Monte Carlo Confidence Intervals to Test Complex Indirect Effects
This function takes an expression for an indirect effect, the parameters and standard errors associated with the expression and returns a confidence interval based on a Monte Carlo test of mediation (MacKinnon, Lockwood, & Williams, 2004).
monteCarloMed(expression, ..., ACM = NULL, object = NULL, rep = 20000, CI = 95, plot = FALSE, outputValues = FALSE)
expression |
A character scalar representing the computation of an indirect effect. Different parameters in the expression should have different alphanumeric values. Expressions can use either addition (+) or multiplication (*) operators. |
... |
Parameter estimates for all parameters named in
|
ACM |
A matrix representing the asymptotic covariance matrix of the
parameters described in |
object |
A lavaan model object fitted after running the running the
|
rep |
The number of replications to compute. Many thousand are reccomended. |
CI |
Width of the confidence interval computed. |
plot |
Should the function output a plot of simulated values of the indirect effect? |
outputValues |
Should the function output all simulated values of the indirect effect? |
This function implements the Monte Carlo test of mediation first described in MacKinnon, Lockwood, & Williams (2004) and extends it to complex cases where the indirect effect is more than a function of two parameters. The function takes an expression for the indirect effect, randomly simulated values of the indirect effect based on the values of the parameters (and the associated standard errors) comprising the indirect effect, and outputs a confidence interval of the indirect effect based on the simulated values. For further information on the Monte Carlo test of mediation see MacKinnon, Lockwood, & Williams (2004) and Preacher & Selig (2012).
The asymptotic covariance matrix can be easily found in many popular SEM software applications.
LISREL: Including the EC option on the OU line will print the ACM to a seperate file. The file contains the lower triangular elements of the ACM in free format and scientific notation
Mplus Include the command TECH3; in the OUTPUT section. The ACM will be printed in the output.
lavaan: Use the command vcov on the fitted lavaan object to
print the ACM to the screen
A list with two elements. The first element is the point estimate
for the indirect effect. The second element is a matrix with values for the
upper and lower limits of the confidence interval generated from the Monte
Carlo test of mediation. If outputValues = TRUE, output will be a list
with a list with the point estimate and values for the upper and lower
limits of the confidence interval as the first element and a vector of
simulated values of the indirect effect as the second element.
Corbin Quick (University of Michigan; corbinq@umich.edu)
Alexander M. Schoemann (East Carolina University; schoemanna@ecu.edu)
James P. Selig (University of New Mexico; selig@unm.edu)
Terrence D. Jorgensen (University of Amsterdam; TJorgensen314@gmail.com)
MacKinnon, D. P., Lockwood, C. M., & Williams, J. (2004). Confidence limits for the indirect effect: Distribution of the product and resampling methods. Multivariate Behavioral Research, 39(1) 99–128. doi: 10.1207/s15327906mbr3901_4
Preacher, K. J., & Selig, J. P. (2010, July). Monte Carlo method for assessing multilevel mediation: An interactive tool for creating confidence intervals for indirect effects in 1-1-1 multilevel models [Computer software]. Available from http://quantpsy.org/.
Preacher, K. J., & Selig, J. P. (2012). Advantages of Monte Carlo confidence intervals for indirect effects. Communication Methods and Measures, 6(2), 77–98. doi: 10.1080/19312458.2012.679848
Selig, J. P., & Preacher, K. J. (2008, June). Monte Carlo method for assessing mediation: An interactive tool for creating confidence intervals for indirect effects [Computer software]. Available from http://quantpsy.org/.
## Simple two path mediation
## Write expression of indirect effect
med <- 'a*b'
## Paramter values from analyses
aparam <- 1
bparam <- 2
## Asymptotic covariance matrix from analyses
AC <- matrix(c(.01,.00002,
.00002,.02), nrow=2, byrow=TRUE)
## Compute CI, include a plot
monteCarloMed(med, coef1 = aparam, coef2 = bparam, outputValues = FALSE,
plot = TRUE, ACM = AC)
## Use a vector of parameter estimates as input
aparam <- c(1,2)
monteCarloMed(med, coef1 = aparam, outputValues = FALSE,
plot = TRUE, ACM = AC)
## Complex mediation with two paths for the indirect effect
## Write expression of indirect effect
med <- 'a1*b1 + a1*b2'
## Paramter values and standard errors from analyses
aparam <- 1
b1param <- 2
b2param <- 1
## Asymptotic covariance matrix from analyses
AC <- matrix(c(1, .00002, .00003,
.00002, 1, .00002,
.00003, .00002, 1), nrow = 3, byrow = TRUE)
## Compute CI do not include a plot
monteCarloMed(med, coef1 = aparam, coef2 = b1param,
coef3 = b2param, ACM = AC)
## WORKING WITH lavaan MODELS. From the mediation tutorial:
## http://lavaan.ugent.be/tutorial/mediation.html
set.seed(1234)
X <- rnorm(100)
M <- 0.5*X + rnorm(100)
Y <- 0.7*M + rnorm(100)
Data <- data.frame(X = X, Y = Y, M = M)
model <- ' # direct effect
Y ~ c*X
# mediator
M ~ a*X
Y ~ b*M
# indirect effect (a*b)
ab := a*b
# total effect
total := c + (a*b)
'
fit <- sem(model, data = Data)
med <- 'a*b'
## Automatically extract information from lavaan object
monteCarloMed(med, object = fit)
## or (unnecessary) manually extract the information first
myParams <- c("a","b")
myCoefs <- coef(fit)[myParams]
myACM <- vcov(fit)[myParams, myParams]
monteCarloMed(med, myCoefs, ACM = myACM)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.