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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")
#>            est     se    R   2.5%  97.5%
#> NARTIC  0.1859 0.0589 5000 0.0841 0.3118
#> PCTGRT  0.1177 0.0488 5000 0.0355 0.2260
#> PCTSUPP 0.0569 0.0340 5000 0.0086 0.1376

Bias Corrected Confidence Intervals 

summary(out, type = "bc")
#>            est     se    R   2.5%  97.5%
#> NARTIC  0.1859 0.0589 5000 0.0940 0.3382
#> PCTGRT  0.1177 0.0488 5000 0.0417 0.2450
#> PCTSUPP 0.0569 0.0340 5000 0.0108 0.1437

Bias Corrected and Accelerated Confidence Intervals 

summary(out, type = "bca")
#>            est     se    R   2.5%  97.5%
#> NARTIC  0.1859 0.0589 5000 0.0980 0.3472
#> PCTGRT  0.1177 0.0488 5000 0.0458 0.2577
#> PCTSUPP 0.0569 0.0340 5000 0.0094 0.1406

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   0.0034719935 -0.0001997241 -0.0002035929
#> PCTGRT  -0.0001997241  0.0023856009 -0.0002806881
#> PCTSUPP -0.0002035929 -0.0002806881  0.0011554583

confint

Return confidence intervals.

Percentile Confidence Intervals 

confint(out, level = 0.95, type = "pc")
#>               2.5 %    97.5 %
#> NARTIC  0.084086820 0.3118446
#> PCTGRT  0.035487360 0.2259744
#> PCTSUPP 0.008636416 0.1375862

Bias Corrected Confidence Intervals 

confint(out, level = 0.95, type = "bc")
#>              2.5 %    97.5 %
#> NARTIC  0.09397235 0.3382464
#> PCTGRT  0.04174721 0.2449696
#> PCTSUPP 0.01077619 0.1436647

Bias Corrected and Accelerated Confidence Intervals 

confint(out, level = 0.95, type = "bca")
#>               2.5 %    97.5 %
#> NARTIC  0.098014885 0.3472307
#> PCTGRT  0.045816598 0.2577377
#> PCTSUPP 0.009402403 0.1406139

References