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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 0.0589 5000 0.0828 0.3131
#> PCTGRT  0.1177 0.0486 5000 0.0360 0.2259
#> PCTSUPP 0.0569 0.0337 5000 0.0089 0.1345

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 0.0589 5000 0.0917 0.3335
#> PCTGRT  0.1177 0.0486 5000 0.0440 0.2437
#> PCTSUPP 0.0569 0.0337 5000 0.0117 0.1522

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 0.0589 5000 0.0957 0.3392
#> PCTGRT  0.1177 0.0486 5000 0.0477 0.2545
#> PCTSUPP 0.0569 0.0337 5000 0.0108 0.1463

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   0.0034691706 -0.0002535082 -0.0002448919
#> PCTGRT  -0.0002535082  0.0023620847 -0.0002433746
#> PCTSUPP -0.0002448919 -0.0002433746  0.0011351322

confint

Return confidence intervals.

Percentile Confidence Intervals 

confint(out, level = 0.95, type = "pc")
#>              2.5 %    97.5 %
#> NARTIC  0.08278082 0.3130850
#> PCTGRT  0.03598906 0.2259309
#> PCTSUPP 0.00888793 0.1345443

Bias Corrected Confidence Intervals 

confint(out, level = 0.95, type = "bc")
#>              2.5 %    97.5 %
#> NARTIC  0.09173452 0.3334696
#> PCTGRT  0.04395415 0.2437100
#> PCTSUPP 0.01172624 0.1521928

Bias Corrected and Accelerated Confidence Intervals 

confint(out, level = 0.95, type = "bca")
#>              2.5 %    97.5 %
#> NARTIC  0.09569846 0.3392472
#> PCTGRT  0.04766694 0.2544546
#> PCTSUPP 0.01078521 0.1463342

References