semmcci (version 1.1.5)

MC: Monte Carlo Confidence Intervals

Description

Calculates Monte Carlo confidence intervals for free and defined parameters.

Usage

MC(
  lav,
  R = 20000L,
  alpha = c(0.001, 0.01, 0.05),
  decomposition = "eigen",
  pd = TRUE,
  tol = 1e-06,
  seed = NULL
)

Value

Returns an object of class semmcci which is a list with the following elements:

call

Function call.

args

List of function arguments.

thetahat

Parameter estimates \(\hat{\theta}\).

thetahatstar

Sampling distribution of parameter estimates \(\hat{\theta}^{\ast}\).

fun

Function used ("MC").

Arguments

lav

Object of class lavaan.

R

Positive integer. Number of Monte Carlo replications.

alpha

Numeric vector. Significance level \(\alpha\).

decomposition

Character string. Matrix decomposition of the sampling variance-covariance matrix for the data generation. If decomposition = "chol", use Cholesky decomposition. If decomposition = "eigen", use eigenvalue decomposition. If decomposition = "svd", use singular value decomposition.

pd

Logical. If pd = TRUE, check if the sampling variance-covariance matrix is positive definite using tol.

tol

Numeric. Tolerance used for pd.

seed

Integer. Random seed for reproducibility.

Author

Ivan Jacob Agaloos Pesigan

Details

A sampling distribution of parameter estimates is generated from the multivariate normal distribution using the parameter estimates and the sampling variance-covariance matrix. Confidence intervals for free and defined parameters are generated using the simulated sampling distribution. Parameters can be defined using the := operator in the lavaan model syntax.

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. tools:::Rd_expr_doi("10.1207/s15327906mbr3901_4")

Pesigan, I. J. A., & Cheung, S. F. (2024). Monte Carlo confidence intervals for the indirect effect with missing data. Behavior Research Methods. tools:::Rd_expr_doi("10.3758/s13428-023-02114-4")

Preacher, K. J., & Selig, J. P. (2012). Advantages of Monte Carlo confidence intervals for indirect effects. Communication Methods and Measures, 6(2), 77–98. tools:::Rd_expr_doi("10.1080/19312458.2012.679848")

See Also

Other Monte Carlo in Structural Equation Modeling Functions: Func(), MCFunc(), MCGeneric(), MCMI(), MCStd()

Examples

library(semmcci)
library(lavaan)

# Data ---------------------------------------------------------------------
data("Tal.Or", package = "psych")
df <- mice::ampute(Tal.Or)$amp

# Monte Carlo --------------------------------------------------------------
## Fit Model in lavaan -----------------------------------------------------
model <- "
  reaction ~ cp * cond + b * pmi
  pmi ~ a * cond
  cond ~~ cond
  indirect := a * b
  direct := cp
  total := cp + (a * b)
"
fit <- sem(data = df, model = model, missing = "fiml")

## MC() --------------------------------------------------------------------
MC(
  fit,
  R = 5L, # use a large value e.g., 20000L for actual research
  alpha = 0.05
)