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betaNB: Example Using the DeltaRSqNB Function

Ivan Jacob Agaloos Pesigan

Source: vignettes/example-delta-r-sq-nb.Rmd
example-delta-r-sq-nb.Rmd

Confidence intervals for improvement in R-squared are generated using the DeltaRSqNB() function from the betaNB package. In this example, we use the data set and the model used in betaNB: Example Using the BetaNB Function.

df <- betaNB::nas1982

Regression

Fit the regression model using the lm() function.

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = df)

Nonparametric Bootstrap 

nb <- NB(object)

Improvement in R-squared

Normal-Theory Approach 

out <- DeltaRSqNB(nb, alpha = 0.05)

Methods

summary

Summary of the results of DeltaRSqNB().

Percentile Confidence Intervals 

summary(out, type = "pc")
#> Call:
#> DeltaRSqNB(object = nb, alpha = 0.05)
#> 
#> Improvement in R-squared
#> type = "pc"
#>            est     se    R   2.5%  97.5%
#> NARTIC  0.1859 0.0601 5000 0.0817 0.3149
#> PCTGRT  0.1177 0.0500 5000 0.0345 0.2280
#> PCTSUPP 0.0569 0.0339 5000 0.0083 0.1346

Bias Corrected Confidence Intervals 

summary(out, type = "bc")
#> Call:
#> DeltaRSqNB(object = nb, alpha = 0.05)
#> 
#> Improvement in R-squared
#> type = "bc"
#>            est     se    R   2.5%  97.5%
#> NARTIC  0.1859 0.0601 5000 0.0927 0.3427
#> PCTGRT  0.1177 0.0500 5000 0.0436 0.2486
#> PCTSUPP 0.0569 0.0339 5000 0.0108 0.1456

Bias Corrected and Accelerated Confidence Intervals 

summary(out, type = "bca")
#> Call:
#> DeltaRSqNB(object = nb, alpha = 0.05)
#> 
#> Improvement in R-squared
#> type = "bca"
#>            est     se    R   2.5%  97.5%
#> NARTIC  0.1859 0.0601 5000 0.0958 0.3536
#> PCTGRT  0.1177 0.0500 5000 0.0474 0.2630
#> PCTSUPP 0.0569 0.0339 5000 0.0100 0.1405

coef

Return the vector of estimates.

coef(out)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.1858925 0.1176542 0.0568722

vcov

Return the sampling covariance matrix.

vcov(out)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   0.0036135787 -0.0002846977 -0.0002311248
#> PCTGRT  -0.0002846977  0.0024977969 -0.0002545603
#> PCTSUPP -0.0002311248 -0.0002545603  0.0011515539

confint

Return confidence intervals.

Percentile Confidence Intervals 

confint(out, level = 0.95, type = "pc")
#>              2.5 %    97.5 %
#> NARTIC  0.08165068 0.3148952
#> PCTGRT  0.03453754 0.2279909
#> PCTSUPP 0.00827500 0.1346119

Bias Corrected Confidence Intervals 

confint(out, level = 0.95, type = "bc")
#>              2.5 %    97.5 %
#> NARTIC  0.09272353 0.3426821
#> PCTGRT  0.04360572 0.2486299
#> PCTSUPP 0.01080113 0.1456063

Bias Corrected and Accelerated Confidence Intervals 

confint(out, level = 0.95, type = "bca")
#>               2.5 %    97.5 %
#> NARTIC  0.095784560 0.3535939
#> PCTGRT  0.047404358 0.2629505
#> PCTSUPP 0.009967509 0.1404835

References