Estimate Improvement in R-Squared and Generate the Corresponding Sampling Distribution Using Nonparametric Bootstrapping

Usage

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

Arguments

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

Value

Returns an object of class betanb 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 ("DeltaRSqNB").

Details

The vector of improvement in R-squared (\(\Delta R^{2}\)) is estimated from bootstrap samples. 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 = "betaNB")

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

# NB -----------------------------------------------------------------------
nb <- NB(
  object,
  R = 100, # use a large value e.g., 5000L for actual research
  seed = 0508
)

# DeltaRSqNB ---------------------------------------------------------------
out <- DeltaRSqNB(nb, alpha = 0.05)

## Methods -----------------------------------------------------------------
print(out)
#> Call:
#> DeltaRSqNB(object = nb, alpha = 0.05)
#> 
#> Improvement in R-squared
#> type = "pc"
#>            est     se   R   2.5%  97.5%
#> NARTIC  0.1859 0.0543 100 0.0797 0.2945
#> PCTGRT  0.1177 0.0507 100 0.0374 0.2216
#> PCTSUPP 0.0569 0.0342 100 0.0091 0.1396
summary(out)
#> Call:
#> DeltaRSqNB(object = nb, alpha = 0.05)
#> 
#> Improvement in R-squared
#> type = "pc"
#>            est     se   R   2.5%  97.5%
#> NARTIC  0.1859 0.0543 100 0.0797 0.2945
#> PCTGRT  0.1177 0.0507 100 0.0374 0.2216
#> PCTSUPP 0.0569 0.0342 100 0.0091 0.1396
coef(out)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.1858925 0.1176542 0.0568722 
vcov(out)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   0.0029458986  0.0003342570 -0.0004080511
#> PCTGRT   0.0003342570  0.0025659708 -0.0002009029
#> PCTSUPP -0.0004080511 -0.0002009029  0.0011699276
confint(out, level = 0.95)
#>               2.5 %    97.5 %
#> NARTIC  0.079688018 0.2944650
#> PCTGRT  0.037358975 0.2216272
#> PCTSUPP 0.009079169 0.1395662