Monte Carlo Confidence Intervals (Function)

Calculates Monte Carlo confidence intervals for defined parameters.

Usage

MCFunc(
  coef,
  vcov,
  func,
  ...,
  R = 20000L,
  alpha = c(0.001, 0.01, 0.05),
  decomposition = "eigen",
  pd = TRUE,
  tol = 1e-06,
  seed = NULL,
  ncores = NULL
)

Arguments

coef

Numeric vector. Vector of estimated parameters.

vcov

Numeric matrix. Sampling variance-covariance matrix of estimated parameters.

func

R function.

1. The first argument x is the argument coef.

2. The function algebraically manipulates coef to return at a new numeric vector. It is best to have a named vector as an output.

3. The function can take additional named arguments passed using ....

...

Additional arguments to pass to func.

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.

ncores

Positive integer. Number of cores to use. If ncores = NULL, use single core.

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 ("MCFunc").

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 defined parameters are generated using the simulated sampling distribution. Parameters are defined using the func argument.

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. doi:10.1207/s15327906mbr3901_4

Pesigan, I. J. A., & Cheung, S. F. (2023). Monte Carlo confidence intervals for the indirect effect with missing data. Behavior Research Methods. 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<U+2013>98. doi:10.1080/19312458.2012.679848

See also

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

Author

Ivan Jacob Agaloos Pesigan

Examples

library(semmcci)

## MCFunc() ----------------------------------------------------------------
### Define func ------------------------------------------------------------
func <- function(x) {
  out <- exp(x)
  names(out) <- "exp"
  return(out)
}
### Generate Confidence Intervals ------------------------------------------
MCFunc(
  coef = 0,
  vcov = matrix(1),
  func = func,
  R = 5L, # use a large value e.g., 20000L for actual research
  alpha = 0.05
)
#>     est     se R   2.5%  97.5%
#> exp   1 0.9025 5 0.3264 2.2427