Monte Carlo Confidence Intervals

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
)

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.

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").

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. 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), 77–98. doi:10.1080/19312458.2012.679848

Author

Ivan Jacob Agaloos Pesigan

Examples

library(semmcci)
library(lavaan)
#> This is lavaan 0.6-17
#> lavaan is FREE software! Please report any bugs.

# 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
)
#> Monte Carlo Confidence Intervals
#>                       est     se R    2.5%  97.5%
#> cp                 0.3796 0.2695 5  0.0821 0.6708
#> b                  0.4880 0.0889 5  0.4749 0.6736
#> a                  0.5426 0.3560 5 -0.0026 0.8971
#> cond~~cond         0.2496 0.0128 5  0.2260 0.2568
#> reaction~~reaction 1.7760 0.1978 5  1.4029 1.8400
#> pmi~~pmi           1.7238 0.2483 5  1.4316 2.0547
#> reaction~1         0.5868 0.4777 5 -0.3956 0.6504
#> pmi~1              5.3616 0.1764 5  5.1393 5.5821
#> cond~1             0.4939 0.0413 5  0.4566 0.5488
#> indirect           0.2648 0.1950 5 -0.0091 0.4848
#> direct             0.3796 0.2695 5  0.0821 0.6708
#> total              0.6444 0.2665 5  0.2695 0.8630