I'm working with the "mediation" package for simulation-based causal mediation analysis.
My question is: Why do percentile-bootstrapped CIs for the proportion mediated sometimes include impossible values?
Here is an example reproduced from the package authors' J Stat Soft paper (page 7) :
library(mediation) # model expected values for mediator and outcome med.fit <- lm(emo ~ treat + age + educ + gender + income, data = framing) out.fit <- glm(cong_mesg ~ emo + treat + age + educ + gender + income, data = framing, family = binomial("probit")) med.out <- mediate(med.fit, out.fit, treat = "treat", mediator = "emo", boot=TRUE, sims = 100) summary(med.out) Causal Mediation Analysis Nonparametric Bootstrap Confidence Intervals with the Percentile Method Estimate 95% CI Lower ACME (control) 0.0848 0.0406 ACME (treated) 0.0858 0.0372 ADE (control) 0.0116 -0.1137 ADE (treated) 0.0127 -0.1252 Total Effect 0.0975 -0.0593 Prop. Mediated (control) 0.8697 -2.5991 Prop. Mediated (treated) 0.8805 -2.3143 ACME (average) 0.0853 0.0386 ADE (average) 0.0122 -0.1201 Prop. Mediated (average) 0.8751 -2.4537 95% CI Upper p-value ACME (control) 0.1302 0.00 ACME (treated) 0.1327 0.00 ADE (control) 0.1272 0.88 ADE (treated) 0.1361 0.88 Total Effect 0.2040 0.22 Prop. Mediated (control) 3.7688 0.22 Prop. Mediated (treated) 3.5059 0.22 ACME (average) 0.1314 0.00 ADE (average) 0.1317 0.88 Prop. Mediated (average) 3.6374 0.22 Sample Size Used: 265 Simulations: 100
Note that the proportion mediated (regardless of standardization to the control, treated, or whole sample) has CI limits for the proportion mediated falling outside [-1, 1]. (Negative values are fine here because the package reports a negative proportion when the sign of ACME is opposite that of the total effect.)
Since I asked for a percentile bootstrap, my understanding is that the package should simply be computing the proportion mediated as ADE / (ADE + ACME) for each sample and then using percentiles for the CI limits. But given the out-of-bound CI limits, this appears not to be the case.
 Tingley, D., Yamamoto, T., Hirose, K., Keele, L., & Imai, K. (2014). Mediation: R package for causal mediation analysis.