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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 0.1321 5000 -0.1503 0.3684
#> NARTIC-PCTSUPP 0.2319 0.1239 5000 -0.0038 0.4770
#> PCTGRT-PCTSUPP 0.1282 0.1262 5000 -0.1157 0.3759

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 0.1321 5000 -0.1589 0.3576
#> NARTIC-PCTSUPP 0.2319 0.1239 5000 -0.0136 0.4729
#> PCTGRT-PCTSUPP 0.1282 0.1262 5000 -0.1127 0.3776

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 0.1321 5000 -0.1601 0.3567
#> NARTIC-PCTSUPP 0.2319 0.1239 5000 -0.0187 0.4713
#> PCTGRT-PCTSUPP 0.1282 0.1262 5000 -0.1028 0.3890

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    0.017442261    0.008432058   -0.009010203
#> NARTIC-PCTSUPP   0.008432058    0.015340284    0.006908226
#> PCTGRT-PCTSUPP  -0.009010203    0.006908226    0.015918429

confint

Return confidence intervals.

Percentile Confidence Intervals 

confint(out, level = 0.95, type = "pc")
#>                       2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.150288282 0.3684040
#> NARTIC-PCTSUPP -0.003762149 0.4769934
#> PCTGRT-PCTSUPP -0.115720525 0.3759245

Bias Corrected Confidence Intervals 

confint(out, level = 0.95, type = "bc")
#>                      2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.15893983 0.3575805
#> NARTIC-PCTSUPP -0.01357186 0.4728913
#> PCTGRT-PCTSUPP -0.11269641 0.3776449

Bias Corrected and Accelerated Confidence Intervals 

confint(out, level = 0.95, type = "bca")
#>                      2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.16007049 0.3567105
#> NARTIC-PCTSUPP -0.01871218 0.4713162
#> PCTGRT-PCTSUPP -0.10282595 0.3889806

References