
2.5000 / 0.0669 / 0.0886 / 0.7549 / 0.4515 / -0.1082 / 0.2420
2.6500 / 0.0242 / 0.0959 / 0.2522 / 0.8012 / -0.1652 / 0.2136
2.8000 / -0.0185 / 0.1060 / -0.1747 / 0.8615 / -0.2281 / 0.1910
2.9500 / -0.0612 / 0.1184 / -0.5171 / 0.6058 / -0.2952 / 0.1727
3.1000 / -0.1039 / 0.1324 / -0.7854 / 0.4335 / -0.3655 / 0.1576
3.2500 / -0.1467 / 0.1474 / -0.9948 / 0.3214 / -0.4379 / 0.1446
3.4000 / -0.1894 / 0.1633 / -1.1596 / 0.2480 / -0.5120 / 0.1333
3.5500 / -0.2321 / 0.1798 / -1.2909 / 0.1987 / -0.5873 / 0.1231
3.7000 / -0.2748 / 0.1967 / -1.3970 / 0.1645 / -0.6634 / 0.1139
3.8500 / -0.3175 / 0.2140 / -1.4839 / 0.1399 / -0.7402 / 0.1053
4.0000 / -0.3602 / 0.2315 / -1.5560 / 0.1218 / -0.8176 / 0.0972
*****************************************************************************************
Data for visualizing conditional effect
of X on Y /
/ IDEALISM / MISANTH / yhat /
0.0000 / 1.6473 / 2.1201
1.0000 / 1.6473 / 2.4298
0.0000 / 2.3208 / 2.3222
1.0000 / 2.3208 / 2.4401
0.0000 / 2.9942 / 2.5243
1.0000 / 2.9942 / 2.4504

Here I use the output “Conditional effect of X on Y at values of the moderator (M)” to produce the Johnson-Neyman plot.

data plot; input Misanthropy Effect llci ulci;

cards;

1.0000 0.4940 0.1295 0.8584

1.1500 0.4513 0.1196 0.7829

1.3000 0.4086 0.1086 0.7085

1.4500 0.3658 0.0962 0.6355

1.6000 0.3231 0.0817 0.5645

1.7500 0.2804 0.0644 0.4964

1.9000 0.2377 0.0432 0.4322

2.0500 0.1950 0.0166 0.3734

2.1286 0.1726 0.0000 0.3453

2.2000 0.1523 -0.0169 0.3215

2.3500 0.1096 -0.0584 0.2776

2.5000 0.0669 -0.1082 0.2420

2.6500 0.0242 -0.1652 0.2136

2.8000 -0.0185 -0.2281 0.1910

2.9500 -0.0612 -0.2952 0.1727

3.1000 -0.1039 -0.3655 0.1576

3.2500 -0.1467 -0.4379 0.1446

3.4000 -0.1894 -0.5120 0.1333

3.5500 -0.2321 -0.5873 0.1231

3.7000 -0.2748 -0.6634 0.1139

3.8500 -0.3175 -0.7402 0.1053

4.0000 -0.3602 -0.8176 0.0972

proc sgplot;

series x=Misanthropy y=ulci/curvelabel = '95% Upper Limit' lineattrs=(color=red pattern=ShortDash);

series x=Misanthropy y=effect/curvelabel = 'Point Estimate' lineattrs=(color=blue pattern=Solid);

series x=Misanthropy y=llci/curvelabel = '95% Lower Limit' lineattrs=(color=red pattern=ShortDash);

xaxis label = 'Misanthropy';

yaxis label = 'Conditional effect of idealism';

refline 0/axis=y transparency=0.5;

refline 2.1286/axis=x transparency=0.5; run;

****************************** ANALYSIS NOTES AND WARNINGS ******************************
Level of confidence
for all confidence
intervals in output: /
95.0000

In the plot below, you can see that the confidence interval for the difference between group means excludes 0 when misanthropy is at or below 2.1286.

As misanthropy continues to increase beyond 2.1286, the (Idealistic Group Mean minus Nonidealistic Group Mean) continues to decrease, becoming negative with high values of misanthropy, but remaining nonsignificant. If we increased misanthropy sufficiently, the difference between the groups would become significant again, but with the Nonidealistic group having the larger mean. Just for fun, I tested the simple effect of Idealism with Misanthropy set to value 7 (which is an out-of-range value). As you can see below, the difference between the groups is significant, with the nonidealistic group having the larger AR mean, larger by 1.21 points.

Parameter Estimates /
Variable / DF / Parameter
Estimate / Standard
Error / tValue / Pr|t| /
Intercept / 1 / 3.72620 / 0.37657 / 9.90 / <.0001
Misanth7 / 1 / 0.30006 / 0.08059 / 3.72 / 0.0003
idealism / 1 / -1.21436 / 0.60066 / -2.02 / 0.0450
Interact7 / 1 / -0.28472 / 0.12641 / -2.25 / 0.0258

Here I use the output from “Data for visualizing conditional effect of X on Y” to produce the interaction plot.

Data plot2; input Misanthropy Idealism Animal_Rights; cards;

1.6473 0.0000 2.1201

2.3208 0.0000 2.3222

2.9942 0.0000 2.5243

1.6473 1.0000 2.4298

2.3208 1.0000 2.4401

2.9942 1.0000 2.4504

proc sgplot; reg x = misanthropy y = Animal_Rights / group = Idealism nomarkers;

yaxis label='Standardized Support of Animal Rights';

xaxis label='Standardized Misanthropy'; run;

Here I used idealism as the moderator and misanthropy as the focal predictor. I wish to see how the relationship between misanthropy and AR differs between the two groups.

%process (data=kevin,vars=ar misanth idealism,y=ar,x=misanth,m=idealism,model=1);

Model and Variables /
Model = / 1
Y = / AR
X = / MISANTH
M = / IDEALISM
Sample size: /
154
*****************************************************************************************
Outcome: / AR
Model Summary /
R / R-sq / F / df1 / df2 / p /
0.3042 / 0.0925 / 5.0987 / 3.0000 / 150.0000 / 0.0022
Model /
/ coeff / se / t / p / LLCI / ULCI /
constant / 1.6258 / 0.1989 / 8.1726 / 0.0000 / 1.2327 / 2.0189
IDEALISM / 0.7787 / 0.3024 / 2.5753 / 0.0110 / 0.1812 / 1.3761
MISANTH / 0.3001 / 0.0806 / 3.7230 / 0.0003 / 0.1408 / 0.4593
INT_1 / -0.2847 / 0.1264 / -2.2523 / 0.0258 / -0.5345 / -0.0349

Notice that the test of the interaction term produces the same result (p = .0258) as it did when misanthropy was the moderator and idealism the focal predictor.

Interactions: /
INT_1 / MISANTH / X / IDEALISM
R-square increase due to interaction(s): /
/ R2-chng / F / df1 / df2 / p /
INT_1 / 0.0307 / 5.0730 / 1.0000 / 150.0000 / 0.0258
*****************************************************************************************
Conditional effect of X on Y at values of the moderator(s) /
/ IDEALISM / Effect / se / t / p / LLCI / ULCI /
0.0000 / 0.3001 / 0.0806 / 3.7230 / 0.0003 / 0.1408 / 0.4593
1.0000 / 0.0153 / 0.0974 / 0.1575 / 0.8751 / -0.1771 / 0.2078

Among the nonidealists, the slope for predicting AR from misanthropy (.3001) is significantly greater than zero. Among the idealists, the slope (.0153) is not significantly different from zero.