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betaNB: Example Using the BetaNB Function

Ivan Jacob Agaloos Pesigan

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

In this example, a multiple regression model is fitted using program quality ratings (QUALITY) as the regressand/outcome variable and number of published articles attributed to the program faculty members (NARTIC), percent of faculty members holding research grants (PCTGRT), and percentage of program graduates who received support (PCTSUPP) as regressor/predictor variables using a data set from 1982 ratings of 46 doctoral programs in psychology in the USA (National Research Council, 1982). Confidence intervals for the standardized regression coefficients are generated using the BetaNB() function from the betaNB package.

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)

Standardized Regression Slopes 

out <- BetaNB(nb, alpha = 0.05)

Methods

summary

Summary of the results of BetaNB().

Percentile Confidence Intervals 

summary(out, type = "pc")
#> Call:
#> BetaNB(object = nb, alpha = 0.05)
#> 
#> Standardized regression slopes
#> type = "pc"
#>            est     se    R   2.5%  97.5%
#> NARTIC  0.4951 0.0730 5000 0.3528 0.6371
#> PCTGRT  0.3915 0.0764 5000 0.2397 0.5419
#> PCTSUPP 0.2632 0.0802 5000 0.1029 0.4198

Bias Corrected Confidence Intervals 

summary(out, type = "bc")
#> Call:
#> BetaNB(object = nb, alpha = 0.05)
#> 
#> Standardized regression slopes
#> type = "bc"
#>            est     se    R   2.5%  97.5%
#> NARTIC  0.4951 0.0730 5000 0.3486 0.6332
#> PCTGRT  0.3915 0.0764 5000 0.2492 0.5508
#> PCTSUPP 0.2632 0.0802 5000 0.1102 0.4245

Bias Corrected and Accelerated Confidence Intervals 

summary(out, type = "bca")
#> Call:
#> BetaNB(object = nb, alpha = 0.05)
#> 
#> Standardized regression slopes
#> type = "bca"
#>            est     se    R   2.5%  97.5%
#> NARTIC  0.4951 0.0730 5000 0.3496 0.6346
#> PCTGRT  0.3915 0.0764 5000 0.2536 0.5597
#> PCTSUPP 0.2632 0.0802 5000 0.1025 0.4187

coef

Return the vector of estimates.

coef(out)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.4951451 0.3914887 0.2632477

vcov

Return the sampling covariance matrix.

vcov(out)
#>               NARTIC       PCTGRT      PCTSUPP
#> NARTIC   0.005326502 -0.003175871 -0.002057181
#> PCTGRT  -0.003175871  0.005831953 -0.001886047
#> PCTSUPP -0.002057181 -0.001886047  0.006435378

confint

Return confidence intervals.

Percentile Confidence Intervals 

confint(out, level = 0.95, type = "pc")
#>             2.5 %    97.5 %
#> NARTIC  0.3527537 0.6370989
#> PCTGRT  0.2397222 0.5419108
#> PCTSUPP 0.1029495 0.4198068

Bias Corrected Confidence Intervals 

confint(out, level = 0.95, type = "bc")
#>             2.5 %    97.5 %
#> NARTIC  0.3485954 0.6331719
#> PCTGRT  0.2491930 0.5507677
#> PCTSUPP 0.1101806 0.4244667

Bias Corrected and Accelerated Confidence Intervals 

confint(out, level = 0.95, type = "bca")
#>             2.5 %    97.5 %
#> NARTIC  0.3496245 0.6346057
#> PCTGRT  0.2536066 0.5596975
#> PCTSUPP 0.1025070 0.4187161

References