Standardized Monte Carlo Confidence Intervals

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

Usage

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

Arguments

mc: Output of the MC() or MCMI() function.
alpha: Numeric vector. Significance level \(\alpha\).

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 ("MCStd").

Details

The empirical sampling distribution of parameter estimates from the argument mc 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.

References

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

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
  indirect := a * b
  direct := cp
  total := cp + (a * b)
"
fit <- sem(data = df, model = model, missing = "fiml")

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

## Standardized Monte Carlo ------------------------------------------------
MCStd(unstd, alpha = 0.05)
#> Standardized Monte Carlo Confidence Intervals
#>                       est     se R    2.5%  97.5%
#> cp                 0.0997 0.1246 5 -0.0433 0.2264
#> b                  0.4399 0.0336 5  0.4471 0.5201
#> a                  0.1703 0.1256 5 -0.0017 0.2840
#> cond~~cond         1.0000 0.0000 5  1.0000 1.0000
#> reaction~~reaction 0.7816 0.0498 5  0.6430 0.7556
#> pmi~~pmi           0.9710 0.0377 5  0.9180 0.9999
#> indirect           0.3622 0.0594 5 -0.0010 0.1320
#> direct             4.0501 0.1246 5 -0.0433 0.2264
#> total              0.9292 0.1721 5 -0.0349 0.3402

# Monte Carlo (Multiple Imputation) ----------------------------------------
## Multiple Imputation -----------------------------------------------------
mi <- mice::mice(
  data = df,
  print = FALSE,
  m = 5L, # use a large value e.g., 100L for actual research,
  seed = 42
)

## Fit Model in lavaan -----------------------------------------------------
fit <- sem(data = df, model = model) # use default listwise deletion

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

## Standardized Monte Carlo ------------------------------------------------
MCStd(unstd, alpha = 0.05)
#> Standardized Monte Carlo Confidence Intervals
#>                       est     se R   2.5%  97.5%
#> cp                 0.1350 0.1145 5 0.0605 0.2908
#> b                  0.4360 0.0659 5 0.4069 0.5655
#> a                  0.1463 0.1037 5 0.0890 0.3335
#> cond~~cond         1.0000 0.0000 5 1.0000 1.0000
#> reaction~~reaction 0.7744 0.0829 5 0.6166 0.8122
#> pmi~~pmi           0.9786 0.0446 5 0.8886 0.9918
#> indirect           0.0638 0.0486 5 0.0488 0.1578
#> direct             0.1350 0.1145 5 0.0605 0.2908
#> total              0.1988 0.1412 5 0.1304 0.4295