Monte Carlo Confidence Intervals (Generic)

Calculates Monte Carlo confidence intervals for defined parameters for any fitted model object with coef and vcov methods.

Usage

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

Arguments

object

R object. Fitted model object with coef and vcov methods that return a named vector of estimated parameters and sampling variance-covariance matrix, respectively.

def

List of character strings. A list of defined functions of parameters. The string should be a valid R expression when parsed and should result a single value when evaluated.

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.

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 ("MCGeneric").

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 def 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(), MCFunc(), MCMI(), MCStd()

Author

Ivan Jacob Agaloos Pesigan

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
"
fit <- sem(data = df, model = model, missing = "fiml")

## MCGeneric() -------------------------------------------------------------
MCGeneric(
  fit,
  R = 5L, # use a large value e.g., 20000L for actual research
  alpha = 0.05,
  def = list(
    "a * b",
    "cp + (a * b)"
  )
)
#>                 est     se R    2.5%  97.5%
#> a * b        0.1730 0.1408 5 -0.0086 0.3181
#> cp + (a * b) 0.4381 0.2928 5  0.2206 0.9274