Estimate Differences of Standardized Slopes and Generate the Corresponding Sampling Distribution Using the Monte Carlo Method

Usage

DiffBetaMC(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 differences of standardized regression slopes.
vcov: Sampling variance-covariance matrix of differences of standardized regression slopes.
est: Vector of estimated differences of standardized regression slopes.
fun: Function used ("DiffBetaMC").

Details

The vector of differences of standardized regression slopes 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 differences of standardized regression slopes, 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
)

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

## Methods -----------------------------------------------------------------
print(out)
#> Call:
#> DiffBetaMC(object = mc, alpha = 0.05)
#> 
#> Differences of standardized regression slopes
#> type = "hc3"
#>                   est     se   R    2.5%  97.5%
#> NARTIC-PCTGRT  0.1037 0.1296 100 -0.1366 0.3402
#> NARTIC-PCTSUPP 0.2319 0.1288 100 -0.0081 0.4676
#> PCTGRT-PCTSUPP 0.1282 0.1256 100 -0.1156 0.3734
summary(out)
#> Call:
#> DiffBetaMC(object = mc, alpha = 0.05)
#> 
#> Differences of standardized regression slopes
#> type = "hc3"
#>                   est     se   R    2.5%  97.5%
#> NARTIC-PCTGRT  0.1037 0.1296 100 -0.1366 0.3402
#> NARTIC-PCTSUPP 0.2319 0.1288 100 -0.0081 0.4676
#> PCTGRT-PCTSUPP 0.1282 0.1256 100 -0.1156 0.3734
coef(out)
#>  NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP 
#>      0.1036564      0.2318974      0.1282410 
vcov(out)
#>                NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP
#> NARTIC-PCTGRT    0.016806528    0.008807174   -0.007999355
#> NARTIC-PCTSUPP   0.008807174    0.016590325    0.007783151
#> PCTGRT-PCTSUPP  -0.007999355    0.007783151    0.015782506
confint(out, level = 0.95)
#>                       2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.136563743 0.3402320
#> NARTIC-PCTSUPP -0.008099405 0.4676292
#> PCTGRT-PCTSUPP -0.115552550 0.3733956