# March 27, 2024

library(tidyverse)

# C for criticism (the mediator)
C <- c(3, 2, 4, 2, 2, 3, 1, 2, 3, 3, 
			 4, 4, 3, 2, 4, 4, 5, 3, 4, 4)

# S for symptoms (the outcome)
S <- c(4, 3, 4, 3, 4, 5, 3, 5, 7, 5,
			 7, 8, 5, 5, 7, 6, 6, 4, 5, 6)

# group is the IV
d <- tibble(group = c(rep("tx", 10), rep("ctrl", 10)),
						C, S)

# group means
d %>% group_by(group) %>% summarise(M = mean(S))

# contrast coding
d <- d %>% 
	mutate(X = ifelse(group == "tx", -1/2, 1/2))

# is there a significant group difference on the outcome?
model1 <- lm(S ~ X, d)
summary(model1)
# check!
pathc <- coef(model1)[2] # total effect of X; path c

# is there a significant group difference on the mediator?
model2 <- lm(C ~ X, d)
summary(model2)
# check!
patha <- coef(model2)[2] # effect of X on C (the mediator); path a

# is the effect of treatment reduced holding the mediator constant (i.e.,
# partialing it out)?
model3 <- lm(S ~ X + C, d)
coef(model1)[2]
coef(model3)[2]
# check!
pathcprime <- coef(model3)[2] # paths c' and b
pathb <- coef(model3)[3]

all.equal(patha*pathb, pathc - pathcprime)

library(mediation)

med <- mediate(model.m = model2, model.y = model3, treat = "X", mediator = "C", boot = TRUE)
summary(med)

# ACME ("Average of Causal Mediation Effect") = a*b {"indirect effect"}
# ADE: "Average Direct Effect" =                c'  {"direct effect"}
# Total effect =                                c {ACME + ADE}
# Proportion Mediated =                         (a*b)/c