Mediation Analysis
Emma Stacy
2026-09-23
Mediation Analysis: bootstrapped method
Variables
X = treat
Y = cong_mesg (binary)
M = emo
Covariates: sex, age, education, gender, income
Data
data ("framing", package = "mediation")
framing = as.data.frame(framing)
framing %>%
headTail() %>%
kable()| cond | anx | age | educ | gender | income | emo | p_harm | tone | eth | treat | english | immigr | anti_info | cong_mesg | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 3 | a little anxious | 45 | high school | male | 13 | 7 | 6 | 0 | 1 | 0 | Oppose | 4 | 0 | 1 |
| 2 | 4 | somewhat anxious | 73 | bachelor’s degree or higher | male | 16 | 6 | 3 | 0 | 0 | 0 | Favor | 3 | 0 | 0 |
| 3 | 2 | a little anxious | 53 | some college | female | 3 | 8 | 7 | 1 | 0 | 0 | Strongly Oppose | 3 | 0 | 0 |
| 4 | 1 | not anxious at all | 45 | high school | male | 14 | 9 | 8 | 1 | 1 | 1 | Strongly Oppose | 4 | 0 | 1 |
| … | NA | NA | … | NA | NA | … | … | … | … | … | … | NA | … | … | … |
| 262 | 4 | somewhat anxious | 28 | bachelor’s degree or higher | female | 14 | 6 | 6 | 0 | 0 | 0 | Strongly Oppose | 1 | 0 | 1 |
| 263 | 2 | very anxious | 38 | bachelor’s degree or higher | female | 14 | 3 | 6 | 1 | 0 | 0 | Favor | 2 | 0 | 0 |
| 264 | 1 | somewhat anxious | 29 | bachelor’s degree or higher | male | 10 | 9 | 7 | 1 | 1 | 1 | Strongly Oppose | 4 | 0 | 1 |
| 265 | 4 | very anxious | 52 | some college | female | 1 | 3 | 2 | 0 | 0 | 0 | Oppose | 2 | 0 | 0 |
Center emo, recode gender, create interaction terms
framing = framing %>%
mutate(emo = emo-mean(emo))
framing = framing %>%
mutate(sex=recode(gender, "female" = 1, "male" = 0))
framing = framing %>%
mutate (treat_emo = treat*emo,
treat_sex = treat*sex,
emo_sex = emo*sex)Single mediator model without covariates (M1) - direct and indirect effects
set.seed (2024)
mediate = mediation::mediate
med.fit1 = lm(emo ~ treat, data = framing) # a path
out.fit1 = glm(cong_mesg ~ emo + treat, data = framing, family = binomial ("probit")) # b path and c' path
med.out1 = mediate(med.fit1, out.fit1, treat = "treat", mediator = "emo", robustSE = TRUE, sims = 1000)
summary(med.out1)##
## Causal Mediation Analysis
##
## Quasi-Bayesian Confidence Intervals
##
## Estimate 95% CI Lower 95% CI Upper p-value
## ACME (control) 0.090799 0.043261 0.148024 <2e-16 ***
## ACME (treated) 0.091291 0.043282 0.147557 <2e-16 ***
## ADE (control) 0.011529 -0.098538 0.129061 0.85
## ADE (treated) 0.012022 -0.109831 0.138365 0.85
## Total Effect 0.102820 -0.027419 0.228637 0.12
## Prop. Mediated (control) 0.799388 -3.583906 6.001514 0.12
## Prop. Mediated (treated) 0.818887 -3.301332 5.615969 0.12
## ACME (average) 0.091045 0.043369 0.148391 <2e-16 ***
## ADE (average) 0.011776 -0.103855 0.132953 0.85
## Prop. Mediated (average) 0.809137 -3.447627 5.808741 0.12
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Sample Size Used: 265
##
##
## Simulations: 1000M1 - solving for individual coefficients
model1 = 'cong_mesg ~ c*treat
emo ~ a*treat
cong_mesg ~ b*emo
ab := a*b
total := c + (a*b)
'
fit1 = sem(model1, data = framing)
summary(fit1, fit.measures=TRUE, standardized=TRUE,rsquare=TRUE)## lavaan 0.7-2 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 5
##
## Number of observations 265
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 54.185
## Degrees of freedom 3
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -795.365
## Loglikelihood unrestricted model (H1) -795.365
##
## Akaike (AIC) 1600.731
## Bayesian (BIC) 1618.629
## Sample-size adjusted Bayesian (SABIC) 1602.776
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Goodness of Fit Index:
##
## Goodness of Fit Index (GFI) 1.000
## 90 Percent confidence interval - lower 1.000
## 90 Percent confidence interval - upper 1.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## cong_mesg ~
## treat (c) 0.015 0.063 0.231 0.818 0.015 0.014
## emo ~
## treat (a) 1.480 0.379 3.906 0.000 1.480 0.233
## cong_mesg ~
## emo (b) 0.063 0.010 6.276 0.000 0.063 0.368
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .cong_mesg 0.191 0.017 11.511 0.000 0.191 0.862
## .emo 7.253 0.630 11.511 0.000 7.253 0.946
##
## R-Square:
## Estimate
## cong_mesg 0.138
## emo 0.054
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ab 0.093 0.028 3.316 0.001 0.093 0.086
## total 0.107 0.066 1.626 0.104 0.107 0.099## lavaan NOTE:
## Standard errors and confidence intervals of the (nonlinear) defined (:=)
## parameters are based on the first-order delta method; for strongly
## nonlinear definitions, se.def = "mc" (Monte Carlo) or se = "bootstrap" may
## be more accurate.M1 - Bootstrapping for indirect effect (ab)
med.out11 = mediate(med.fit1, out.fit1, boot = TRUE, treat = "treat", mediator = "emo", sims = 1000)## Running nonparametric bootstrapsummary(med.out11)##
## Causal Mediation Analysis
##
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
##
## Estimate 95% CI Lower 95% CI Upper p-value
## ACME (control) 0.0914692 0.0411799 0.1547408 <2e-16 ***
## ACME (treated) 0.0923476 0.0400259 0.1526879 <2e-16 ***
## ADE (control) 0.0095796 -0.0977230 0.1258384 0.862
## ADE (treated) 0.0104579 -0.1109980 0.1359675 0.862
## Total Effect 0.1019272 -0.0276142 0.2274098 0.124
## Prop. Mediated (control) 0.8973980 -4.1840963 7.1683299 0.124
## Prop. Mediated (treated) 0.9060155 -3.8134399 6.2812620 0.124
## ACME (average) 0.0919084 0.0410999 0.1544160 <2e-16 ***
## ADE (average) 0.0100188 -0.1042986 0.1308804 0.862
## Prop. Mediated (average) 0.9017068 -3.9994471 6.7649858 0.124
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Sample Size Used: 265
##
##
## Simulations: 1000Model 1 with covariates (M2) - direct and indirect effects
med.fit2 = lm(emo ~ treat + age + educ + sex +income, data = framing)
out.fit2 = glm(cong_mesg ~ emo + treat + age + educ + sex + income, data = framing, family = binomial("probit"))
med.out2 = mediate(med.fit2, out.fit2, treat = "treat", mediator = "emo",
robustSE = TRUE, sims = 1000)
summary(med.out2)##
## Causal Mediation Analysis
##
## Quasi-Bayesian Confidence Intervals
##
## Estimate 95% CI Lower 95% CI Upper p-value
## ACME (control) 0.0825692 0.0336174 0.1420394 0.002 **
## ACME (treated) 0.0827035 0.0340365 0.1393389 0.002 **
## ADE (control) 0.0091973 -0.1045786 0.1289743 0.880
## ADE (treated) 0.0093316 -0.1153011 0.1365178 0.880
## Total Effect 0.0919008 -0.0327006 0.2249734 0.154
## Prop. Mediated (control) 0.8100225 -7.6754353 7.5767577 0.152
## Prop. Mediated (treated) 0.8241335 -6.9615413 6.8407080 0.152
## ACME (average) 0.0826364 0.0337485 0.1405705 0.002 **
## ADE (average) 0.0092645 -0.1093045 0.1330040 0.880
## Prop. Mediated (average) 0.8170780 -7.3236651 7.1841352 0.152
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Sample Size Used: 265
##
##
## Simulations: 1000M2 - individual coefficients
model2 = 'cong_mesg ~ c*treat + age + sex + income
emo ~ a*treat + age + sex + income
cong_mesg ~ b*emo
ab := a*b
total := c + (a*b)
'
fit2 = sem(model2, data = framing)
summary(fit2, fit.measures=TRUE, standardized=TRUE,rsquare=TRUE) ## lavaan 0.7-2 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
##
## Number of observations 265
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 76.092
## Degrees of freedom 9
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -784.411
## Loglikelihood unrestricted model (H1) -784.411
##
## Akaike (AIC) 1590.823
## Bayesian (BIC) 1630.200
## Sample-size adjusted Bayesian (SABIC) 1595.324
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Goodness of Fit Index:
##
## Goodness of Fit Index (GFI) 1.000
## 90 Percent confidence interval - lower 1.000
## 90 Percent confidence interval - upper 1.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## cong_mesg ~
## treat (c) 0.010 0.062 0.159 0.874 0.010 0.009
## age 0.002 0.002 1.225 0.221 0.002 0.069
## sex -0.122 0.053 -2.316 0.021 -0.122 -0.129
## income 0.020 0.007 2.936 0.003 0.020 0.166
## emo ~
## treat (a) 1.517 0.374 4.051 0.000 1.517 0.239
## age 0.009 0.010 0.859 0.390 0.009 0.051
## sex 0.099 0.329 0.300 0.764 0.099 0.018
## income -0.102 0.042 -2.422 0.015 -0.102 -0.144
## cong_mesg ~
## emo (b) 0.067 0.010 6.806 0.000 0.067 0.394
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .cong_mesg 0.181 0.016 11.511 0.000 0.181 0.816
## .emo 7.059 0.613 11.511 0.000 7.059 0.920
##
## R-Square:
## Estimate
## cong_mesg 0.184
## emo 0.080
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ab 0.102 0.029 3.481 0.000 0.102 0.094
## total 0.111 0.065 1.713 0.087 0.111 0.103## lavaan NOTE:
## Standard errors and confidence intervals of the (nonlinear) defined (:=)
## parameters are based on the first-order delta method; for strongly
## nonlinear definitions, se.def = "mc" (Monte Carlo) or se = "bootstrap" may
## be more accurate.M2 bootstrapping for indirect effect (ab)
med.out22 = mediate(med.fit2, out.fit2, boot = TRUE, treat = "treat", mediator = "emo", sims = 1000)## Running nonparametric bootstrapsummary(med.out22)##
## Causal Mediation Analysis
##
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
##
## Estimate 95% CI Lower 95% CI Upper p-value
## ACME (control) 0.084676 0.035120 0.142844 0.002 **
## ACME (treated) 0.085766 0.034584 0.142195 0.002 **
## ADE (control) 0.011616 -0.103141 0.149562 0.832
## ADE (treated) 0.012706 -0.117830 0.157626 0.832
## Total Effect 0.097382 -0.040137 0.246686 0.152
## Prop. Mediated (control) 0.869526 -3.886964 6.588640 0.154
## Prop. Mediated (treated) 0.880717 -3.515250 6.259787 0.154
## ACME (average) 0.085221 0.034574 0.142987 0.002 **
## ADE (average) 0.012161 -0.110885 0.153629 0.832
## Prop. Mediated (average) 0.875121 -3.701546 6.439923 0.154
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Sample Size Used: 265
##
##
## Simulations: 1000Moderation effect (M3) - direct and indirect effects
med.fit3 = lm(emo ~ treat + sex + treat_sex + age + educ + income, data = framing)
out.fit3 = glm(cong_mesg ~ treat + emo + sex + treat_sex + emo_sex + age + educ + income, data = framing, family = binomial("probit"))
# Mediated effect for female
med.female = mediate(med.fit3, out.fit3, treat = "treat", mediator = "emo", covariates = list(sex = 1), sims = 1000)
# Mediated effect for male
med.male = mediate(med.fit3, out.fit3, treat = "treat", mediator = "emo",
covariates = list(sex=0), sims = 1000)
summary(med.fit3)##
## Call:
## lm(formula = emo ~ treat + sex + treat_sex + age + educ + income,
## data = framing)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.9090 -2.0655 -0.3542 1.7491 6.6581
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.655556 0.886806 1.867 0.06306 .
## treat 1.671838 0.535378 3.123 0.00200 **
## sex 0.226423 0.365054 0.620 0.53565
## treat_sex -0.608006 0.723071 -0.841 0.40121
## age 0.001259 0.010054 0.125 0.90042
## educhigh school -1.055228 0.634088 -1.664 0.09730 .
## educsome college -1.852526 0.666234 -2.781 0.00583 **
## educbachelor's degree or higher -3.062183 0.660378 -4.637 5.64e-06 ***
## income -0.033484 0.041748 -0.802 0.42326
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.533 on 256 degrees of freedom
## Multiple R-squared: 0.1918, Adjusted R-squared: 0.1666
## F-statistic: 7.596 on 8 and 256 DF, p-value: 4.12e-09summary(out.fit3)##
## Call:
## glm(formula = cong_mesg ~ treat + emo + sex + treat_sex + emo_sex +
## age + educ + income, family = binomial("probit"), data = framing)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.236617 0.507492 -2.437 0.014821 *
## treat 0.382214 0.296081 1.291 0.196735
## emo 0.205294 0.049761 4.126 3.7e-05 ***
## sex -0.220780 0.204660 -1.079 0.280693
## treat_sex -0.662937 0.411821 -1.610 0.107448
## emo_sex 0.001710 0.067793 0.025 0.979875
## age 0.004868 0.005605 0.869 0.385060
## educhigh school -0.205649 0.337480 -0.609 0.542280
## educsome college -0.639750 0.365862 -1.749 0.080358 .
## educbachelor's degree or higher -0.381445 0.369916 -1.031 0.302463
## income 0.086807 0.025738 3.373 0.000744 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 336.89 on 264 degrees of freedom
## Residual deviance: 276.55 on 254 degrees of freedom
## AIC: 298.55
##
## Number of Fisher Scoring iterations: 5summary(med.male)##
## Causal Mediation Analysis
##
## Quasi-Bayesian Confidence Intervals
##
## (Inference Conditional on the Covariate Values Specified in `covariates')
##
## Estimate 95% CI Lower 95% CI Upper p-value
## ACME (control) 0.101854 0.031817 0.190630 0.004 **
## ACME (treated) 0.106350 0.035959 0.192598 0.004 **
## ADE (control) 0.114317 -0.051157 0.280195 0.180
## ADE (treated) 0.118812 -0.055537 0.288819 0.180
## Total Effect 0.220666 0.043773 0.387824 0.014 *
## Prop. Mediated (control) 0.454610 0.138858 1.628791 0.018 *
## Prop. Mediated (treated) 0.473360 0.149097 1.593041 0.018 *
## ACME (average) 0.104102 0.034153 0.191631 0.004 **
## ADE (average) 0.116564 -0.053124 0.285657 0.180
## Prop. Mediated (average) 0.463985 0.146171 1.610916 0.018 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Sample Size Used: 265
##
##
## Simulations: 1000summary(med.female)##
## Causal Mediation Analysis
##
## Quasi-Bayesian Confidence Intervals
##
## (Inference Conditional on the Covariate Values Specified in `covariates')
##
## Estimate 95% CI Lower 95% CI Upper p-value
## ACME (control) 0.095339 0.030709 0.185923 0.002 **
## ACME (treated) 0.102178 0.033833 0.192158 0.002 **
## ADE (control) 0.103152 -0.059548 0.276319 0.244
## ADE (treated) 0.109990 -0.069308 0.280948 0.244
## Total Effect 0.205329 0.026661 0.380407 0.020 *
## Prop. Mediated (control) 0.451443 0.125024 2.200149 0.022 *
## Prop. Mediated (treated) 0.498001 0.149336 2.095363 0.022 *
## ACME (average) 0.098759 0.031895 0.188456 0.002 **
## ADE (average) 0.106571 -0.063229 0.281056 0.244
## Prop. Mediated (average) 0.474722 0.139990 2.170861 0.022 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Sample Size Used: 265
##
##
## Simulations: 1000plot(med.male,
col = "blue",
main = "M3: Male")
plot(med.female,
col = "pink",
main = "M3: Female")
M3 - individual coefficients of male and female groups
model3 = 'cong_mesg ~ c(cg1,cg2)*treat
emo ~ c(ag1,ag2)*treat
cong_mesg ~ c(bg1,bg2)*emo
ab_g1 := ag1*bg1
ab_g2 := ag2*bg2
total_g1 := cg1 + (ag1*bg1)
total_g2 := cg2 + (ag2*bg2)
'
fit3 = sem(model3, data = framing,group="sex")
summary(fit3, fit.measures=TRUE, standardized=TRUE,rsquare=TRUE) ## lavaan 0.7-2 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Number of observations per group:
## 0 126
## 1 139
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
## Test statistic for each group:
## 0 0.000
## 1 0.000
##
## Model Test Baseline Model:
##
## Test statistic 58.344
## Degrees of freedom 6
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -790.855
## Loglikelihood unrestricted model (H1) -790.855
##
## Akaike (AIC) 1609.711
## Bayesian (BIC) 1659.827
## Sample-size adjusted Bayesian (SABIC) 1615.439
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Goodness of Fit Index:
##
## Goodness of Fit Index (GFI) 1.000
## 90 Percent confidence interval - lower 1.000
## 90 Percent confidence interval - upper 1.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [0]:
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## cong_mesg ~
## treat (cg1) 0.108 0.096 1.123 0.261 0.108 0.094
## emo ~
## treat (ag1) 1.850 0.560 3.304 0.001 1.850 0.282
## cong_mesg ~
## emo (bg1) 0.068 0.015 4.607 0.000 0.068 0.387
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .cong_mesg 0.371 0.046 8.101 0.000 0.371 0.761
## .emo -0.557 0.273 -2.038 0.042 -0.557 -0.200
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .cong_mesg 0.195 0.025 7.937 0.000 0.195 0.820
## .emo 7.168 0.903 7.937 0.000 7.168 0.920
##
## R-Square:
## Estimate
## cong_mesg 0.180
## emo 0.080
##
##
## Group 2 [1]:
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## cong_mesg ~
## treat (cg2) -0.055 0.082 -0.672 0.502 -0.055 -0.054
## emo ~
## treat (ag2) 1.159 0.513 2.257 0.024 1.159 0.188
## cong_mesg ~
## emo (bg2) 0.058 0.013 4.369 0.000 0.058 0.354
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .cong_mesg 0.289 0.042 6.890 0.000 0.289 0.644
## .emo -0.211 0.268 -0.787 0.431 -0.211 -0.077
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .cong_mesg 0.177 0.021 8.337 0.000 0.177 0.879
## .emo 7.274 0.873 8.337 0.000 7.274 0.965
##
## R-Square:
## Estimate
## cong_mesg 0.121
## emo 0.035
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ab_g1 0.125 0.047 2.685 0.007 0.125 0.109
## ab_g2 0.067 0.033 2.006 0.045 0.067 0.067
## total_g1 0.233 0.100 2.337 0.019 0.233 0.204
## total_g2 0.012 0.085 0.143 0.886 0.012 0.012## lavaan NOTE:
## Standard errors and confidence intervals of the (nonlinear) defined (:=)
## parameters are based on the first-order delta method; for strongly
## nonlinear definitions, se.def = "mc" (Monte Carlo) or se = "bootstrap" may
## be more accurate.Bootstrapping male and female samples for indirect effect (ab)
# Male
med.out30 = mediate(med.fit3, out.fit3, boot = TRUE, treat = "treat", mediator = "emo",
covariates = list(sex=0), sims = 1000)## Running nonparametric bootstrapsummary(med.out30)##
## Causal Mediation Analysis
##
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
##
## (Inference Conditional on the Covariate Values Specified in `covariates')
##
## Estimate 95% CI Lower 95% CI Upper p-value
## ACME (control) 0.104989 0.028671 0.199485 0.002 **
## ACME (treated) 0.111307 0.029872 0.197394 0.002 **
## ADE (control) 0.117463 -0.066977 0.314680 0.208
## ADE (treated) 0.123781 -0.071890 0.317275 0.208
## Total Effect 0.228770 0.025164 0.429102 0.028 *
## Prop. Mediated (control) 0.458928 0.111284 1.953191 0.030 *
## Prop. Mediated (treated) 0.486546 0.124012 1.876747 0.030 *
## ACME (average) 0.108148 0.029268 0.197168 0.002 **
## ADE (average) 0.120622 -0.069904 0.314433 0.208
## Prop. Mediated (average) 0.472737 0.115263 1.914969 0.030 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Sample Size Used: 265
##
##
## Simulations: 1000# Female
med.out31 = mediate(med.fit3, out.fit3, boot = TRUE, treat = "treat", mediator = "emo", covariates = list(sex = 1), sims = 1000)## Running nonparametric bootstrapsummary(med.out31)##
## Causal Mediation Analysis
##
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
##
## (Inference Conditional on the Covariate Values Specified in `covariates')
##
## Estimate 95% CI Lower 95% CI Upper p-value
## ACME (control) 0.097037 0.025141 0.196250 0.006 **
## ACME (treated) 0.108803 0.026581 0.204371 0.006 **
## ADE (control) 0.108888 -0.055233 0.296616 0.190
## ADE (treated) 0.120654 -0.061036 0.302604 0.190
## Total Effect 0.217691 0.023116 0.415958 0.030 *
## Prop. Mediated (control) 0.445755 0.093263 1.851392 0.032 *
## Prop. Mediated (treated) 0.499806 0.110593 1.721065 0.032 *
## ACME (average) 0.102920 0.027028 0.199626 0.006 **
## ADE (average) 0.114771 -0.058925 0.301207 0.190
## Prop. Mediated (average) 0.472780 0.101992 1.786012 0.032 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Sample Size Used: 265
##
##
## Simulations: 1000Moderation significance test between males and females
med.init = mediate(med.fit3, out.fit3, treat = "treat", mediator = "emo", sims = 1000)
test.modmed(med.init, covariates.1 = list(sex=1), covariates.2 = list(sex=0))##
## Test of ACME(covariates.1) - ACME(covariates.2) = 0
##
## data: estimates from med.init
## ACME(covariates.1) - ACME(covariates.2) = -0.0015659, p-value = 0.998
## alternative hypothesis: true ACME(covariates.1) - ACME(covariates.2) is not equal to 0
## 95 percent confidence interval:
## -0.1219402 0.1044566
##
##
## Test of ADE(covariates.1) - ADE(covariates.2) = 0
##
## data: estimates from med.init
## ADE(covariates.1) - ADE(covariates.2) = -0.0014891, p-value = 0.998
## alternative hypothesis: true ADE(covariates.1) - ADE(covariates.2) is not equal to 0
## 95 percent confidence interval:
## -0.2352679 0.2296625