Standardized Monte Carlo Confidence Intervals

Calculates standardized Monte Carlo confidence intervals for free and defined parameters.

Usage

MCStd(object, alpha = c(0.001, 0.01, 0.05))

Arguments

object: object of class semmcci. Output of the MC() function.
alpha: Numeric vector. Significance level \(\alpha\).

Value

Returns an object of class semmccistd

which is a list with the following elements:

R: Number of Monte Carlo replications.
alpha: Significance level \(\alpha\) specified.
lavaan: lavaan object.
decomposition: Matrix decomposition used to generate multivariate normal random variates.
thetahat: Parameter estimates \(\hat{\theta}\).
thetahatstar: Sampling distribution of parameter estimates \(\hat{\theta}^{\ast}\).
ci: Confidence intervals.
thetahat_std: Standardized parameter estimates \(\hat{\theta}_{\mathrm{std}}\).
thetahatstar_std: Standardized sampling distribution of parameter estimates \(\hat{\theta}^{\ast}_{\mathrm{std}}\).

Details

The empirical sampling distribution of parameter estimates from the argument object is standardized, that is, each randomly generated vector of parameters is standardized. Defined parameters are computed from the standardized component parameters. Confidence intervals are generated using the standardized empirical sampling distribution.

Author

Ivan Jacob Agaloos Pesigan

Examples

library(semmcci)
library(lavaan)

# Generate Data ------------------------------------------------------------
n <- 1000
a <- 0.50
b <- 0.50
cp <- 0.25
s2_em <- 1 - a^2
s2_ey <- 1 - cp^2 - a^2 * b^2 - b^2 * s2_em - 2 * cp * a * b
em <- rnorm(n = n, mean = 0, sd = sqrt(s2_em))
ey <- rnorm(n = n, mean = 0, sd = sqrt(s2_ey))
X <- rnorm(n = n)
M <- a * X + em
Y <- cp * X + b * M + ey
df <- data.frame(X, M, Y)

# Fit Model in lavaan ------------------------------------------------------
model <- "
  Y ~ cp * X + b * M
  M ~ a * X
  indirect := a * b
  direct := cp
  total := cp + (a * b)
"
fit <- sem(data = df, model = model, fixed.x = FALSE)

# Monte Carlo --------------------------------------------------------------
output <- MC(
  fit,
  R = 100L, # use a large value e.g., 20000L for actual research
  alpha = c(0.001, 0.01, 0.05)
)

# Standardized Monte Carlo -------------------------------------------------
MCStd(output)
#> Standardized Monte Carlo Confidence Intervals
#>             est     se   R  0.05%   0.5%   2.5%  97.5%  99.5% 99.95%
#> cp       0.2644 0.0257 100 0.2038 0.2046 0.2116 0.3076 0.3168 0.3223
#> b        0.4968 0.0220 100 0.4427 0.4429 0.4526 0.5437 0.5456 0.5461
#> a        0.4889 0.0277 100 0.4223 0.4229 0.4326 0.5350 0.5457 0.5474
#> Y~~Y     0.5548 0.0207 100 0.5121 0.5132 0.5178 0.5970 0.6072 0.6090
#> M~~M     0.7610 0.0269 100 0.7003 0.7023 0.7138 0.8129 0.8212 0.8217
#> X~~X     1.0000 0.0000 100 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
#> indirect 0.2429 0.0165 100 0.2040 0.2048 0.2069 0.2728 0.2788 0.2794
#> direct   0.2644 0.0257 100 0.2038 0.2046 0.2116 0.3076 0.3168 0.3223
#> total    0.5073 0.0240 100 0.4483 0.4505 0.4569 0.5480 0.5554 0.5618