Estimate Improvement in R-Squared and Generate the Corresponding Sampling Distribution Using the Monte Carlo Method

Usage

DeltaRSqMC(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 \(\Delta R^{2}\).
vcov: Sampling variance-covariance matrix of \(\Delta R^{2}\).
est: Vector of estimated \(\Delta R^{2}\).
fun: Function used ("DeltaRSqMC").

Details

The vector of improvement in R-squared (\(\Delta R^{2}\)) 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 \(\Delta R^{2}\), 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
)

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

## Methods -----------------------------------------------------------------
print(out)
#> Call:
#> DeltaRSqMC(object = mc, alpha = 0.05)
#> 
#> Improvement in R-squared
#> type = "hc3"
#>            est     se   R   2.5%  97.5%
#> NARTIC  0.1859 0.0673 100 0.0527 0.3163
#> PCTGRT  0.1177 0.0496 100 0.0272 0.2156
#> PCTSUPP 0.0569 0.0323 100 0.0079 0.1274
summary(out)
#> Call:
#> DeltaRSqMC(object = mc, alpha = 0.05)
#> 
#> Improvement in R-squared
#> type = "hc3"
#>            est     se   R   2.5%  97.5%
#> NARTIC  0.1859 0.0673 100 0.0527 0.3163
#> PCTGRT  0.1177 0.0496 100 0.0272 0.2156
#> PCTSUPP 0.0569 0.0323 100 0.0079 0.1274
coef(out)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.1858925 0.1176542 0.0568722 
vcov(out)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   0.0045232624  0.0005521534 -0.0001510877
#> PCTGRT   0.0005521534  0.0024592635 -0.0002500184
#> PCTSUPP -0.0001510877 -0.0002500184  0.0010413251
confint(out, level = 0.95)
#>               2.5 %    97.5 %
#> NARTIC  0.052718279 0.3162597
#> PCTGRT  0.027238743 0.2156250
#> PCTSUPP 0.007917799 0.1273978