monteCarloCI  R Documentation 
Robust confidence intervals for functions of parameter estimates, based on empirical sampling distributions of estimated model parameters.
monteCarloCI(object = NULL, expr, coefs, ACM, nRep = 20000, standardized = FALSE, fast = TRUE, level = 0.95, na.rm = TRUE, append.samples = FALSE, plot = FALSE, ask = getOption("device.ask.default"), ...)
object 
A object of class 
expr 
Optional 
coefs 

ACM 
Symmetric 
nRep 

standardized 

fast 

level 

na.rm 

append.samples 

plot 

ask 
whether to prompt user before printing each plot 
... 
arguments passed to 
This function implements the Monte Carlo method of obtaining an empirical
sampling distriution of estimated model parameters, as described by
MacKinnon et al. (2004) for testing indirect effects in mediation models.
The easiest way to use the function is to fit a SEM to data with
lavaan
, using the :=
operator in the
model.syntax
to specify userdefined parameters.
All information is then available in the resulting
lavaan
object. Alternatively (especially when using
external SEM software to fit the model), the expression(s) can be explicitly
passed to the function, along with the vector of estimated model parameters
and their associated asymptotic sampling covariance matrix (ACOV).
For further information on the Monte Carlo method, see MacKinnon et al.
(2004) and Preacher & Selig (2012).
The asymptotic covariance matrix can be obtained easily from many popular SEM software packages.
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 vcov
method on the fitted
lavaan
object to return the ACM.
A lavaan.data.frame
(to use lavaan's print
method)
with point estimates and confidence limits of each requested function of
parameters in expr
is returned. If append.samples = TRUE
,
output will be a list
with the same $Results
along with a
second data.frame
with the $Samples
(in rows) of each
parameter (in columns), and an additional column for each requested
function of those parameters.
Terrence D. Jorgensen (University of Amsterdam; TJorgensen314@gmail.com)
MacKinnon, D. P., Lockwood, C. M., & Williams, J. (2004). Confidence limits for the indirect effect: Distribution of the product and resampling methods. Multivariate Behavioral Research, 39(1) 99–128. doi: 10.1207/s15327906mbr3901_4
Preacher, K. J., & Selig, J. P. (2010, July). Monte Carlo method for assessing multilevel mediation: An interactive tool for creating confidence intervals for indirect effects in 111 multilevel models [Computer software]. Available from http://quantpsy.org/.
Preacher, K. J., & Selig, J. P. (2012). Advantages of Monte Carlo confidence intervals for indirect effects. Communication Methods and Measures, 6(2), 77–98. doi: 10.1080/19312458.2012.679848
Selig, J. P., & Preacher, K. J. (2008, June). Monte Carlo method for assessing mediation: An interactive tool for creating confidence intervals for indirect effects [Computer software]. Available from http://quantpsy.org/.
## From the mediation tutorial: ## http://lavaan.ugent.be/tutorial/mediation.html set.seed(1234) X < rnorm(100) M < 0.5*X + rnorm(100) Y < 0.7*M + rnorm(100) dat < data.frame(X = X, Y = Y, M = M) mod < ' # direct effect Y ~ c*X # mediator M ~ a*X Y ~ b*M # indirect effect (a*b) ind := a*b # total effect total := ind + c ' fit < sem(mod, data = dat) summary(fit, ci = TRUE) # print deltamethod CIs ## Automatically extract information from lavaan object set.seed(1234) monteCarloCI(fit) # CIs more robust than delta method in smaller samples ## save samples to calculate more precise intervals: ## Not run: set.seed(1234) foo < monteCarloCI(fit, append.samples = TRUE) library(HDInterval) hdi(fit$Samples) ## End(Not run) ## Parameters can also be obtained from an external analysis myParams < c("a","b","c") (coefs < coef(fit)[myParams]) # names must match those in the "expression" ## Asymptotic covariance matrix from an external analysis (AsyCovMat < vcov(fit)[myParams, myParams]) ## Compute CI, include a plot set.seed(1234) monteCarloCI(expr = c(ind = 'a*b', total = 'ind + c', ## other arbitrary functions are also possible meaningless = 'sqrt(a)^b / log(abs(c))'), coefs = coefs, ACM = AsyCovMat, plot = TRUE, ask = TRUE) # print a plot for each
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