Examples using the supported estimation methods
Source:vignettes/articles/estimation_methods.Rmd
estimation_methods.RmdThe currently supported estimation methods are:
- covariance-based SEM estimated with the lavaan package
- PLS-SEM estimated using cSEM
- Bayesian SEM estimated using blavaan
Lavaan
Example 1 (lavaan)
library(lavaan)
library(rmedsem)
mod.txt <- "
read ~ math
science ~ read + math
"
mod <- lavaan::sem(mod.txt, data=rmedsem::hsbdemo)
out <- rmedsem(mod, indep="math", med="read", dep="science",
standardized=T, mcreps=5000,
approach = c("bk","zlc"))
print(out)
#> Significance testing of indirect effect (standardized)
#> Model estimated with package 'lavaan'
#> Mediation effect: 'math' -> 'read' -> 'science'
#>
#> Sobel Delta Monte-Carlo
#> Indirect effect 0.2506 0.251 0.2506
#> Std. Err. 0.0456 0.046 0.0454
#> z-value 5.5006 5.446 5.5164
#> p-value 3.79e-08 5.15e-08 3.46e-08
#> CI [0.161, 0.34] [0.16, 0.341] [0.163, 0.341]
#>
#> Baron and Kenny approach to testing mediation
#> STEP 1 - 'math:read' (X -> M) with B=0.662 and p=0.000
#> STEP 2 - 'read:science' (M -> Y) with B=0.378 and p=0.000
#> STEP 3 - 'math:science' (X -> Y) with B=0.380 and p=0.000
#> As STEP 1, STEP 2 and STEP 3 as well as the Sobel's test above
#> are significant the mediation is partial.
#>
#> Zhao, Lynch & Chen's approach to testing mediation
#> Based on p-value estimated using Monte-Carlo
#> STEP 1 - 'math:science' (X -> Y) with B=0.380 and p=0.000
#> As the Monte-Carlo test above is significant, STEP 1 is
#> significant and their coefficients point in same direction,
#> there is complementary mediation (partial mediation).
#>
#> Effect sizes
#> RIT = (Indirect effect / Total effect)
#> (0.251/0.631) = 0.397
#> Meaning that about 40% of the effect of 'math'
#> on 'science' is mediated by 'read'
#> RID = (Indirect effect / Direct effect)
#> (0.251/0.380) = 0.659
#> That is, the mediated effect is about 0.7 times as
#> large as the direct effect of 'math' on 'science'
#> Upsilon (v) = Variance in 'science' explained indirectly by 'math' through 'read'
#> v(unadj) = 0.063, v(adj) = 0.061Example 2 (lavaan)
model02 <- "
# measurement model
ind60 =~ x1 + x2 + x3
dem60 =~ y1 + y2 + y3 + y4
dem65 =~ y5 + y6 + y7 + y8
# regressions
dem60 ~ ind60
dem65 ~ ind60 + dem60
"
mod <- sem(model02, data=lavaan::PoliticalDemocracy)
out <- rmedsem(mod, indep="ind60", med="dem60", dep="dem65",
standardized=T, mcreps=5000,
approach = c("bk","zlc"))
print(out)
#> Significance testing of indirect effect (standardized)
#> Model estimated with package 'lavaan'
#> Mediation effect: 'ind60' -> 'dem60' -> 'dem65'
#>
#> Sobel Delta Monte-Carlo
#> Indirect effect 0.4091 0.4091 0.4091
#> Std. Err. 0.0956 0.0946 0.0948
#> z-value 4.2817 4.3248 4.2916
#> p-value 1.85e-05 1.53e-05 1.77e-05
#> CI [0.222, 0.596] [0.224, 0.595] [0.226, 0.596]
#>
#> Baron and Kenny approach to testing mediation
#> STEP 1 - 'ind60:dem60' (X -> M) with B=0.448 and p=0.000
#> STEP 2 - 'dem60:dem65' (M -> Y) with B=0.913 and p=0.000
#> STEP 3 - 'ind60:dem65' (X -> Y) with B=0.146 and p=0.038
#> As STEP 1, STEP 2 and STEP 3 as well as the Sobel's test above
#> are significant the mediation is partial.
#>
#> Zhao, Lynch & Chen's approach to testing mediation
#> Based on p-value estimated using Monte-Carlo
#> STEP 1 - 'ind60:dem65' (X -> Y) with B=0.146 and p=0.038
#> As the Monte-Carlo test above is significant, STEP 1 is
#> significant and their coefficients point in same direction,
#> there is complementary mediation (partial mediation).
#>
#> Effect sizes
#> RIT = (Indirect effect / Total effect)
#> (0.409/0.555) = 0.738
#> Meaning that about 74% of the effect of 'ind60'
#> on 'dem65' is mediated by 'dem60'
#> RID = (Indirect effect / Direct effect)
#> (0.409/0.146) = 2.811
#> That is, the mediated effect is about 2.8 times as
#> large as the direct effect of 'ind60' on 'dem65'
#> Upsilon (v) = Variance in 'dem65' explained indirectly by 'ind60' through 'dem60'
#> v(unadj) = 0.167, v(adj) = 0.158Example 3 (lavaan)
model03 <- "
Attractive =~ face + sexy
Appearance =~ body + appear + attract
Muscle =~ muscle + strength + endur
Weight =~ lweight + calories + cweight
Appearance ~ Attractive + age
Muscle ~ Appearance + Attractive + age
Weight ~ Appearance + Attractive + age
"
mod <- sem(model03, data=rmedsem::workout)
rmedsem(mod, indep="Attractive", med="Appearance", dep="Muscle",
standardized=T, mcreps=5000,
approach = c("bk","zlc"))
#> Significance testing of indirect effect (standardized)
#> Model estimated with package 'lavaan'
#> Mediation effect: 'Attractive' -> 'Appearance' -> 'Muscle'
#>
#> Sobel Delta Monte-Carlo
#> Indirect effect 0.0654 0.0654 0.0654
#> Std. Err. 0.0331 0.0335 0.0339
#> z-value 1.9748 1.9544 1.9490
#> p-value 0.0483 0.0507 0.0513
#> CI [0.000491, 0.13] [-0.000187, 0.131] [0.0043, 0.137]
#>
#> Baron and Kenny approach to testing mediation
#> STEP 1 - 'Attractive:Appearance' (X -> M) with B=0.158 and p=0.033
#> STEP 2 - 'Appearance:Muscle' (M -> Y) with B=0.414 and p=0.000
#> STEP 3 - 'Attractive:Muscle' (X -> Y) with B=-0.014 and p=0.850
#> As STEP 1, STEP 2 and the Sobel's test above are significant
#> and STEP 3 is not significant the mediation is complete.
#>
#> Zhao, Lynch & Chen's approach to testing mediation
#> Based on p-value estimated using Monte-Carlo
#> STEP 1 - 'Attractive:Muscle' (X -> Y) with B=-0.014 and p=0.850
#> As the Monte-Carlo test above is not significant and STEP 1 is
#> not significant there is no effect nonmediation (no mediation).
#>
#> Effect sizes
#> WARNING: Total effect is smaller than indirect effect!
#> Effect sizes should not be interpreted.
#> RIT = (Indirect effect / Total effect)
#> Total effect 0.052 is too small to calculate RIT
#> RID = (Indirect effect / Direct effect)
#> (0.065/0.014) = 4.714
#> That is, the mediated effect is about 4.7 times as
#> large as the direct effect of 'Attractive' on 'Muscle'
#> Upsilon (v) = Variance in 'Muscle' explained indirectly by 'Attractive' through 'Appearance'
#> v(unadj) = 0.004, v(adj) = 0.003
rmedsem(mod, indep="Attractive", med="Appearance", dep="Weight",
standardized=T, mcreps=5000,
approach = c("bk","zlc"))
#> Significance testing of indirect effect (standardized)
#> Model estimated with package 'lavaan'
#> Mediation effect: 'Attractive' -> 'Appearance' -> 'Weight'
#>
#> Sobel Delta Monte-Carlo
#> Indirect effect 0.0979 0.0979 0.0979
#> Std. Err. 0.0470 0.0483 0.0484
#> z-value 2.0810 2.0267 2.0318
#> p-value 0.0374 0.0427 0.0422
#> CI [0.00569, 0.19] [0.00322, 0.193] [0.0062, 0.196]
#>
#> Baron and Kenny approach to testing mediation
#> STEP 1 - 'Attractive:Appearance' (X -> M) with B=0.158 and p=0.033
#> STEP 2 - 'Appearance:Weight' (M -> Y) with B=0.619 and p=0.000
#> STEP 3 - 'Attractive:Weight' (X -> Y) with B=-0.125 and p=0.073
#> As STEP 1, STEP 2 and the Sobel's test above are significant
#> and STEP 3 is not significant the mediation is complete.
#>
#> Zhao, Lynch & Chen's approach to testing mediation
#> Based on p-value estimated using Monte-Carlo
#> STEP 1 - 'Attractive:Weight' (X -> Y) with B=-0.125 and p=0.073
#> As the Monte-Carlo test above is significant and STEP 1 is not
#> significant there indirect-only mediation (full mediation).
#>
#> Effect sizes
#> WARNING: Total effect is smaller than indirect effect!
#> Effect sizes should not be interpreted.
#> RIT = (Indirect effect / Total effect)
#> Total effect 0.027 is too small to calculate RIT
#> RID = (Indirect effect / Direct effect)
#> (0.098/0.125) = 0.784
#> That is, the mediated effect is about 0.8 times as
#> large as the direct effect of 'Attractive' on 'Weight'
#> Upsilon (v) = Variance in 'Weight' explained indirectly by 'Attractive' through 'Appearance'
#> v(unadj) = 0.010, v(adj) = 0.007
rmedsem(mod, indep="age", med="Appearance", dep="Muscle",
standardized=T, mcreps=5000,
approach = c("bk","zlc"))
#> Significance testing of indirect effect (standardized)
#> Model estimated with package 'lavaan'
#> Mediation effect: 'age' -> 'Appearance' -> 'Muscle'
#>
#> Sobel Delta Monte-Carlo
#> Indirect effect -0.1602 -0.1602 -0.1602
#> Std. Err. 0.0397 0.0405 0.0403
#> z-value -4.0391 -3.9565 -3.9719
#> p-value 5.37e-05 7.61e-05 7.13e-05
#> CI [-0.238, -0.0825] [-0.24, -0.0808] [-0.245, -0.0873]
#>
#> Baron and Kenny approach to testing mediation
#> STEP 1 - 'age:Appearance' (X -> M) with B=-0.387 and p=0.000
#> STEP 2 - 'Appearance:Muscle' (M -> Y) with B=0.414 and p=0.000
#> STEP 3 - 'age:Muscle' (X -> Y) with B=-0.147 and p=0.065
#> As STEP 1, STEP 2 and the Sobel's test above are significant
#> and STEP 3 is not significant the mediation is complete.
#>
#> Zhao, Lynch & Chen's approach to testing mediation
#> Based on p-value estimated using Monte-Carlo
#> STEP 1 - 'age:Muscle' (X -> Y) with B=-0.147 and p=0.065
#> As the Monte-Carlo test above is significant and STEP 1 is not
#> significant there indirect-only mediation (full mediation).
#>
#> Effect sizes
#> RIT = (Indirect effect / Total effect)
#> (0.160/0.307) = 0.521
#> Meaning that about 52% of the effect of 'age'
#> on 'Muscle' is mediated by 'Appearance'
#> RID = (Indirect effect / Direct effect)
#> (0.160/0.147) = 1.089
#> That is, the mediated effect is about 1.1 times as
#> large as the direct effect of 'age' on 'Muscle'
#> Upsilon (v) = Variance in 'Muscle' explained indirectly by 'age' through 'Appearance'
#> v(unadj) = 0.026, v(adj) = 0.024
rmedsem(mod, indep="age", med="Appearance", dep="Weight",
standardized=T, mcreps=5000,
approach = c("bk","zlc"))
#> Significance testing of indirect effect (standardized)
#> Model estimated with package 'lavaan'
#> Mediation effect: 'age' -> 'Appearance' -> 'Weight'
#>
#> Sobel Delta Monte-Carlo
#> Indirect effect -0.2397 -0.2397 -0.2397
#> Std. Err. 0.0453 0.0496 0.0495
#> z-value -5.2867 -4.8356 -4.8734
#> p-value 1.25e-07 1.33e-06 1.1e-06
#> CI [-0.329, -0.151] [-0.337, -0.143] [-0.346, -0.15]
#>
#> Baron and Kenny approach to testing mediation
#> STEP 1 - 'age:Appearance' (X -> M) with B=-0.387 and p=0.000
#> STEP 2 - 'Appearance:Weight' (M -> Y) with B=0.619 and p=0.000
#> STEP 3 - 'age:Weight' (X -> Y) with B=0.341 and p=0.000
#> As STEP 1, STEP 2 and STEP 3 as well as the Sobel's test above
#> are significant the mediation is partial.
#>
#> Zhao, Lynch & Chen's approach to testing mediation
#> Based on p-value estimated using Monte-Carlo
#> STEP 1 - 'age:Weight' (X -> Y) with B=0.341 and p=0.000
#> As the Monte-Carlo test above is significant, STEP 1 is
#> significant and their coefficients point in opposite
#> direction, there is competitive mediation (partial mediation).
#>
#> Effect sizes
#> WARNING: Total effect is smaller than indirect effect!
#> Effect sizes should not be interpreted.
#> RIT = (Indirect effect / Total effect)
#> Total effect 0.101 is too small to calculate RIT
#> RID = (Indirect effect / Direct effect)
#> (0.240/0.341) = 0.704
#> That is, the mediated effect is about 0.7 times as
#> large as the direct effect of 'age' on 'Weight'
#> Upsilon (v) = Variance in 'Weight' explained indirectly by 'age' through 'Appearance'
#> v(unadj) = 0.057, v(adj) = 0.055cSEM
Example 1 (cSEM)
library(cSEM)
library(rmedsem)
mod.txt <- "
# need to use single-item measurement models for PLS-SEM
Read =~ read
Math =~ math
Science =~ science
# the actual path model
Read ~ Math
Science ~ Read + Math
"
mod <- cSEM::csem(.model=mod.txt, .data=rmedsem::hsbdemo,
.resample_method = "bootstrap", .R = 200)
rmedsem(mod, indep="Math", med="Read", dep="Science",
approach = c("bk", "zlc"))
#> Significance testing of indirect effect (standardized)
#> Model estimated with package 'cSEM'
#> Mediation effect: 'Math' -> 'Read' -> 'Science'
#>
#> Sobel Delta Bootstrap
#> Indirect effect 0.2506 0.2506 0.2506
#> Std. Err. 0.0529 0.0513 0.0513
#> z-value 4.7380 4.8833 4.8898
#> p-value 2.16e-06 1.04e-06 1.01e-06
#> CI [0.147, 0.354] [0.15, 0.351] [0.151, 0.349]
#>
#> Baron and Kenny approach to testing mediation
#> STEP 1 - 'Math:Read' (X -> M) with B=0.662 and p=0.000
#> STEP 2 - 'Read:Science' (M -> Y) with B=0.378 and p=0.000
#> STEP 3 - 'Math:Science' (X -> Y) with B=0.380 and p=0.000
#> As STEP 1, STEP 2 and STEP 3 as well as the Sobel's test above
#> are significant the mediation is partial.
#>
#> Zhao, Lynch & Chen's approach to testing mediation
#> Based on p-value estimated using Bootstrap
#> STEP 1 - 'Math:Science' (X -> Y) with B=0.380 and p=0.000
#> As the Bootstrap test above is significant, STEP 1 is
#> significant and their coefficients point in same direction,
#> there is complementary mediation (partial mediation).
#>
#> Effect sizes
#> RIT = (Indirect effect / Total effect)
#> (0.251/0.631) = 0.397
#> Meaning that about 40% of the effect of 'Math'
#> on 'Science' is mediated by 'Read'
#> RID = (Indirect effect / Direct effect)
#> (0.251/0.380) = 0.659
#> That is, the mediated effect is about 0.7 times as
#> large as the direct effect of 'Math' on 'Science'
#> Upsilon (v) = Variance in 'Science' explained indirectly by 'Math' through 'Read'
#> v(unadj) = 0.063, v(adj) = 0.060Example 2 (cSEM)
model02 <- "
# measurement model
ind60 =~ x1 + x2 + x3
dem60 =~ y1 + y2 + y3 + y4
dem65 =~ y5 + y6 + y7 + y8
# regressions
dem60 ~ ind60
dem65 ~ ind60 + dem60
"
mod <- cSEM::csem(.model=model02, .data=lavaan::PoliticalDemocracy,
.resample_method = "bootstrap", .R = 200)
rmedsem(mod, indep="ind60", med="dem60", dep="dem65",
approach = c("bk","zlc"))
#> Significance testing of indirect effect (standardized)
#> Model estimated with package 'cSEM'
#> Mediation effect: 'ind60' -> 'dem60' -> 'dem65'
#>
#> Sobel Delta Bootstrap
#> Indirect effect 0.3988 0.3988 0.3988
#> Std. Err. 0.0957 0.0897 0.0873
#> z-value 4.1648 4.4468 4.5678
#> p-value 3.12e-05 8.72e-06 4.93e-06
#> CI [0.211, 0.586] [0.223, 0.575] [0.257, 0.586]
#>
#> Baron and Kenny approach to testing mediation
#> STEP 1 - 'ind60:dem60' (X -> M) with B=0.439 and p=0.000
#> STEP 2 - 'dem60:dem65' (M -> Y) with B=0.909 and p=0.000
#> STEP 3 - 'ind60:dem65' (X -> Y) with B=0.159 and p=0.018
#> As STEP 1, STEP 2 and STEP 3 as well as the Sobel's test above
#> are significant the mediation is partial.
#>
#> Zhao, Lynch & Chen's approach to testing mediation
#> Based on p-value estimated using Bootstrap
#> STEP 1 - 'ind60:dem65' (X -> Y) with B=0.159 and p=0.018
#> As the Bootstrap test above is significant, STEP 1 is
#> significant and their coefficients point in same direction,
#> there is complementary mediation (partial mediation).
#>
#> Effect sizes
#> RIT = (Indirect effect / Total effect)
#> (0.399/0.557) = 0.715
#> Meaning that about 72% of the effect of 'ind60'
#> on 'dem65' is mediated by 'dem60'
#> RID = (Indirect effect / Direct effect)
#> (0.399/0.159) = 2.514
#> That is, the mediated effect is about 2.5 times as
#> large as the direct effect of 'ind60' on 'dem65'
#> Upsilon (v) = Variance in 'dem65' explained indirectly by 'ind60' through 'dem60'
#> v(unadj) = 0.159, v(adj) = 0.150Example 3 (cSEM)
model03 <- "
Attractive =~ face + sexy
Appearance =~ body + appear + attract
Muscle =~ muscle + strength + endur
Weight =~ lweight + calories + cweight
Age =~ age ## need single-indicator LV for cSEM
Appearance ~ Attractive + Age
Muscle ~ Appearance + Attractive + Age
Weight ~ Appearance + Attractive + Age
"
mod <- cSEM::csem(.model=model03, .data=na.omit(rmedsem::workout),
.resample_method = "bootstrap", .R = 200)
rmedsem(mod, indep="Attractive", med="Appearance", dep="Muscle",
approach = c("bk","zlc"))
#> Significance testing of indirect effect (standardized)
#> Model estimated with package 'cSEM'
#> Mediation effect: 'Attractive' -> 'Appearance' -> 'Muscle'
#>
#> Sobel Delta Bootstrap
#> Indirect effect 0.1124 0.1124 0.1124
#> Std. Err. 0.0401 0.0394 0.0412
#> z-value 2.8043 2.8523 2.7257
#> p-value 0.00504 0.00434 0.00642
#> CI [0.0338, 0.191] [0.0352, 0.19] [0.0422, -0.272]
#>
#> Baron and Kenny approach to testing mediation
#> STEP 1 - 'Attractive:Appearance' (X -> M) with B=0.236 and p=0.001
#> STEP 2 - 'Appearance:Muscle' (M -> Y) with B=0.475 and p=0.000
#> STEP 3 - 'Attractive:Muscle' (X -> Y) with B=-0.010 and p=0.903
#> As STEP 1, STEP 2 and the Sobel's test above are significant
#> and STEP 3 is not significant the mediation is complete.
#>
#> Zhao, Lynch & Chen's approach to testing mediation
#> Based on p-value estimated using Bootstrap
#> STEP 1 - 'Attractive:Muscle' (X -> Y) with B=-0.010 and p=0.903
#> As the Bootstrap test above is significant and STEP 1 is not
#> significant there indirect-only mediation (full mediation).
#>
#> Effect sizes
#> WARNING: Total effect is smaller than indirect effect!
#> Effect sizes should not be interpreted.
#> RIT = (Indirect effect / Total effect)
#> Total effect 0.102 is too small to calculate RIT
#> RID = (Indirect effect / Direct effect)
#> (0.112/0.010) = 10.768
#> That is, the mediated effect is about 10.8 times as
#> large as the direct effect of 'Attractive' on 'Muscle'
#> Upsilon (v) = Variance in 'Muscle' explained indirectly by 'Attractive' through 'Appearance'
#> v(unadj) = 0.013, v(adj) = 0.011blavaan
Example 2 (blavaan)
model02 <- "
# measurement model
ind60 =~ x1 + x2 + x3
dem60 =~ y1 + y2 + y3 + y4
dem65 =~ y5 + y6 + y7 + y8
# regressions
dem60 ~ ind60
dem65 ~ ind60 + dem60
"
mod <- bsem(model02, data=lavaan::PoliticalDemocracy, std.lv=T,
meanstructure=T, n.chains=3,
save.lvs=T, burnin=1000, sample=1000, bcontrol = list(cores = 3))
rmedsem(mod, indep="ind60", med="dem60", dep="dem65")