Test of Mediation

# out is a temporary data frame, one row per replication.
# out is reinitialized for each r.s/samp combination.
# Summary data will be saved in lia.results and lia.descrs.

out = data.frame(a = rep(NA,nreps),
b = rep(NA,nreps),
ab = rep(NA,nreps),
c = rep(NA,nreps),
c2 = rep(NA,nreps),
bca.lower = rep(NA,nreps),
bca.upper = rep(NA,nreps),
bca.ciwidth = rep(NA,nreps),
bca.reject.pos = rep(NA,nreps),
bca.reject.neg = rep(NA,nreps),
bca.HO.reject = rep(NA,nreps),
acl.lower = rep(NA,nreps),
acl.upper = rep(NA,nreps),
acl.ciwidth = rep(NA,nreps),
acl.reject.pos = rep(NA,nreps),
acl.reject.neg = rep(NA,nreps),
acl.HO.reject = rep(NA,nreps),
bt.pa = rep(NA,nreps),
bt.pb = rep(NA,nreps),
bt.reject.pos = rep(0,nreps),
bt.reject.neg = rep(0,nreps),
bt.HO.reject = rep(0,nreps),
ACLBT = rep(0,nreps),
ACLBCA = rep(0,nreps),
BCABT = rep(0, nreps),
acl_bca.diff = rep(NA, nreps),
acl_bca.lower.diff = rep(NA,nreps),
acl_bca.upper.diff = rep(NA,nreps),
acl.tries = rep(l, nreps))

# k loops through designated number of replications (nreps)

# at each sample size (n).

for (k in 1:nreps) {

x=mvrnorm(n,rep(0,3),sigma)
regrl = lm(scale(x[,2])-scale(x [,1])-1)
regr2 = lm(scale(x[,3])-scale(x[,2])+scale(x[,1])-1)
r e g r 3 = l m ( s c a l e ( x [ , 3 ] ) - s c a l e ( x [ , 1] )-1)
out$a[k] = regrl$coef
out$b[k] = regr2$coef[1]
out$ab[k] = regrl$coef*regr2$coef[1]
out$c[k] = regr3$coef
out$c2[k] = regr2$coef[2]
# B o o t s t r a p (BCA)
boot.out = boot(x,abprod,R=nboot,stype="i")
bootci.out<-boot.ci(boot.out,conf=0.95,type = "bca")
out$bca.lower[k]<-bootci.out$bca[4]
out$bca.upper[k]<-bootci.out$bca[5]
o u t $ b c a . c i w i d t h [ k ] < - b o o t c i . o u t $ b c a [ 5 ] - b o o t c i . o u t $ b c a [4]

out$bca.reject.pos[k]<- out$bca.lower[k]>0
out$bca.reject.neg[k]<- out$bca.upper[k]<0
out$bca.HO.reject[k]<- out$bca.reject.pos[k] +

out$bca.rej ect.neg[k]

# Asymmetric Confidence Limits (ACL)
cprime = regr2$coef[2]
ahat=round(out$a[k] ,5)
bhat=round(out$b[k] ,5)
sea=round(summary(regrl)$coef[2],5)
seb=round(summary(regr2)$coef[1,2] ,5)
pcout=prodclin(ahat,sea,bhat,seb,0,0.05)
# Guard against nonconvergent results from ACL:

if(is.na(pcout[13])) {
ahat=round(out$a[k] ,4)
bhat=round(out$b[k],4)
sea=round(summary(regrl)$coef[2],4)
seb=round(summary(regr2)$coef[1,2],4)
pcout=prodclin(ahat,sea,bhat,seb,0, 0.05)
out$acl.tries[k] <- 2

if(is.na(pcout[13])) {
ahat=round(out$a[k] ,3)
bhat=round(out$b[k] , 3)
sea=round(summary(regrl)$coef[2],3)
seb=round(summary(regr2)$coef[1,2] ,3)
pcout=prodclin(ahat,sea,bhat,seb,0,0.05)
out$acl.tries[k] <- 3

if(is.na(pcout[13])) {
ahat=round(out$a[k],2)
bhat=round(out$b[k],2)
sea=round(summary(regrl)$coef[2] ,2)
seb=round(summary(regr2)$coef[1,2] ,2)
pcout=prodclin(ahat,sea,bhat,seb,0,0.05)
o u t $ a c l . t r i e s [ k ] <- 4

if(is.na(pcout[13])) {
ahat=round(out$a[k] ,1)
bhat=round(out$b[k] , 1)
sea=round(summary(regrl)$coef[2] ,1)
seb=round(summary(regr2)$coef[1,2] ,1)
p c o u t = p r o d c l i n ( a h a t , s e a , b h a t , s e b , 0, 0.05)
o u t $ a c l . t r i e s [ k ] <- 5
}
}
}
}

out$acl.lower[k]<-as.numeric(pcout[13])
out$acl.upper[k]<-as.numeric(pcout[14])
out$acl.ciwidth[k]<-as.numeric(pcout[14]) - as.numeric(pcout [13])
out$acl.reject.pos[k]<- out$acl.lower[k]>0
out$acl.reject.neg[k]<- out$acl.upper[k]<0
o u t $ a c l . H O . r e j e c t [ k ] < - o u t $ a c l . r e j e c t . p o s [k] + o u t $ a c l . r e j e c t . n e g [ k ]

o u t $ a c l _ b c a . d i f f [ k ] <- o u t $ a c l . c i w i d t h [ k ] - o u t $ b c a . c i w i d t h [ k ]
o u t $ a c l b c a . l o w e r . d i f f [ k ] <- o u t $ a c l . l o w e r [ k ] - out$bca.lower[k]

out$acl_bca.upper.diff[k] <- out$acl.upper[k] - out$bca.upper[k]

# Kenny, Kashy & Bolger(1998) 2-step (BT)
out$bt.pa[k]=summary(regrl)$coef[4]
out$bt.pb[k]=summary(regr2)$coef[1,4]

# (Note a l l three b t . r e j e c t v a r i a b l e s were i n i t i a l i z e d to zero

(FALSE) {
if((out$bt.pa[k]<.05)*(out$bt.pb[k]<.05))
out$bt.HO.rej ect[k]=1
i f ( o u t $ a b [k] > 0) o u t $ b t . r e j e c t . p o s [ k ] = 1
i f ( o u t $ a b [ k ] < 0) o u t $ b t . r e j e c t . n e g [ k ] = 1

}

# Comparisons (ACLBT, ACLBCA, and BCABT)

if(out$acl.reject.pos[k]==1) {
out$ACLBT[k]=2
if(out$bt.reject.pos[k] =1) out$ACLBT[k]=1
if(out$bt.reject.neg[k] =1) out$ACLBT[k]=8

}

i f ( o u t $ a c l . r e j e c t . n e g [ k ] = = 1) { =1) out$ACLBT[k]=7
=1) out$ACLBT[k]=6
out$ACLBT[k]=4
if(out$bt.reject.pos[k]
if(out$bt.reject.neg[k]

}

i f ( o u t $ a c l . r e j e c t . n e g [ k ] = = 0 & o u t $ a c l . r e j e c t . p o s [k]= = 0) {
i f ( o u t $ b t . r e j e c t . p o s [ k ] = = 1 ) out$ACLBT[k]=3
i f ( o u t $ b t . r e j e c t . n e g [ k ] = = 1 ) out$ACLBT[k]=5

}

if(out$acl.reject.pos[k]==1) { out$ACLBCA[k]=1
OUt$ACLBCA[k] =2 out$ACLBCA[k]=8
if(out$bca.reject.pos[k]==1)
if(out$bca.reject.neg[k]==1)

}

if(out$acl.reject.neg[k]==1) {
OUt$ACLBCA[k]=4
if(out$bca.reject.pos[k]==1) out$ACLBCA[k]=7
if(out$bca.reject.neg[k]==1) out$ACLBCA[k]=6

}

if(out$acl.reject.neg[k]==0 & out$acl.reject.pos[k]==0) {
if(out$bca.rej ect.pos[k]= = 1) out$ACLBCA[k]=3
if(out$bca.reject.neg[k]==1) out$ACLBCA[k]=5

}

if(out$bca.reject.pos[k]==1) { out$BCABT[k]=1
Out$BCABT[k]=2 out$BCABT[k]=8
if(out$bt.reject.pos[k]==1)
if(out$bt.reject.neg[k]==1)

}

if(out$bca.reject.neg[k]==1) { =1) OUt$BCABT[k]=7
out$BCABT[k]=4 =1) Out$BCABT[k]=6
if(out$bt.reject.pos[k]
if(out$bt.reject.neg[k]

}

if(out$bca.reject.neg[k]==0 & out$acl.reject.pos[k]==0) {

if(out$bt.reject.pos[k]==1) out$BCABT[k]=3
if(out$bt.reject.neg[k]==l) out$BCABT[k]=5

}

} # (end of k loop)

nrun < - 4* (iii-1) + jjj
lia.results$run[nrun] <- nrun
lia.results$iii[nrun] <- iii
lia.results$jjj [nrun] <- jjj
lia.results$n[nrun]
lia.results$pop.rMX[nrun] <- samp[j j j]
lia.results$pop.rYM[nrun] <- as.vector(sigma [2])
lia.results$pop.rYX[nrun] <- as.vector(sigma [6])
<- as.vector(sigma [3])

lia.results$bca.pet.rej.pos[nrun] <- sum(out$bca.reject.pos)/
lia.results$bca.pet.rej.neg[nrun] length(out$bca.reject.pos)
lia.results$bca.pet.rej [nrun]
lia.results$acl.pet.rej.pos[nrun] <- sum(out$bca.reject.neg)/
lia.results$acl.pet.rej.neg[nrun] length(out$bca.rej ect.neg)
lia.results$acl.pct.rej[nrun]
lia.results$bt.pet.rej.pos[nrun] <- sum(out$bca.HO.reject)/
lia.results$bt.pet.rej.neg[nrun] length(out$bca.HO.reject)
lia.results$bt.pet.rej [nrun]
<- sum(out$acl.reject.pos)/
length(out$acl.reject.pos)

<- sum(out$acl.reject.neg)/
length(out$acl.reject.neg)

<- sum(out$acl.HO.reject)/
length(out$acl.HO.reject)

<- sum(out$bt.reject.pos)/
length(out$bt.reject.pos)

<- sum(out$bt.reject.neg)/
length(out$bt.reject.neg)

<- sum(out$bt.HO.reject)/
length(out$bt.HO.reject)

lia.results$ACLBTO[nrun] <- sum(out$ACLBT == 0)
lia.results$ACLBTl[nrun]
lia.results$ACLBT2[nrun] <- sum(out$ACLBT == 1)
lia.results$ACLBT3[nrun]
lia.results$ACLBT4[nrun] <- sum(out$ACLBT == 2)
lia.results$ACLBT5[nrun]
lia.results$ACLBT6[nrun] <- sum(out$ACLBT == 3)
lia.results$ACLBT7[nrun]
lia.results$ACLBT8[nrun] <- sum(out$ACLBT == 4)
lia.results$ACLBCAO[nrun] <- sum(out$ACLBT == 5)
lia.results$ACLBCAl[nrun] <- sum(out$ACLBT == 6)
lia.results$ACLBCA2[nrun] <- sum(out$ACLBT == 7)
<- sum(out$ACLBT == 8)
<- sum(out$ACLBCA == 0)
<- sum(out$ACLBCA == 1)
<- sum(out$ACLBCA == 2)

lia.results$ACLBCA3[nrun] <- sum(out $ACLBCA = = 3)
lia.results$ACLBCA4[nrun] <- sum(out$ACLBCA = = 4)
lia.results$ACLBCA5[nrun] <- sum(out$ACLBCA = = 5)
lia.results$ACLBCA6[nrun] <- sum(out $ACLBCA = = 6)
lia.results$ACLBCA7[nrun] <- sum(out $ACLBCA = = 7)
lia.results$ACLBCA8[nrun] <- sum(out $ACLBCA = = 8)
lia.results$BCABTO[nrun] <- sum(out$BCABT == 0)
lia.results$BCABTl[nrun] <- sum(out$BCABT == 1)
lia.results$BCABT2[nrun] <- sum(out$BCABT == 2)
lia.results$BCABT3[nrun] <- sum(out$BCABT == 3)
lia.results$BCABT4[nrun] <- sum(out$BCABT == 4)
lia.results$BCABT5[nrun] <- sum(out$BCABT == 5)
lia.results$BCABT6[nrun] < - sum(out$BCABT == 6)
lia.results$BCABT7[nrun] <- sum(out$BCABT == 7)
lia.results$BCABT8[nrun] <- sum(out$BCABT == 8)

lia.descrs$run[nrun] <- nrun
lia.descrs$iii[nrun]
lia.descrs$jjj [nrun] <- iii
lia.descrs$n[nrun] <- jjj
lia.descrs$nreps[nrun]
lia.descrs$nboot[nrun] <- samp[j j j]
lia.descrs$pop.rMX[nrun]
lia.descrs$pop.rYM[nrun] < - nreps
lia.descrs$pop.rYX[nrun]
lia.descrs$a.min[nrun] <- nboot
lia.descrs$a.lq[nrun]
lia.descrs$a.2q[nrun] <- as.vector(sigma[2])
lia.descrs$a.3q[nrun]
lia.descrs$a.max[nrun] <- as.vector(sigma[6])
lia.descrs$a.mean[nrun]
lia.descrs$rYM.min[nrun] < - as.vector(sigma [3])
lia.descrs$rYM.lq[nrun]
lia.descrs$rYM.2q[nrun] <- summary(out$a)[1]
lia.descrs$rYM.3q[nrun]
lia.descrs$rYM.max[nrun] <- summary(out$a)[2]
lia.descrs$rYM.mean[nrun]
lia.descrs$c.min[nrun] <- summary(out$a)[3]
lia.descrs$c.lq[nrun]
lia.descrs$c.2q[nrun] <- summary(out$a)[5]
lia.descrs$c.3q[nrun]
lia.descrs$c.max[nrun] <- summary(out$a)[6]
lia.descrs$c.mean[nrun]
lia.descrs$ab.min[nrun] <- summary(out$a)[4]
lia.descrs$ab.lq[nrun]
lia.descrs$ab.2q[nrun] <- summary(out$b + out$a*out$c2)[1]
lia.descrs$ab.3q[nrun]
lia.descrs$ab.max[nrun] <- summary(out$b + out$a*out$c2)[2]
lia.descrs$ab.mean[nrun]
<- summary(out$b + out$a*out$c2)[3]

< - summary(out$b + out$a*out$c2)[5]

<- summary(out$b + out$a*out$c2)[6]

<- summary(out$b + out$a*out$c2)[4]
<- summary(out$c)[1]
<- summary(out$c)[2]
<- summary(out$c)[3]
<- summary(out$c)[5]
<- summary(out$c)[6]
<- summary(out$c)[4]
<- summary(out$ab)[1]
<- summary(out$ab)[2]
<- summary(out$ab)[3]
<- summary(out$ab)[5]
<- summary(out$ab)[6]
<- summary(out$ab)[4]

acl.ciwidth <- out$acl.upper - out$acl.lower
•deleted

bca.ciwidth <- out$bca.upper - out$bca.lower
•deleted

lia.descrs$acl.ciwidth.mm[nrun] <- summary(out$acl.ciwidth, na.rm =
T) [1] <- summary(out$acl.ciwidth, na.rm =
<- summary(out$acl.ciwidth, na.rm =
lia.descrs$acl.ciwidth.lq[nrun] <- summary(out$acl.ciwidth, na.rm =
T) [2] <- summary(out$acl.ciwidth, na.rm =
<- summary(out$acl.ciwidth, na.rm =
lia.descrs$acl.ciwidth.2q[nrun]
T) [3]

lia.descrs$acl.ciwidth.3q[nrun]
T) [5]

lia.descrs$acl.ciwidth.max[nrun]
T) [6]

lia.descrs$acl.ciwidth.mean[nrun]
T) [4]

lia.descrs$bca.ciwidth.min[nrun] <- summary(out$bca.ciwidth, na.rm =
T) [1]

lia.descrs$bca.ciwidth.lq[nrun] <- summary(out$bca.ciwidth, na.rm =
T) [2]

lia.descrs$bca.ciwidth.2q[nrun] <- summary(out$bca.ciwidth, na.rm =
T) [3]

lia.descrs$bca.ciwidth.3q[nrun] <- summary(out$bca.ciwidth, na.rm =
T) [5]

lia.descrs$bca.ciwidth.max[nrun] <- summary(out$bca.ciwidth, na.rm =
T) [6]

lia.descrs$bca.ciwidth.mean[nrun]<- summary(out$bca.ciwidth, na.rm =
T) [4]

# acl_bca.diff is the difference between the two ciwidths (ACL - BCA)
lia.descrs$acl_bca.diff.min[nrun] <- summary(out$acl_bca.diff, na.rm =

T) [1]
lia.descrs$acl_bca.diff.lq[nrun] <- summary(out$acl_bca.diff, na.rm =

T) [2]
lia.descrs$acl_bca.diff.2q[nrun] <- summary(out$acl_bca.diff, na.rm =

T) [3]
lia.descrs$acl_bca.diff.3q[nrun] <- summary(out$acl_bca.diff, na.rm =

T) [5]
lia.descrs$acl_bca.diff.max[nrun] <- summary(out$acl_bca.diff, na.rm =

T) [6]
lia.descrs$acl_bca.diff.mean[nrun]<- summary(out$acl_bca.diff, na.rm =

T) [4]
lia.descrs$acl_bca.diff.ItO[nrun]<- sum(out$acl_bca.diff <

0)/length(out$acl_bca.diff)

# lower.diff is the difference between the two CI lower limits (ACL - BCA)
lia.descrs$lower.diff.min[nrun] <- summary(out$lower.diff, na.rm = T)[1]
lia.descrs$lower.diff.lq[nrun] <- summary(out$lower.diff, na.rm = T)[2]
lia.descrs$lower.diff.2q[nrun] <- summary(out$lower.diff, na.rm = T)[3]
lia.descrs$lower.diff.3q[nrun] <- summary(out$lower.diff, na.rm = T)[5]
lia.descrs$lower.diff.max[nrun] <- summary(out$lower.diff, na.rm = T)[6]
lia.descrs$lower.diff.mean[nrun]<- summary(out$lower.diff, na.rm = T)[4]
lia.descrs$lower.diff.ItO[nrun]<- sum(out$lower.diff <

0)/length(out$lower.diff)

# upper.diff is the difference between the two CI upper limits (ACL - BCA)
lia.descrs$upper.diff.min[nrun] <- summary(out$upper.diff, na.rm = T)[1]

146

lia.descrs$upper.diff.lq [nrun] <- summary(out$upper.diff, na,. rm = T) [2]
lia.descrs$upper.diff.2q[nrun] <- summary(out$upper.diff, na,. rm = T) [3]
lia.descrs$upper.diff.3q[nrun] <• summary(out$upper.diff, na.. rm = T) [5]
lia.descrs$upper.diff.max[nrun] < - summary(out$upper.diff, na..rm = T) [6]
lia.descrs$upper.diff.mean[nrun]<- summary(out$upper.diff, na.. rm = T) [4]
lia.descrs$upper.diff.ltO[nrun]<- sum(out$upper.diff <
0)/length(out$upper.diff)

# acl.tries = 1 means ACL converged with 5 decimal places.

# acl.tries > 1 means further rounding (fewer dec places) was needed.

lia.descrs$acl.triesl[nrun] <- sum(out$acl.tries==l)

lia.descrs$acl.tries2[nrun] <- sum(out$acl.tries==2)

lia.descrs$acl.tries3[nrun] <- sum(out$acl.tries==3)
lia.descrs$acl.tries4[nrun] <- sum(out$acl.tries==4)
lia.descrs$acl.tries5[nrun] <- sum(out$acl.tries==5)

} # end of jjj loop (next sample size)

} # end of iii loop (next row of r.s)

res <- lia.results[nrun,]
des <- lia.descrs[nrun,]
dump("res", file="res.R")
dump("des", file="des.R")

147

Table A. 1
Summary of Simulation Conditions: No Indirect Effect Exists

Condition n a b ab
0
1 50 0 0 0
2 100 0 0 0
3 200 0 0 0
4 500 0 0

5 50 0 0.14 0
6 100 0 0.14 0
7 200 0 0.14 0
8 500 0 0.14 0

9 50 0 0.39 0
10 100 0 0.39 0
11 200 0 0.39 0
12 500 0 0.39 0

13 50 0 0.59 0
14 100 0 0.59 0
15 200 0 0.59 0
16 500 0 0.59 0

17 50 0.14 0 0
0
18 100 0.14 0 0
0
19 200 0.14 0
0
20 500 0.14 0 0
0
33 50 0.39 0 0

34 100 0.39 0 0
0
35 200 0.39 0 0
0
36 500 0.39 0

49 50 0.59 0

50 100 0.59 0

51 200 0.59 0

52 500 0.59 0

Note, a = population path coefficient for effect of X on M; b = population path coefficient
for effect of M on Y (controlling for X); ab = product (indirect effect). Direct effects of X on
Y (path c) are zero for all conditions.

Table A.2

Summary of Simulation Conditions: An Indirect Effect Exists

Condition n a b ab

21 50 0.14 0.14 0.02

22 100 0.14 0.14 0.02

23 200 0.14 0.14 0.02

24 500 0.14 0.14 0.02

25 50 0.14 0.39 0.05

26 100 0.14 0.39 0.05

27 200 0.14 0.39 0.05

28 500 0.14 0.39 0.05

29 50 0.14 0.59 0.08
30 100 0.14 0.59 0.08
31 200 0.14 0.59 0.08
32 500 0.14 0.59 0.08

37 50 0.39 0.14 0.05

38 100 0.39 0.14 0.05

39 200 0.39 0.14 0.05

40 500 0.39 0.14 0.05

41 50 0.39 0.39 0.15
42 100 0.39 0.39 0.15
43 200 0.39 0.39 0.15
44 500 0.39 0.39 0.15

45 50 0.39 0.59 0.23

46 100 0.39 0.59 0.23

47 200 0.39 0.59 0.23

48 500 0.39 0.59 0.23

53 50 0.59 0.14 0.08

54 100 0.59 0.14 0.08

55 200 0.59 0.14 0.08

56 500 0.59 0.14 0.08

57 50 0.59 0.39 0.23

58 100 0.59 0.39 0.23

59 200 0.59 0.39 0.23

60 500 0.59 0.39 0.23

61 50 0.59 0.59 0.35
62 100 0.59 0.59 0.35
63 200 0.59 0.59 0.35

64 500 0.59 0.59 0.35

149

Note, a = population path coefficient for effect of X on M; b — population path coefficient
for effect of M on Y (controlling for X); ab = product (indirect effect). Direct effects of X on
Y (path c) are zero for all conditions.

150

Table A.3

Optimal a and bfor the Indirect Effect (ab)

ab optimal a optimal b
0.02 0.14 0.14
0.05 0.22 0.23
0.08 0.27 0.29
0.15 0.36 0.41
0.23 0.44 0.53
0.35 0.52 0.67

Note, ab = product (indirect effect); optimal a = optimal size of path coefficient for effect of
X on M; optimal b = optimal size of path coefficient for effect of M on Y (controlling for X).

151

Table A.4

ACL-BT Comparisons: No Indirect Effect Exists (ab=0)

c na ACL- ACL- ACL- ACL- ACL- ACL- ACL- ACL- ACL-
b ab BT 0 BT 1 BT 2 BT 3 BT 4 BT 5 BT 6 BT 7 BT 8
1 50 0
2 100 0 0 0 998 0 1 0 0 0 1 0 0
3 200 0 0 0 996 2 0 0 0 0 2 0 0
4 500 0 0 0 999 1 0 0 0 0 0 0 0
0 0 997 2 0 0 0 0 1 0 0

5 50 0 0.14 0 993 2 0 0 2 0 3 0 0
6 100 0 0.14 0 983 9 1 1 1 0 5 0 0
7 200 0 0.14 0 975 11 2 0 0 0 12 0 0
8 500 0 0.14 0 950 22 6 0 2 1 19 0 0

9 50 0 0.39 0 945 21 6 0 9 1 18 0 0
10 100 0 0.39 0 947 22 2 0 4 0 25 0 0
11 200 0 0.39 0 944 26 1 0 2 0 27 0 0
12 500 0 0.39 0 964 12 1 0 3 0 20 0 0

13 50 0 0.59 0 938 22 5 0 8 0 27 0 0
14 100 0 0.59 0 932 33 1 0 1 0 33 0 0
15 200 0 0.59 0 942 30 2 0 0 0 26 0 0
16 500 0 0.59 0 942 32 2 0 0 0 24 0 0

17 50 0.14 0 0 993 1 0 0 1 0 5 0 0
18 100 0.14 0 0 980 7 1 1 0 0 11 0 0
19 200 0.14 0 0 963 16 4 0 0 0 17 0 0
20 500 0.14 0 0 951 15 4 0 3 1 26 0 0

33 50 0.39 0 0 959 15 4 0 4 0 18 0 0
34 100 0.39 0 0 948 19 5 0 3 0 25 0 0
35 200 0.39 0 0 938 26 2 0 1 0 33 0 0
36 500 0.39 0 0 953 21 2 0 0 0 24 0 0

49 50 0.59 0 0 917 42 7 0 6 0 28 0 0
50 100 0.59 0 0 933 32 2 0 4 0 29 0 0
51 200 0.59 0 0 945 28 1 0 0 0 26 0 0
52 500 0.59 0 0 972 11 0 0 0 0 17 0 0

Note. C = condition; a - population path coefficient for effect of X on M; b = population
path coefficient for effect of M on Y (controlling for X); ab = product (indirect effect); ACL
= asymmetric confidence limits method; BT = basic test of mediation.

152

Table A.5
BCa -BT Comparisons: No Indirect Effect Exists (ab=0)

BCa- BCa- BCa- BCa- BCa- BCa- BCa- BCa- BCa-

c n a b ab BTO BT1 BT2 BT3 BT4 B T 5 BT6 B T 7 BT8

1 50 0 0 0 990 0 5 0 4 0 1 0 0
2 100 0 0 0 993 2 2 0 1 0 2 0 0
3 200 0 0 0 993 1 4 0 2 0 0 0 0
4 500 0 0 0 994 2 1 0 2 0 1 0 0

5 50 0 0.14 0 981 2 5 0 9 0 3 0 0
6 100 0 0.14 0 975 9 6 1 4 2 3 0 0
7 200 0 0.14 0 956 11 8 0 13 2 10 0 0
8 500 0 0.14 0 931 21 17 0 11 0 20 0 0

9 50 0 0.39 0 913 20 22 0 26 0 19 0 0
10 100 0 0.39 0 922 21 15 0 17 0 25 0 0
11 200 0 0.39 0 936 23 8 0 6 0 27 0 0
12 500 0 0.39 0 959 10 5 0 6 2 18 0 0

13 50 0 0.59 0 917 22 18 0 16 6 21 0 0
14 100 0 0.59 0 916 30 9 0 12 2 31 0 0
15 200 0 0.59 0 933 28 5 0 8 3 23 0 0
16 500 0 0.59 0 934 28 6 0 8 0 24 0 0

17 50 0.14 0 0 982 1 10 0 2 0 5 0 0
18 100 0.14 0 0 965 7 8 1 8 1 10 0 0
19 200 0.14 0 0 948 16 10 0 9 1 16 0 0
20 500 0.14 0 0 933 15 15 0 10 1 26 0 0

33 50 0.39 0 0 929 14 17 0 22 2 16 0 0
34 100 0.39 0 0 929 18 18 0 10 1 24 0 0
35 200 0.39 0 0 924 23 7 0 13 2 31 0 0
36 500 0.39 0 0 946 19 5 0 6 3 21 0 0

49 50 0.59 0 0 898 41 15 0 18 3 25 0 0
50 100 0.59 0 0 927 29 8 0 7 2 27 0 0
51 200 0.59 0 0 934 24 9 0 7 1 25 0 0
52 500 0.59 0 0 963 8 3 0 9 3 14 0 0

Note. C = condition; a = population path coefficient for effect of X on M; b = population
path coefficient for effect of M on Y (controlling for X); ab = product (indirect effect); BCa =
bias corrected and accelerated bootstrap; BT = basic test of mediation.

153

Table A.6

ACL- BCa Comparisons: No Indirect Effect Exists (ab=0)

ACL- ACL- ACL- ACL- ACL- ACL- ACL- ACL- ACL-
BCa BCa BCa BCa BCa BCa BCa BCa BCa

c n a b ab 0 1 2 3 4 5 6 7 8

1 50 0 0 0 990 1 0 4 0 4 1 0 0
2 100 0 0 0 993 2 0 2 0 1 2 0 0
3 200 0 0 0 993 1 0 4 0 2 0 0 0
4 500 0 0 0 994 2 0 1 0 2 1 0 0

5 50 0 0.14 0 981 2 0 5 0 75 0 0
6 100 0 0.14 0 976 10 0 5 2 34 0 0
7 200 0 0.14 0 955 12 1 7 2 13 10 0 0
8 500 0 0.14 0 930 27 1 11 0 10 21 0 0

9 50 0 0.39 0 908 26 1 16 4 22 23 0 0
10 100 0 0.39 0 919 22 2 14 1 14 28 0 0
11 200 0 0.39 0 932 24 3 7 1 5 28 0 0
12 500 0 0.39 0 956 11 2 4 3 4 20 0 0

13 50 0 0.59 0 914 25 2 15 7 9 28 0 0
14 100 0 0.59 0 912 30 4 9 2 11 32 0 0
15 200 0 0.59 0 931 30 2 3 3 8 23 0 0
16 500 0 0.59 0 928 28 6 6 0 8 24 0 0

17 50 0.14 0 0 982 1 0 10 0 160 0
8 10 0 0
18 100 0.14 0 0 965 8 0 8 1 9 16 0 0
7 29 0 0
19 200 0.14 0 0 947 19 1 7 1

20 500 0.14 0 0 933 18 1 12 0

33 50 0.39 0 0 925 16 3 15 3 19 19 0 0
34 100 0.39 0 0 926 22 2 14 2 8 26 0 0
35 200 0.39 0 0 921 25 3 5 2 12 32 0 0
36 500 0.39 0 0 942 19 4 5 3 6 21 0 0

49 50 0.59 0 0 893 47 2 9 6 15 28 0 0
50 100 0.59 0 0 922 29 5 8 2 3 31 0 0
51 200 0.59 0 0 930 25 4 8 1 7 25 0 0
52 500 0.59 0 0 960 8 3 3 3 9 14 0 0

Note. C = condition; a = population path coefficient for effect of X on M; b = population
path coefficient for effect of M on Y (controlling for X); ab = product (indirect effect); ACL
= asymmetric confidence limits method; BCa = bias corrected and accelerated bootstrap.

154

Table A.7

ACL-BT Comparisons: An Indirect Effect Ex •ts (ab>0) ACL- ACL- ACL- ACL- ACL-
BT4 BT 5 BT 6 BT 7 BT 8
ACL- ACL- ACL- ACL-
C n a b ab BT 0 BT1 BT2 BT3 0 0 0 0 0
0 0 0 0 0
21 50 0.14 0.14 0.02 972 20 80 0 0 0 0 0
22 100 0.14 0.14 0.02 899 80 19 2 0 0 0 0 0
23 200 0.14 0.14 0.02 707 272 19 2
24 500 0.14 0.14 0.02 215 765 18 2

25 50 0.14 0.39 0.05 849 122 26 0 0 0 3 0 0
26 100 0.14 0.39 0.05 697 276 23 1 1 0 2 0 0
27 200 0.14 0.39 0.05 462 520 18 0 0 0 0 0 0
28 500 0.14 0.39 0.05 93 901 6 0 0 0 0 0 0

29 50 0.14 0.59 0.08 802 180 16 0 0 0 2 0 0
30 100 0.14 0.59 0.08 672 313 13 0 0 0 2 0 0
31 200 0.14 0.59 0.08 485 512 3 0 0 0 0 0 0
32 500 0.14 0.59 0.08 102 896 2 0 0 0 0 0 0

37 50 0.39 0.14 0.05 859 116 22 1 2 0 0 0 0
38 100 0.39 0.14 0.05 732 239 26 1 1 0 1 0 0
39 200 0.39 0.14 0.05 528 458 14 0 0 0 0 0 0
40 500 0.39 0.14 0.05 179 818 3 0 0 0 0 0 0

41 50 0.39 0.39 0.15 349 617 33 1 0 0 0 0 0
42 100 0.39 0.39 0.15 40 952 8 0 0 0 0 0 0
43 200 0.39 0.39 0.15 1 999 0 0 0 0 0 0 0
44 500 0.39 0.39 0.15 0 1000 0 0 0 0 0 0 0

45 50 0.39 0.59 0.23 182 799 19 0 0 0 0 0 0
46 100 0.39 0.59 0.23 22 978 0 0 0 0 0 0 0
47 200 0.39 0.59 0.23 0 1000 0 0 0 0 0 0 0
48 500 0.39 0.59 0.23 0 1000 0 0 0 0 0 0 0

53 50 0.59 0.14 0.08 862 117 17 0 3 0 1 0 0
54 100 0.59 0.14 0.08 807 179 12 0 1 0 1 0 0
55 200 0.59 0.14 0.08 646 342 12 0 0 0 0 0 0
56 500 0.59 0.14 0.08 282 718 0 0 0 0 0 0 0

57 50 0.59 0.39 0.23 326 651 23 0 0 0 0 0 0
58 100 0.59 0.39 0.23 74 920 6 0 0 0 0 0 0
59 200 0.59 0.39 0.23 4 996 0 0 0 0 0 0 0
60 500 0.59 0.39 0.23 0 1000 0 0 0 0 0 0 0

61 50 0.59 0.59 0.35 30 965 5 0 0 0 0 0 0
62 100 0.59 0.59 0.35 0 1000 0 0 0 0 0 0 0
63 200 0.59 0.59 0.35 0 1000 0 0 0 0 0 0 0
64 500 0.59 0.59 0.35 0 1 0 0 0 0 0 0 0 0 0 0

155

Note. C = condition; a = population path coefficient for effect of X on M; b = population
path coefficient for effect of M on Y (controlling for X); ab = product (indirect effect); ACL
= asymmetric confidence limits method; BT = basic test of mediation.

156

Table A. 8

BCa -BT Comparisons: An Indirect Effect Exists (ab>0) BCa- BCa- BCa- BCa- BCa-
BCa- BCa- BCa- BCa- BT4 BT5 BT6 BT7 BT8

c n a b ab B T O B T 1 B T 2 B T 3 0 0 0 0 0
0
21 50 0.14 0.14 0.02 955 19 26 0 0 0 0 0 0
0 0
22 100 0.14 0.14 0.02 890 78 30 2 0 0 0 0
23 200 0.14 0.14 0.02 661 267 70 2 0 0 0
24 500 0.14 0.14 0.02 178 765 55 2

25 50 0.14 0.39 0.05 818 113 66 0 0 1 2 0 0
26 100 0.14 0.39 0.05 665 265 66 1 1 0 2 0 0
27 200 0.14 0.39 0.05 441 512 47 0 0 0 0 0 0
28 500 0.14 0.39 0.05 93 895 12 0 0 0 0 0 0

29 50 0.14 0.59 0.08 770 172 55 0 1 1 1 0 0
30 100 0.14 0.59 0.08 652 300 46 0 0 0 2 0 0
31 200 0.14 0.59 0.08 474 491 35 0 0 0 0 0 0
32 500 0.14 0.59 0.08 107 884 9 0 0 0 0 0 0

37 50 0.39 0.14 0.05 827 110 59 1 3 0 0 0 0
38 100 0.39 0.14 0.05 706 230 61 1 1 0 1 0 0
39 200 0.39 0.14 0.05 504 443 53 0 0 0 0 0 0
40 500 0.39 0.14 0.05 180 808 12 0 0 0 0 0 0

41 50 0.39 0.39 0.15 311 593 95 1 0 0 0 0 0
42 100 0.39 0.39 0.15 40 950 10 0 0 0 0 0 0
43 200 0.39 0.39 0.15 1 999 0 0 0 0 0 0 0
44 500 0.39 0.39 0.15 0 1000 0 0 0 0 0 0 0

45 50 0.39 0.59 0.23 180 779 41 0 0 0 0 0 0
46 100 0.39 0.59 0.23 24 972 4 0 0 0 0 0 0
47 200 0.39 0.59 0.23 0 1000 0 0 0 0 0 0 0
48 500 0.39 0.59 0.23 0 1000 0 0 0 0 0 0 0

53 50 0.59 0.14 0.08 844 104 48 0 3 0 1 0 0
54 100 0.59 0.14 0.08 795 165 38 0 1 0 1 0 0
55 200 0.59 0.14 0.08 644 322 34 0 0 0 0 0 0
56 500 0.59 0.14 0.08 287 699 14 0 0 0 0 0 0

57 50 0.59 0.39 0.23 316 629 55 0 0 0 0 0 0
58 100 0.59 0.39 0.23 80 909 11 0 0 0 0 0 0
59 200 0.59 0.39 0.23 5 995 0 0 0 0 0 0 0
60 500 0.59 0.39 0.23 0 1000 0 0 0 0 0 0 0

61 50 0.59 0.59 0.35 41 955 4 0 0 0 0 0 0
62 100 0.59 0.59 0.35 0 1000 0 0 0 0 0 0 0
63 200 0.59 0.59 0.35 0 1000 0 0 0 0 0 0 0
64 500 0.59 0.59 0.35 0 1000 0 0 0 0 0 0 0

157

Note. C = condition; a = population path coefficient for effect of X on M; b = population
path coefficient for effect of M on Y (controlling for X); ab = product (indirect effect); BCa =
bias corrected and accelerated bootstrap; BT = basic test of mediation.

158

Table A.9

ACL- BCa Comparisons: An Indirect Effect Exists (ab>0)

ACL- ACL- ACL- ACL- ACL- ACL- ACL- ACL- ACL-
BCa4 BCa5 BCa6 BCa7 BCa8
c n a b ab B C a 0 BCa1 B C a 2 B C a 3
0 0 0 0 0
21 50 0.14 0.14 0.02 951 24 4 21 0 0 0 0 0
0 0 0 0 0
22 100 0.14 0.14 0.02 879 88 11 22 0 0 0 0 0

23 200 0.14 0.14 0.02 653 283 8 56

24 500 0.14 0.14 0.02 176 781 2 41

25 50 0.14 0.39 0.05 803 133 15 46 1 0 20 0

26 100 0.14 0.39 0.05 646 280 19 52 0 0 3 0 0

27 200 0.14 0.39 0.05 425 522 16 37 0 0 00 0

28 500 0.14 0.39 0.05 83 897 10 10 0 0 0 0 0

29 50 0.14 0.59 0.08 755 181 15 46 1 1 10 0

30 100 0.14 0.59 0.08 634 308 18 38 0 0 20 0

31 200 0.14 0.59 0.08 451 492 23 34 0 0 00 0

32 500 0.14 0.59 0.08 94 885 13 8 0 0 00 0

37 50 0.39 0.14 0.05 816 127 11 43 0 1 20 0

38 100 0.39 0.14 0.05 687 246 19 46 0 0 20 0

39 200 0.39 0.14 0.05 485 453 19 43 0 0 00 0

40 500 0.39 0.14 0.05 169 810 11 10 0 0 0 0 0

41 50 0.39 0.39 0.15 278 617 33 72 0 0 00 0

42 100 0.39 0.39 0.15 36 956 4 4 0 0 0 0 0

43 200 0.39 0.39 0.15 1 999 0 0 0 0 0 0 0

44 500 0.39 0.39 0.15 0 1000 0 0 0 0 0 0 0

45 50 0.39 0.59 0.23 155 793 25 27 0 0 00 0

46 100 0.39 0.59 0.23 18 972 6 4 0 0 00 0

47 200 0.39 0.59 0.23 0 1000 0 0 0 0 0 0 0

48 500 0.39 0.59 0.23 0 1000 0 0 0 0 0 0 0

53 50 0.59 0.14 0.08 820 112 22 40 2 2 20 0

54 100 0.59 0.14 0.08 773 169 22 34 0 0 20 0

55 200 0.59 0.14 0.08 620 330 24 26 0 0 00 0

56 500 0.59 0.14 0.08 268 699 19 14 0 0 0 0 0

57 50 0.59 0.39 0.23 286 644 30 40 0 0 00 0

58 100 0.59 0.39 0.23 65 911 15 9 0 0 00 0

59 200 0.59 0.39 0.23 4 995 1 0 0 0 0 0 0

60 500 0.59 0.39 0.23 0 1000 0 0 0 0 0 0 0

61 50 0.59 0.59 0.35 27 956 14 3 0 0 00 0

62 100 0.59 0.59 0.35 0 1000 0 0 0 0 0 0 0

63 200 0.59 0.59 0.35 0 1000 0 0 0 0 0 0 0

64 500 0.59 0.59 0.35 0 1 0 0 0 0 0 0 0 0 0 0

159

Note. C = condition; a = population path coefficient for effect of X on M; b = population
path coefficient for effect of M on Y (controlling for X); ab = product (indirect effect); ACL
= asymmetric confidence limits method; BCa = bias corrected and accelerated bootstrap.

ACZIT Disagreement: No Indirect Effect Exists (db=0)

ACL-BT Comparisons: n = 200

a=59, b=0
a=0, b=.59
a=39, b=0
a=0, b=.39 k r

a=.14, b=0
a=0, b=.14

a=0, b=0

- : S : S ^ S C 5 B S «'yes,no" = ACL rejected

Figure A.2
ACL-BTDisagreement: No Indirect Effect Exists (db=0)

ACL-BT Comparisons: n = 500

a=59, b=0
a=0, b=.59
a=.39, b=0 b
a=0, b=.39

a=.14, b=0
a=0, b=.14

a=0, b=0

Note: "no,yes" - ACL fai.ed * f * * » g * % g % £ £ £ &

"yes,no" = ACL rejected H0 (lype i error;, <mu

162

Figure A.3
BCa -BT Disagreement: No Indirect Effect Exists (ab=0)

BCa-BT Comparisons: n = 200

a=.59, b=0

a=0, b=.59

a=0, b=.39
a=.14, b=0
a=0, b=.14

a=0, b=0

^ ::^:::S^^^S^^S;

163

Figure A.4
BCa -BT Disagreement: No Indirect Effect Exists (db=0)

BCa-BT Comparisons: n = 500

a=.59, b=0
a=0, b=.59
a=.39, b=0
a=0, b=.39

a=.14, b=0
a=0, b=.14

a=0, b=0

- BC failed to reject H0, and BT rejected H0 (Type I error);
Note: "no,yes - B U ta lea xo rej u,
tQ t H Q

yes,no = BCa rejected H0 (Type 1 error;, <mu

Figure A. 5
BCa-ACL Disagreement: No Indirect Effect Exists (ab=0)

BCa-ACL Comparisons: N = 200

a=.59, b=0

a=0, b=.59

a=.39, b=0

a=0, b=.39

a=.14, b=0

a=0, b=.14

a=0, b=0

10 20 25

Note: "no,yes" = BCa failed to reject Ho, and ACL rejected Ho (Type I error);
"yes,no" = BCa rejected Ho (Type I error), and ACL failed to reject Ho.

Figure A.6
BCa-ACL Disagreement: No Indirect Effect Exists (ab=0)

BCa-ACL Comparisons: n = 500
a=59, b=0
a=0, b=59
a=.39, b=0
a=0, b=.39
a=.14, b=0
a=0, b=.14

a=0, b=0

Note: "no,yes" = BCa failed to reject Ho, and ACL rejected Ho (Type I error);
"yes,no" = BCa rejected Ho (Type I error), and ACL failed to reject Ho.

Figure A.7
ACL-BT Disagreement: An Indirect Effect Exists (ab>0)

ACL-BT Comparisons: n = 200

a=.59, b=.59

a=59, b=.39

a=.39, b=.59

a=. 39, b=39

a=.59, b=.14
•:-:-:-\\"::-:x-.\":::-:-:::::-::-::::::::::v:-:x

a=14, b=.59 •W:-i\

•:•:•:•:•:•!

b=.39, a=.14

g&m&M8i®^^

|

a=14, b=.39

XVXV:V::«VXV:-:V:VKV:V:V:M^^^^

wmm 1 1 JZ 1 1 1 I

a=.14,b=.14 l_J
H*:*:™:™:™^^^^^^^

11

10 12 14 16 18 20

Note: "no,yes" = ACL failed to reject Ho (Type II error), and BT rejected Ho;
"yes,no" = ACL rejected Ho, and BT failed to reject Ho (Type II error).

Figure A. 8
ACL-BTDisagreement: An Indirect Effect Exists (ab>0)

ACL-BT Comparisons: n = 500

a=.59, b=59

a=59, b=.39

a=.39, b=.59

a=39, b=.39

a=.59, b=.14

a=.14, b=59

b=.39, a=.14 :::::-:i

•;•;•;•;•:•!

a=.14,b=.39 1111111

wmma=.14,b=.14 10 12 14 16 18 20

1

Note: "no,yes" = ACL failed to reject Ho (Type II error), and BT rejected Ho;
"yes,no" = ACL rejected Ho, and BT failed to reject Ho (Type II error).

Figure A.9
BCa -BTDisagreement: An Indirect Effect Exists (ab>0)

BCa-BT Comparisons: n = 200

a=59, b=59
a=59, b=.39
a=.39, b=.59
a=.39, b=.39
a=59, b=14 .:.:.:.:.:.:•:•:•:•:•:.:•:•:.::.:.;.;.:.:.:.:.;:;.;.;.:.:.:j.;.:.:.:.;.:.:.;.:.:.:.;.;.:.j.:.;.;.;.;.i

a=. 14, b = 5 9 ^.:.:.:.:.v:^^^^^^^:L:•:•:•:•:•:•:•^:•:•^:•:•U•:•:•:•:•^:•:•:•:•:•::l:•:•:•:•:•^:•i

b=39, a=14 W:.tt:.v.:.;.^J^;.:.w.:.^

a=.14, b=39 ,y,:,;.:,:.;,:.:,:.:.:,:,.J:,v,,,,,,:.:.:,,;,.J,;,,:,;.:.;,;^

a=.14, b=.14 ffl.....,.,...,.......,.,. ...,.,...,.....,..•.•••••.•.•.'.•.•.•.•••••.•••.•••••.•••.^i.^^^^^^^^v•v•^•L^v/.v.^•.•.•.•••.•. ••,•••••.•••.•••••••,•.•.•••••'••••••••.•.•.•••••••••••••••••

/—^

0 10 20 30 40 50 60 70 80

Note: "no,yes" = BCa failed to reject Ho (Type II error), and BT rejected Ho;
"yes,no" = BCa rejected Ho, and BT failed to reject Ho (Type II error).

Figure A. 10
BCa -BT Disagreement: An Indirect Effect Exists (ab>0)

BCa-BT Comparisons: n = 500

a=.59, b=59

a=59, b=.39

a=.39, b=.59

a=39, b=.39

a=.59, b=.14

•:-:-:-:-:-:-:-::-::-::::-:::-:-::::-:-:-:-:-:|

a=.14, b=59 mmsmm

b=.39, a=.14

<mmmm±m

a=.14,b=.39

yymmmmm

a=.14, b=14 •:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•: :-:<v-:-:-:-:-:-:-:o^-:->:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:-:->:-:-:-:-:-:-:-:-:-:-:-:-:<<-:-:-::::-:-|

• I •• I • 'T- - = i 4^-

10 20 30 40 50 60

Note: "no,yes" = BCa failed to reject Ho (Type II error), and BT rejected Ho;
"yes,no" = BCa rejected Ho, and BT failed to reject Ho (Type II error).

Figure A. 11
BCa-ACL Disagreement: An Indirect Effect Exists (ab>0)

BCa-ACL Comparisons: n = 200

a=59, b=.59
a=.59, b=.39
a=.39, b=.59
a=.39, b=.39
a=.59, b=14
a=14, b=.59
b=.39, a=14
a=.14, b=.39
a=14, b=14

Note: "no,yes" = BCa failed to reject Ho (Type II error), and ACL rejected Ho;
"yes,no" = BCa rejected Ho, and ACL failed to reject Ho (Type II error).

Figure A. 12
BCa-ACL Disagreement: An Indirect Effect Exists (ab>0)

BCa-ACL Comparisons: n = 500

a=59, b=59
a=59, b=.39
a=.39, b=.59
a=. 39, b=.39
a=.59, b=14
a=.14,b=.59
b=.39, a=14
a=.14, b=.39
a=14, b=.14

10 15 20 25 30 35 40 45

Note: "no,yes" - BCa failed to reject Ho (Type II error), and ACL rejected Ho;
"yes,no" = BCa rejected Ho, and ACL failed to reject Ho (Type II error).