/
mediationTestPermMethods.R
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mediationTestPermMethods.R
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################################################################################
### file: mediation.testPermMethods.R
### authors: Miranda Kroehl, miranda.kroehl@ucdenver.edu
### date: 31 May 2013
###
### purpose: Evaluate tests for mediation using different permutation methods
###
###
### change log:
### 31 May 2013 - file created. original code from newMediationTest function
### March/Apr 2018 - edit file to incorporate bootstraps
################################################################################
#################################################################################################
# mediation.testPermMethods: evaluated 3 permutation methods for testing mediation
#
# Adjusted Model: Y = gamma0 + gamma1*x1 + gamma2*x2 + gamma3*m + ey
# IE Model: M = alpha0 + alpha1*x1 + alpha2*x2
#
# Arguments:
# size: sample size
# n.perms number of times permutation is performed
# n.boots number of bootstrap samples created to construct CIs
# mu.x1, mu.x2, mu.em, mu.ey: means for random variable generation
# sd.x1, sd.x2, sd.em, sd.ey: sd for random variable generation
# cor.x1.x2, cor.x1.m, cor.x2.m: Correlations for data generation
# cor.x1.y, cor.x2.y, cor.m.y: Correlations for data generaion
#
# Returns:
# a list (rtn)
#################################################################################################
mediationTestPermMethods <-
function(size, n.perms, n.boots,
cor.x1.x2, cor.x1.m, cor.x2.m,
cor.x1.y, cor.x2.y, cor.m.y){
rtn <- list(tt = NULL,
means = NULL,
sds = NULL,
cormat = NULL,
beta.ols = NULL,
gamma.ols = NULL,
alpha.ols = NULL,
se.beta.ols = NULL,
se.gamma.ols = NULL,
se.alpha.ols = NULL,
tx1.orig.ols = NULL,
p.tx1.null = NULL,
p.tx1.null.Mstar = NULL,
p.alpha.null = NULL,
p.gamma.null = NULL,
ci.tx1star.alt.ols = NULL,
ci.tx1star.alt.ols.Mstar = NULL,
accept.ho.tx1 = NULL,
accept.ho.tx1.Mstar = NULL,
accept.ho.joint = NULL,
accept.ho.ci = NULL,
accept.ho.ci.Mstar = NULL,
ci.covered = NULL,
ci.covered.Mstar = NULL,
bootci.perc = NULL,
bootci.bc = NULL,
bootci.bca = NULL,
accept.ho.boot.perc = NULL,
accept.ho.boot.bc = NULL,
accept.ho.boot.bca = NULL
)
simdat <- rdata(size,
cor.x1.x2, cor.x1.m, cor.x2.m,
cor.x1.y, cor.x2.y, cor.m.y)
############################################################
# true regression coefficient values
tt <- true.Coef(cor.x1.x2, cor.x1.m, cor.x2.m,
cor.x1.y, cor.x2.y, cor.m.y)
rtn$tt <- tt
############################################################
############################################################
# summary statistics about the generated data set
rtn$means <- colMeans(simdat)
rtn$sds <- apply(simdat, 2, sd)
rtn$cormat <- cor(simdat)
############################################################
# model fits
crude.ols <- lm(y ~ x1 + x2, data = simdat, model = FALSE)
adj.ols <- update(crude.ols, formula = . ~ . + m)
ie.ols <- update(crude.ols, formula = m ~ .)
# extract coeffiencts
rtn$beta.ols <- coef(crude.ols)
rtn$gamma.ols <- coef(adj.ols)
rtn$alpha.ols <- coef(ie.ols)
# standard errors
rtn$se.beta.ols <- sqrt(diag(vcov(crude.ols)))
rtn$se.gamma.ols <- sqrt(diag(vcov(adj.ols)))
rtn$se.alpha.ols <- sqrt(diag(vcov(ie.ols)))
############################################################
# Data needs to be in matrix form for the following functions
my.matrix <- as.matrix(simdat)
y <- as.matrix(my.matrix[,1])
adj.mod0 <- as.matrix(my.matrix[, 2:3])
adj.mod <- as.matrix(my.matrix[, 2:4])
m <- as.matrix(my.matrix[,4])
ie.mod0 <- as.matrix(my.matrix[,3])
ie.mod <- as.matrix(my.matrix[,2:3])
# Set design matrices
adj.design <- cbind(1, adj.mod)
adj.reduced.design <- cbind(1, adj.mod0)
ie.design <- cbind(1, ie.mod)
ie.reduced.design <- cbind(1, ie.mod0)
# Obtain fitted outcomes and residuals
adj.fit <- lm.fit(adj.design, y)
adj.fitted <- t(adj.fit$fitted.values)
adj.resid <- t(adj.fit$residuals)
adj.fit0 <- lm.fit(adj.reduced.design, y)
adj.reduced.fitted <- t(adj.fit0$fitted.values)
adj.reduced.resid <- t(adj.fit0$residuals)
ie.fit <- lm.fit(ie.design, m)
ie.fitted <- t(ie.fit$fitted.values)
ie.resid <- t(ie.fit$residuals)
ie.fit0 <- lm.fit(ie.reduced.design, m)
ie.reduced.fitted <- t(ie.fit0$fitted.values)
ie.reduced.resid <- t(ie.fit0$residuals)
############################################################
# Calculate test statistic
adj.stat <- setdiff(colnames(adj.mod), colnames(adj.mod0))
gamma.orig <- adj.fit$coef[adj.stat]
# ie.stat <- setdiff(colnames(ie.mod), colnames(ie.mod0))
ie.stat <- "x1"
alpha.orig <- ie.fit$coef[ie.stat]
tx1.orig.ols <- alpha.orig * gamma.orig
rtn$tx1.orig.ols <- alpha.orig * gamma.orig
############################################################
# Permutations
n.greater.tx1 <- 0
n.greater.tx1.Mstar <- 0
n.greater.alpha <- 0
n.greater.gamma <- 0
n.greater.gamma.Mstar <- 0
li <- freedman_lane_sim(adj.design, adj.reduced.design, ie.design, ie.reduced.design,
adj.fitted, adj.reduced.fitted, adj.resid, adj.reduced.resid,
ie.fitted, ie.reduced.fitted, ie.resid, ie.reduced.resid,
n.greater.tx1, n.greater.tx1.Mstar, n.greater.alpha, n.greater.gamma,
n.perms, adj.stat, ie.stat,
gamma.orig, alpha.orig, tx1.orig.ols)
p.tx1.null <- (1 + li$n.greater.tx1) / (1 + n.perms)
p.tx1.null.Mstar <- (1 + li$n.greater.tx1.Mstar) / (1 + n.perms)
p.alpha.null <- (1 + li$n.greater.alpha) / (1 + n.perms)
p.gamma.null <- (1 + li$n.greater.gamma) / (1 + n.perms)
ci.tx1star.alt.ols <- li$ci.tx1star.alt.ols
ci.tx1star.alt.ols.Mstar <- li$ci.tx1star.alt.ols.Mstar
rtn$p.tx1.null <- p.tx1.null
rtn$p.tx1.null.Mstar <- p.tx1.null.Mstar
rtn$p.alpha.null <- p.alpha.null
rtn$p.gamma.null <- p.gamma.null
rtn$ci.tx1star.alt.ols <- ci.tx1star.alt.ols
rtn$ci.tx1star.alt.ols.Mstar <- ci.tx1star.alt.ols.Mstar
rtn$accept.ho.tx1 <- as.numeric(p.tx1.null > 0.05)
rtn$accept.ho.tx1.Mstar <- as.numeric(p.tx1.null.Mstar > 0.05)
rtn$accept.ho.joint <- as.numeric(p.alpha.null > 0.05 | p.gamma.null > 0.05)
rtn$accept.ho.ci <- as.numeric(coverZero(rbind(li$ci.tx1star.alt.ols)))
rtn$accept.ho.ci.Mstar <- as.numeric(coverZero(rbind(li$ci.tx1star.alt.ols.Mstar)))
# Evaluate Coverage for ho.ci
t.alpha1 <- tt[1]
t.gamma3 <- tt[5]
t.product <- t.alpha1*t.gamma3
rtn$ci.covered <- as.numeric(t.product >= ci.tx1star.alt.ols[1] && t.product <= ci.tx1star.alt.ols[2])
rtn$ci.covered.Mstar <- as.numeric(t.product >= ci.tx1star.alt.ols.Mstar[1] && t.product <= ci.tx1star.alt.ols.Mstar[2])
############################################################
# Bootstrap
############################################################
ie.fcn <- function(simdat)
{
# Data needs to be in matrix form
my.matrix <- as.matrix(simdat)
y <- as.matrix(my.matrix[,1])
m <- as.matrix(my.matrix[,4])
ie.mod <- as.matrix(my.matrix[,2:3])
adj.mod <- as.matrix(my.matrix[, 2:4])
# Set design matrices
adj.design <- cbind(1, adj.mod)
ie.design <- cbind(1, ie.mod)
# Calculate regression coefficients
adj.fit <- lm.fit(adj.design, y)
ie.fit <- lm.fit(ie.design, m)
# Calculate test statistic
adj.stat <- setdiff(colnames(adj.mod), colnames(adj.mod0))
gamma.orig <- adj.fit$coef[adj.stat]
# ie.stat <- setdiff(colnames(ie.mod), colnames(ie.mod0))
ie.stat <- "x1"
alpha.orig <- ie.fit$coef[ie.stat]
tx1.orig.ols <- alpha.orig * gamma.orig
return(tx1.orig.ols)
}
#create function that calculates indirect effect for a given set of data
medi<-function(idf,i,...)
{
dt<-idf[i,]
bsmdl<-ie.fcn(dt)
}
#Run bootstrap (Data, function, Num of iterations, ordinary type, using indicies)
boot_qty <- n.boots
bs<-boot(simdat,medi,R=boot_qty,sim="ordinary", stype="i")
# Pull off CI for percentile, bias corrected, and bias corrected accelerated
perc <- boot.ci(bs, type="perc")
bootci.perc <- perc$percent[4:5]
bc <- boot.ci(bs, type="bca", L=1)
bootci.bc <- bc$bca[4:5]
bca <- boot.ci(bs, type="bca")
bootci.bca <- bca$bca[4:5]
rtn$bootci.perc <- bootci.perc
rtn$bootci.bc <- bootci.bc
rtn$bootci.bca <- bootci.bca
rtn$accept.ho.boot.perc <- as.numeric(coverZero(rbind(bootci.perc)))
rtn$accept.ho.boot.bc <- as.numeric(coverZero(rbind(bootci.bc)))
rtn$accept.ho.boot.bca <- as.numeric(coverZero(rbind(bootci.bca)))
############################################################
return(rtn)
}
# Example run with default settings
# system.time({
# testrslt <- mediation.testPermMethods(size=100, n.perms=1000, n.boot=1000,
# cor.x1.x2=0, cor.x1.m=0, cor.x2.m=0,
# cor.x1.y=0.3, cor.x2.y=0.3, cor.m.y=0.3)
# })
###################
### End of File ###
###################