Hi everyone,
I have a question about mediation when there is an interaction between 2
categorical variables, one with two levels and one with three levels.
Using the âmediationâ package by Tingley and colleagues in R, Iâm trying
to
conduct a bootstrapped mediation analysis for an interaction between a
2-level categorical IV (âcondstormâ) and another 3-level categorical IV
(âcondmeanâ). The mediator (âtrustmed2â) is dichotomous, and the
dependent
variable (âAttIndâ) is continuous.
Categorical 2-level IV âcondstormâ
table(d$condstorm)
nostorm storm
604 570
Categorical 3-level IV âcondmeanâ
table(d$condmean)
both high mean
413 375 386
Dichotomous mediator âtrustmed2â
table(d$trustmed2)
0 1
305 866
Continuous DV âAttIndâ
summary(d$AttInd)
Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
0.0000 0.3571 0.6200 0.5801 0.8214 1.0000 3
The code and output for the model with the mediator is:
contrasts(d$condstorm)
storm
nostorm 0
storm 1
contrasts(d$condmean)
nonevhigh nonevboth
both 0 1
high 1 0
mean 0 0
med.fit <- glm(trustmed2 ~ condmean*condstorm + gwbelief + trustmed1 +
coastdwell + partyID + polor + gender + age + race + educ + income + region,
weights=weight1, data = d, family = binomial('probit'))
summary(med.fit)
Call:
glm(formula = trustmed2 ~ condmean * condstorm + gwbelief +
trustmed1 + coastdwell
+ partyID + polor + gender + age + race + educ + income + region, family =
binomial("probit"), data = d, weights = weight1)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.9982 -0.1429 0.2196 0.4594 3.2721
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.876115 0.284494 -6.595 4.27e-11 ***
condmeannonevhigh 0.170809 0.175454 0.974 0.33029
condmeannonevboth 0.497041 0.181383 2.740 0.00614 **
condstormstorm 0.285569 0.182081 1.568 0.11680
gwbeliefnotvref 0.056512 0.631022 0.090 0.92864
gwbeliefnotvprobs 0.746556 0.129610 5.760 8.41e-09 ***
trustmed1 1.908566 0.121064 15.765 < 2e-16 ***
coastdwellyes 0.320369 0.128445 2.494 0.01262 *
partyIDvdem 0.585477 0.148862 3.933 8.39e-05 ***
partyIDvref -0.468275 0.654078 -0.716 0.47403
partyIDvrep 0.058146 0.130621 0.445 0.65621
polorvref -0.316949 0.508007 -0.624 0.53269
polorvlib -0.058482 0.160609 -0.364 0.71577
polorvcons -0.369565 0.122246 -3.023 0.00250 **
genderMale -0.009229 0.105253 -0.088 0.93013
agev1824 0.235127 0.194856 1.207 0.22756
agev2534 0.099723 0.178256 0.559 0.57587
agev3544 0.119399 0.169987 0.702 0.48243
agev4554 0.221921 0.176420 1.258 0.20842
agev5564 0.173343 0.170355 1.018 0.30890
racevhisp 0.033141 0.177162 0.187 0.85161
racevblack -0.323867 0.188305 -1.720 0.08545 .
racevother 0.475179 0.234313 2.028 0.04256 *
educhsvsome -0.002255 0.132574 -0.017 0.98643
educhsvcollgrad 0.201980 0.146240 1.381 0.16723
educhsvref 1.304337 0.666427 1.957 0.05032 .
incomev3050 -0.095963 0.159290 -0.602 0.54688
incomev5075 0.184528 0.168946 1.092 0.27473
incomev75100 0.028269 0.191474 0.148 0.88263
incomev100 -0.249873 0.167648 -1.490 0.13610
regionvmw -0.058581 0.163619 -0.358 0.72032
regionvne 0.315495 0.177227 1.780 0.07505 .
regionvs 0.204790 0.145384 1.409 0.15895
condmeannonevhigh:condstormstorm -0.061962 0.263472 -0.235 0.81407
condmeannonevboth:condstormstorm -0.665467 0.253958 -2.620 0.00878
**
---
Signif. codes: 0 â***â 0.001 â**â 0.01 â*â 0.05 â.â 0.1
â â 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 1316.98 on 1170 degrees of freedom
Residual deviance: 767.03 on 1136 degrees of freedom
(3 observations deleted due to missingness)
AIC: 836.49
Number of Fisher Scoring iterations: 6
And the code and output for the model with the mediator included as a
predictor on the dependent variable:
out.fit <- lm(AttInd ~ trustmed2 + condmean*condstorm + trustmed1 +
gwbelief + coastdwell + partyID + polor + gender + age + race + educ +
income + region, weights=weight1, data = d)
summary(out.fit)
Call:
lm(formula = AttInd ~ trustmed2 + condmean * condstorm + trustmed1 +
gwbelief + coastdwell + partyID + polor + gender + age +
race + educ + income + region, data = d, weights = weight1)
Weighted Residuals:
Min 1Q Median 3Q Max
-0.79365 -0.12054 0.00739 0.12351 0.72377
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.754e-01 3.411e-02 5.143 3.18e-07 ***
trustmed2 2.777e-01 1.940e-02 14.313 < 2e-16 ***
condmeannonevhigh -8.754e-03 2.174e-02 -0.403 0.687311
condmeannonevboth 2.548e-02 2.148e-02 1.186 0.235756
condstormstorm 3.977e-02 2.250e-02 1.767 0.077433 .
trustmed1 2.084e-02 2.014e-02 1.035 0.301053
gwbeliefnotvref -1.063e-01 9.071e-02 -1.172 0.241589
gwbeliefnotvprobs 1.574e-01 1.818e-02 8.656 < 2e-16 ***
coastdwellyes 1.100e-02 1.485e-02 0.740 0.459293
partyIDvdem 6.283e-02 1.618e-02 3.884 0.000109 ***
partyIDvref -2.558e-01 8.716e-02 -2.934 0.003408 **
partyIDvrep -4.893e-02 1.688e-02 -2.898 0.003829 **
polorvref 8.509e-02 6.617e-02 1.286 0.198751
polorvlib 6.199e-02 1.742e-02 3.558 0.000389 ***
polorvcons -7.015e-03 1.571e-02 -0.447 0.655204
genderMale -5.778e-03 1.267e-02 -0.456 0.648363
agev1824 4.624e-03 2.391e-02 0.193 0.846692
agev2534 -1.773e-02 2.222e-02 -0.798 0.425121
agev3544 2.952e-02 2.107e-02 1.401 0.161448
agev4554 1.590e-02 2.159e-02 0.736 0.461613
agev5564 -9.967e-03 2.073e-02 -0.481 0.630765
racevhisp 4.936e-02 2.030e-02 2.432 0.015174 *
racevblack -1.585e-02 2.224e-02 -0.713 0.476104
racevother 4.969e-02 2.518e-02 1.973 0.048687 *
educhsvsome -1.016e-02 1.612e-02 -0.630 0.528528
educhsvcollgrad -1.209e-02 1.713e-02 -0.706 0.480595
educhsvref 2.383e-01 8.213e-02 2.901 0.003791 **
incomev3050 -9.128e-04 1.964e-02 -0.046 0.962941
incomev5075 1.522e-02 1.996e-02 0.762 0.446132
incomev75100 -3.185e-02 2.280e-02 -1.397 0.162813
incomev100 1.344e-02 2.013e-02 0.668 0.504422
regionvmw 3.467e-02 2.027e-02 1.710 0.087541 .
regionvne 1.861e-02 2.015e-02 0.924 0.355812
regionvs -7.531e-05 1.716e-02 -0.004 0.996499
condmeannonevhigh:condstormstorm -4.354e-03 3.152e-02 -0.138 0.890175
condmeannonevboth:condstormstorm -5.284e-02 3.090e-02 -1.710 0.087514
.
---
Signif. codes: 0 â***â 0.001 â**â 0.01 â*â 0.05 â.â 0.1
â â 1
Residual standard error: 0.2103 on 1135 degrees of freedom
(3 observations deleted due to missingness)
Multiple R-squared: 0.4546, Adjusted R-squared: 0.4378
F-statistic: 27.03 on 35 and 1135 DF, p-value: < 2.2e-16
The model without the mediator is:
out.fit <- lm(AttInd ~ condmean*condstorm + trustmed1 + gwbelief +
coastdwell +
partyID + polor + gender + age + race + educ + income +
region, weights=weight1, data = d)
summary(out.fit)
Call:
lm(formula = AttInd ~ condmean * condstorm + trustmed1 + gwbelief +
coastdwell + partyID + polor + gender + age + race + educ +
income + region, data = d, weights = weight1)
Weighted Residuals:
Min 1Q Median 3Q Max
-1.1727 -0.1371 0.0130 0.1366 0.8077
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.1940313 0.0370161 5.242 1.89e-07 ***
condmeannonevhigh -0.0019461 0.0236085 -0.082 0.93432
condmeannonevboth 0.0474046 0.0232707 2.037 0.04187 *
condstormstorm 0.0527524 0.0244159 2.161 0.03094 *
trustmed1 0.1833521 0.0180674 10.148 < 2e-16 ***
gwbeliefnotvref -0.1093369 0.0985135 -1.110 0.26729
gwbeliefnotvprobs 0.2074035 0.0193781 10.703 < 2e-16 ***
coastdwellyes 0.0241253 0.0161011 1.498 0.13432
partyIDvdem 0.0858665 0.0174835 4.911 1.04e-06 ***
partyIDvref -0.2999944 0.0945990 -3.171 0.00156 **
partyIDvrep -0.0468268 0.0183366 -2.554 0.01079 *
polorvref 0.0560635 0.0718304 0.780 0.43526
polorvlib 0.0568556 0.0189179 3.005 0.00271 **
polorvcons -0.0293808 0.0169730 -1.731 0.08372 .
genderMale -0.0072970 0.0137554 -0.530 0.59588
agev1824 0.0162995 0.0259507 0.628 0.53007
agev2534 -0.0134314 0.0241301 -0.557 0.57790
agev3544 0.0326065 0.0228762 1.425 0.15433
agev4554 0.0281826 0.0234333 1.203 0.22935
agev5564 -0.0042263 0.0225102 -0.188 0.85111
racevhisp 0.0484325 0.0220418 2.197 0.02820 *
racevblack -0.0292002 0.0241349 -1.210 0.22658
racevother 0.0682464 0.0273067 2.499 0.01259 *
educhsvsome -0.0130208 0.0175088 -0.744 0.45723
educhsvcollgrad -0.0052682 0.0185980 -0.283 0.77703
educhsvref 0.3522019 0.0887800 3.967 7.73e-05 ***
incomev3050 -0.0065261 0.0213276 -0.306 0.75967
incomev5075 0.0200734 0.0216792 0.926 0.35468
incomev75100 -0.0336651 0.0247648 -1.359 0.17429
incomev100 -0.0006802 0.0218303 -0.031 0.97515
regionvmw 0.0293874 0.0220138 1.335 0.18216
regionvne 0.0317515 0.0218553 1.453 0.14655
regionvs 0.0085483 0.0186236 0.459 0.64632
condmeannonevhigh:condstormstorm -0.0068725 0.0342330 -0.201 0.84092
condmeannonevboth:condstormstorm -0.0860072 0.0334623 -2.570 0.01029
*
---
Signif. codes: 0 â***â 0.001 â**â 0.01 â*â 0.05 â.â 0.1
â â 1
Residual standard error: 0.2284 on 1136 degrees of freedom
(3 observations deleted due to missingness)
Multiple R-squared: 0.3562, Adjusted R-squared: 0.3369
F-statistic: 18.49 on 34 and 1136 DF, p-value: < 2.2e-16
We want to examine mediation in this interaction effect. We have tried
using the code:
mediate(med.fit, out.fit, treat = 'condstorm', control.value = 'nostorm',
treat.value = 'storm', mediator = 'trustmed2',
covariates=list(condmean='both'), boot=TRUE, sims=5000)
Which gave the following output:
Causal Mediation Analysis
Confidence Intervals Based on Nonparametric Bootstrap
(Inference Conditional on the Covariate Values Specified in
`covariates')
Estimate 95% CI Lower 95% CI Upper p-value
ACME -0.017705 -0.036626 -0.003284 0.04
ADE -0.014082 -0.045811 0.023155 0.53
Total Effect -0.031788 -0.069698 0.012371 0.14
Prop. Mediated 0.516591 1.174065 8.857665 0.04
Sample Size Used: 1171
Simulations: 5000
But this mediation only compares respondents at the level of âbothâ for the
condmean variable and excludes other conditions, so examines the effect of
"Both Condmean x Condstorm" MINUS the effect "condstorm", which is -.08 -
(.05) = -.03 (the total effect in the output above).
The total effect should instead be the same as the coefficient of
"condmeannonevboth:condstormstorm" in the second interaction term in the
model, which is -.086, p < .01.
Is it possible for us to examine this effect using the âmediationâ package
in R? Any help would be much appreciated!
-------------------------
Lauren C. Howe
PhD Candidate
Stanford University
Department of Psychology
Jordan Hall, Building 420
450 Serra Mall
Stanford, CA 94305
Tel.: +1.434.305.8363
<lc...@virginia.edu>
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