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betaNB: Example Using the DiffBetaNB Function

Ivan Jacob Agaloos Pesigan

Source: vignettes/example-diff-beta-nb.Rmd
example-diff-beta-nb.Rmd

Confidence intervals for differences of standardized regression slopes are generated using the DiffBetaNB() 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)

Differences of Standardized Regression Slopes

Normal-Theory Approach 

out <- DiffBetaNB(nb, alpha = 0.05)

Methods

summary

Summary of the results of DiffBetaNB().

Percentile Confidence Intervals 

summary(out, type = "pc")
#> Call:
#> DiffBetaNB(object = nb, alpha = 0.05)
#> 
#> Differences of standardized regression slopes
#> type = "pc"
#>                   est     se    R    2.5%  97.5%
#> NARTIC-PCTGRT  0.1037 0.1296 5000 -0.1390 0.3629
#> NARTIC-PCTSUPP 0.2319 0.1219 5000 -0.0070 0.4746
#> PCTGRT-PCTSUPP 0.1282 0.1279 5000 -0.1186 0.3840

Bias Corrected Confidence Intervals 

summary(out, type = "bc")
#> Call:
#> DiffBetaNB(object = nb, alpha = 0.05)
#> 
#> Differences of standardized regression slopes
#> type = "bc"
#>                   est     se    R    2.5%  97.5%
#> NARTIC-PCTGRT  0.1037 0.1296 5000 -0.1437 0.3594
#> NARTIC-PCTSUPP 0.2319 0.1219 5000 -0.0103 0.4673
#> PCTGRT-PCTSUPP 0.1282 0.1279 5000 -0.1110 0.3890

Bias Corrected and Accelerated Confidence Intervals 

summary(out, type = "bca")
#> Call:
#> DiffBetaNB(object = nb, alpha = 0.05)
#> 
#> Differences of standardized regression slopes
#> type = "bca"
#>                   est     se    R    2.5%  97.5%
#> NARTIC-PCTGRT  0.1037 0.1296 5000 -0.1448 0.3564
#> NARTIC-PCTSUPP 0.2319 0.1219 5000 -0.0124 0.4642
#> PCTGRT-PCTSUPP 0.1282 0.1279 5000 -0.1011 0.4026

coef

Return the vector of estimates.

coef(out)
#>  NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP 
#>      0.1036564      0.2318974      0.1282410

vcov

Return the sampling covariance matrix.

vcov(out)
#>                NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP
#> NARTIC-PCTGRT    0.016796288    0.007643631   -0.009152657
#> NARTIC-PCTSUPP   0.007643631    0.014859415    0.007215785
#> PCTGRT-PCTSUPP  -0.009152657    0.007215785    0.016368441

confint

Return confidence intervals.

Percentile Confidence Intervals 

confint(out, level = 0.95, type = "pc")
#>                       2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.139032096 0.3628926
#> NARTIC-PCTSUPP -0.007034197 0.4746073
#> PCTGRT-PCTSUPP -0.118561717 0.3840491

Bias Corrected Confidence Intervals 

confint(out, level = 0.95, type = "bc")
#>                      2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.14370664 0.3594454
#> NARTIC-PCTSUPP -0.01026321 0.4672611
#> PCTGRT-PCTSUPP -0.11103882 0.3890321

Bias Corrected and Accelerated Confidence Intervals 

confint(out, level = 0.95, type = "bca")
#>                     2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.1448315 0.3564058
#> NARTIC-PCTSUPP -0.0124456 0.4641806
#> PCTGRT-PCTSUPP -0.1011013 0.4026161

References