The goal of rmedsem is to conduct a mediation analysis based on a structural equation model (SEM), including observed and/or latent variables as well as combination of observed and latent variables. The package supports:
The rmedsem package also supports estimating moderated
mediation and mediated moderation models using the modsem package.
Currently, only continuous independent and mediator variables are supported. See this article for technical details on the estimation procedure used.
See the examples in the section below and refer to the
rmedsem() documentation. Examples covering the different
estimation methods (CB-SEM, PLS-SEM, Bayesian SEM) are detailed in this
article.
You can install the released version of rmedsem from CRAN with:
install.packages("rmedsem")The development version can be installed from GitHub with:
# install.packages("pak")
pak::pak("ihrke/rmedsem")We start with a simple example using the hsbdemo dataset
included in rmedsem. In this model, we include only
observed variables and have a simple case in which mathematical skills
math directly affect performance in science-related areas
science and where part of this association is mediated
through their ability to read.
graph LR
math --> read
read --> science
math --> scienceWe can express this model in lavaan syntax as
follows:
mod.txt <- "
read ~ math
science ~ read + math
"Once specified, we can use lavaan to fit the model using
CB-SEM:
library(lavaan)
mod <- lavaan::sem(mod.txt, data=rmedsem::hsbdemo)We can inspect the estimated coefficients using lavaans
methods (summary() etc). To run the mediation analysis, we
use rmedsem() and specify the independent variable
(indep="math"), the mediator (med="read") and
the dependent variable (dep="science"). The output is
captured in an output object out which implements a
printing function (print.rmedsem()) to show a summary of
the results:
library(rmedsem)
out <- rmedsem(mod, indep="math", med="read", dep="science")
print(out)
#> Significance testing of indirect effect (standardized)
#> Model estimated with package 'lavaan'
#> Mediation effect: 'math' -> 'read' -> 'science'
#>
#> Sobel Delta Monte-Carlo
#> Indirect effect 0.251 0.251 0.251
#> Std. Err. 0.046 0.046 0.047
#> z-value 5.501 5.446 5.374
#> p-value 3.79e-08 5.15e-08 7.71e-08
#> CI [0.161, 0.340] [0.160, 0.341] [0.160, 0.343]
#>
#> Baron and Kenny approach to testing mediation
#> STEP 1 - 'math' -> 'read' (X -> M) with B=0.662 and p<0.001
#> STEP 2 - 'read' -> 'science' (M -> Y) with B=0.378 and p<0.001
#> STEP 3 - 'math' -> 'science' (X -> Y) with B=0.380 and p<0.001
#> 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<0.001
#> 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 Y explained indirectly by X through M
#> v(unadj) = 0.063, v(adj) = 0.061The result reports the estimated indirect effect using the Sobel, Delta and Monte-Carlo methods (see technical details) and also explains the Baron-Kenny procedure in detail.
A compact overview of the effects, the type of mediation and the
effect sizes is provided by summary():
summary(out)
#> Mediation analysis: 'math' -> 'read' -> 'science'
#> Estimated with 'lavaan' (standardized), N = 200
#>
#> Effects (95% CI):
#> Estimate Std. Err. z-value p-value Lower Upper
#> Indirect (Sobel) 0.251 0.046 5.501 3.79e-08 0.161 0.340
#> Indirect (Delta) 0.251 0.046 5.446 5.15e-08 0.160 0.341
#> Indirect (Monte-Carlo) 0.251 0.047 5.374 7.71e-08 0.160 0.343
#> Direct 0.380 0.065 4.43e-09 0.253 0.507
#> Total 0.631 0.037 0.559 0.703
#>
#> Type of mediation (significant: p < 0.05):
#> Baron & Kenny: partial mediation
#> Zhao, Lynch & Chen: complementary mediation (partial mediation)
#> (based on Monte-Carlo test)
#>
#> Effect sizes:
#> RIT = 0.397
#> RID = 0.659
#> Upsilon = 0.061
#> Upsilon (unadj.) = 0.063The estimates can also be extracted with the usual functions,
e.g. coef() for the indirect, direct and total effects and
confint() for their intervals (see this
article for more ways of working with the results, including effect
sizes and plots):
coef(out)
#> indirect direct total
#> 0.2506159 0.3801172 0.6309719
confint(out)
#> 2.5 % 97.5 %
#> indirect 0.1602372 0.3433785
#> direct 0.2531357 0.5070988
#> total 0.5588379 0.7028962We can switch to an alternative method by Zhao, Lynch & Chen
(2010) using the approach="zlc" option (here we also
switched to standardized coefficients using
standardized=T):
rmedsem(mod, indep="math", med="read", dep="science",
standardized=T, approach = "zlc")
#> Significance testing of indirect effect (standardized)
#> Model estimated with package 'lavaan'
#> Mediation effect: 'math' -> 'read' -> 'science'
#>
#> Sobel Delta Monte-Carlo
#> Indirect effect 0.251 0.251 0.251
#> Std. Err. 0.046 0.046 0.047
#> z-value 5.501 5.446 5.351
#> p-value 3.79e-08 5.15e-08 8.76e-08
#> CI [0.161, 0.340] [0.160, 0.341] [0.161, 0.345]
#>
#> 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<0.001
#> 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 Y explained indirectly by X through M
#> v(unadj) = 0.063, v(adj) = 0.061We can also apply rmedsem() to more complex SEM’s that
contain both latent and observed variables:
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)
Here, we have latent variables Appearance,
Attractiveness, Muscle and Weight
that measure the motivation of people going to a gym to workout.
This model features several complex mediation pathways. We can use
rmedsem() to investigate those one by one. We start by
considering the pathway Attractive ->
Appearance -> Muscle (the more attractive
the person perceives her/himself, the more this will indirectly
influence her/him to want to work out more to build up muscles):
rmedsem(mod, indep="Attractive", med="Appearance", dep="Muscle",
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 0.065 0.065 0.065
#> Std. Err. 0.033 0.033 0.034
#> z-value 1.975 1.954 1.919
#> p-value 0.0483 0.0507 0.0550
#> CI [0.000, 0.130] [-0.000, 0.131] [0.005, 0.138]
#>
#> 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<0.001
#> 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)
#> RIT is not reported: total effect 0.052 is too small (< 0.2)
#> RID = (Indirect effect / Direct effect)
#> RID is not reported: direct effect 0.014 is not significant (p = 0.850)
#> Upsilon (v) = Variance in Y explained indirectly by X through M
#> v(unadj) = 0.004, v(adj) = 0.003Similarly, we could investigate the pathway Attractive
-> Appearance -> Weight (the more
attractive the person perceives her/himself, the more this will
indirectly influence her/him to want to work out more to lose
weight):
rmedsem(mod, indep="Attractive", med="Appearance", dep="Weight",
approach = "zlc")
#> Significance testing of indirect effect (standardized)
#> Model estimated with package 'lavaan'
#> Mediation effect: 'Attractive' -> 'Appearance' -> 'Weight'
#>
#> Sobel Delta Monte-Carlo
#> Indirect effect 0.098 0.098 0.098
#> Std. Err. 0.047 0.048 0.049
#> z-value 2.081 2.027 2.014
#> p-value 0.0374 0.0427 0.0440
#> CI [0.006, 0.190] [0.003, 0.193] [0.007, 0.197]
#>
#> 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 is 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)
#> RIT is not reported: total effect 0.027 is too small (< 0.2)
#> RID = (Indirect effect / Direct effect)
#> RID is not reported: direct effect 0.125 is not significant (p = 0.073)
#> Upsilon (v) = Variance in Y explained indirectly by X through M
#> v(unadj) = 0.010, v(adj) = 0.007Note that these models involve latent variables. It is also possible to use a combination of latent and observed variables and to use different packages/estimation techniques to fit the models.