Estimate Standardized Regression Coefficients and Generate the Corresponding Sampling Distribution Using the Monte Carlo Method

Estimate Standardized Regression Coefficients and Generate the Corresponding Sampling Distribution Using the Monte Carlo Method

Usage

BetaMC(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 \(\boldsymbol{\hat{\beta}}\).

vcov

Sampling variance-covariance matrix of \(\boldsymbol{\hat{\beta}}\).

est

Vector of estimated \(\boldsymbol{\hat{\beta}}\).

fun

Function used ("BetaMC").

Details

The vector of standardized regression coefficients (\(\boldsymbol{\hat{\beta}}\)) 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 \(\boldsymbol{\hat{\beta}}\), where \(\alpha\) is the significance level.

See also

Other Beta Monte Carlo Functions: DeltaRSqMC(), DiffBetaMC(), MC(), MCMI(), PCorMC(), RSqMC(), SCorMC()

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
)

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

## Methods -----------------------------------------------------------------
print(out)
#> Call:
#> BetaMC(object = mc, alpha = 0.05)
#> 
#> Standardized regression slopes
#> type = "hc3"
#>            est     se   R   2.5%  97.5%
#> NARTIC  0.4951 0.0760 100 0.3508 0.6231
#> PCTGRT  0.3915 0.0732 100 0.2643 0.5224
#> PCTSUPP 0.2632 0.0808 100 0.1014 0.4009
summary(out)
#> Call:
#> BetaMC(object = mc, alpha = 0.05)
#> 
#> Standardized regression slopes
#> type = "hc3"
#>            est     se   R   2.5%  97.5%
#> NARTIC  0.4951 0.0760 100 0.3508 0.6231
#> PCTGRT  0.3915 0.0732 100 0.2643 0.5224
#> PCTSUPP 0.2632 0.0808 100 0.1014 0.4009
coef(out)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.4951451 0.3914887 0.2632477 
vcov(out)
#>               NARTIC       PCTGRT      PCTSUPP
#> NARTIC   0.005776525 -0.002834952 -0.002143637
#> PCTGRT  -0.002834952  0.005360100 -0.001947940
#> PCTSUPP -0.002143637 -0.001947940  0.006526525
confint(out, level = 0.95)
#>             2.5 %    97.5 %
#> NARTIC  0.3507721 0.6231028
#> PCTGRT  0.2643226 0.5224279
#> PCTSUPP 0.1013892 0.4008517