semmcci: Monte Carlo Confidence Intervals in Structural Equation Modeling
Ivan Jacob Agaloos Pesigan
2023-03-12
Source:vignettes/semmcci.Rmd
semmcci.Rmd
Installation
You can install the CRAN release of semmcci
with:
install.packages("semmcci")
You can install the development version of semmcci
from
GitHub with:
if (!require("remotes")) install.packages("remotes")
remotes::install_github("jeksterslab/semmcci")
The Monte Carlo Method
In the Monte Carlo method, a sampling distribution of parameter estimates \(\hat{\boldsymbol{\theta}}^{\ast}\) is generated from the multivariate normal distribution using the parameter estimates \(\hat{\boldsymbol{\theta}}\) and the sampling variance-covariance matrix \(\mathrm{Var} \left( \hat{\boldsymbol{\theta}} \right)\).
\[\begin{equation} \hat{\boldsymbol{\theta}}^{\ast} \sim \mathcal{N} \left( \hat{\boldsymbol{\theta}}, \mathrm{Var} \left( \hat{\boldsymbol{\theta}} \right) \right) \end{equation}\]
Confidence intervals for defined parameters \(\mathbf{g} \left( \hat{\boldsymbol{\theta}} \right)\) are generated by obtaining percentiles corresponding to \(100(1 - \alpha)\%\) from the generated sampling distribution, where \(\alpha\) is the significance level.
semmcci
Monte Carlo confidence intervals for free and defined parameters in
models fitted in the structural equation modeling package
lavaan
can be generated using the semmcci
package. The package has two main functions, namely, MC()
and MCStd()
. The output of lavaan
is passed as
the first argument to the MC()
function to generate Monte
Carlo confidence intervals. Monte Carlo confidence intervals for the
standardized estimates can also be generated by passing the output of
the MC()
function to the MCStd()
function.
References
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. https://doi.org/10.1207/s15327906mbr3901_4
Preacher, K. J., & Selig, J. P. (2012). Advantages of Monte Carlo confidence intervals for indirect effects. Communication Methods and Measures, 6(2), 77–98. https://doi.org/10.1080/19312458.2012.679848
Tofighi, D., & Kelley, K. (2019). Indirect effects in sequential mediation models: Evaluating methods for hypothesis testing and confidence interval formation. Multivariate Behavioral Research, 55(2), 188–210. https://doi.org/10.1080/00273171.2019.1618545
Tofighi, D., & MacKinnon, D. P. (2015). Monte Carlo confidence intervals for complex functions of indirect effects. Structural Equation Modeling: A Multidisciplinary Journal, 23(2), 194–205. https://doi.org/10.1080/10705511.2015.1057284