Estimate Semipartial Correlation Coefficients and Generate the Corresponding Sampling Distribution Using the Monte Carlo Method

Usage

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

Arguments

object: Object of class mc, that is, the output of the MC() function.
alpha: Numeric vector. Significance level \(\alpha\).

Value

Returns an object of class betamc which is a list with the following elements:

call: Function call.
args: Function arguments.
thetahatstar: Sampling distribution of \(r_{s}\).
vcov: Sampling variance-covariance matrix of \(r_{s}\).
est: Vector of estimated \(r_{s}\).
fun: Function used ("SCorMC").

Details

The vector of semipartial correlation coefficients (\(r_{s}\)) is derived from each randomly generated vector of parameter estimates. Confidence intervals are generated by obtaining percentiles corresponding to \(100(1 - \alpha)\%\) from the generated sampling distribution of \(r_{s}\), where \(\alpha\) is the significance level.

Author

Ivan Jacob Agaloos Pesigan

Examples

# Data ---------------------------------------------------------------------
data("nas1982", package = "betaMC")

# Fit Model in lm ----------------------------------------------------------
object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)

# MC -----------------------------------------------------------------------
mc <- MC(
  object,
  R = 100, # use a large value e.g., 20000L for actual research
  seed = 0508
)

# SCorMC -------------------------------------------------------------------
out <- SCorMC(mc, alpha = 0.05)

## Methods -----------------------------------------------------------------
print(out)
#> Call:
#> SCorMC(object = mc, alpha = 0.05)
#> 
#> Semipartial correlations
#> type = "hc3"
#>            est     se   R   2.5%  97.5%
#> NARTIC  0.4312 0.0903 100 0.1956 0.5623
#> PCTGRT  0.3430 0.0855 100 0.1256 0.4756
#> PCTSUPP 0.2385 0.0744 100 0.0898 0.3832
summary(out)
#> Call:
#> SCorMC(object = mc, alpha = 0.05)
#> 
#> Semipartial correlations
#> type = "hc3"
#>            est     se   R   2.5%  97.5%
#> NARTIC  0.4312 0.0903 100 0.1956 0.5623
#> PCTGRT  0.3430 0.0855 100 0.1256 0.4756
#> PCTSUPP 0.2385 0.0744 100 0.0898 0.3832
coef(out)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.4311525 0.3430075 0.2384789 
vcov(out)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   0.0081518614  0.0023726959 -0.0005171414
#> PCTGRT   0.0023726959  0.0073186846 -0.0009176858
#> PCTSUPP -0.0005171414 -0.0009176858  0.0055423734
confint(out, level = 0.95)
#>              2.5 %    97.5 %
#> NARTIC  0.19556200 0.5622509
#> PCTGRT  0.12564206 0.4755556
#> PCTSUPP 0.08983456 0.3832122