betaNB

Ivan Jacob Agaloos Pesigan 2025-01-13

Description

Generates nonparametric bootstrap confidence intervals (Efron & Tibshirani, 1993: https://doi.org/10.1201/9780429246593) for standardized regression coefficients (beta) and other effect sizes, including multiple correlation, semipartial correlations, improvement in R-squared, squared partial correlations, and differences in standardized regression coefficients, for models fitted by lm().

Installation

You can install the CRAN release of betaNB with:

install.packages("betaNB")

You can install the development version of betaNB from GitHub with:

if (!require("remotes")) install.packages("remotes")
remotes::install_github("jeksterslab/betaNB")

Example

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.

library(betaNB)

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

BetaNB(nb, alpha = 0.05)
#> Call:
#> BetaNB(object = nb, alpha = 0.05)
#> 
#> Standardized regression slopes
#> type = "pc"
#>            est     se    R   2.5%  97.5%
#> NARTIC  0.4951 0.0719 5000 0.3566 0.6407
#> PCTGRT  0.3915 0.0772 5000 0.2337 0.5377
#> PCTSUPP 0.2632 0.0795 5000 0.1036 0.4149

Other Effect Sizes

The betaNB package also has functions to generate nonparametric bootstrap confidence intervals for other effect sizes such as RSqNB() for multiple correlation coefficients (R-squared and adjusted R-squared), DeltaRSqNB() for improvement in R-squared, SCorNB() for semipartial correlation coefficients, PCorNB() for squared partial correlation coefficients, and DiffBetaNB() for differences of standardized regression coefficients.

Multiple Correlation Coefficients (R-squared and adjusted R-squared)

RSqNB(nb, alpha = 0.05)
#> Call:
#> RSqNB(object = nb, alpha = 0.05)
#> 
#> R-squared and adjusted R-squared
#> type = "pc"
#>        est     se    R   2.5%  97.5%
#> rsq 0.8045 0.0536 5000 0.6949 0.8991
#> adj 0.7906 0.0574 5000 0.6731 0.8919

Improvement in R-squared

DeltaRSqNB(nb, alpha = 0.05)
#> 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 0.0823 0.3103
#> PCTGRT  0.1177 0.0493 5000 0.0348 0.2255
#> PCTSUPP 0.0569 0.0337 5000 0.0086 0.1380

Semipartial Correlation Coefficients

SCorNB(nb, alpha = 0.05)
#> Call:
#> SCorNB(object = nb, alpha = 0.05)
#> 
#> Semipartial correlations
#> type = "pc"
#>            est     se    R   2.5%  97.5%
#> NARTIC  0.4312 0.0695 5000 0.2868 0.5570
#> PCTGRT  0.3430 0.0738 5000 0.1865 0.4748
#> PCTSUPP 0.2385 0.0711 5000 0.0928 0.3715

Squared Partial Correlation Coefficients

PCorNB(nb, alpha = 0.05)
#> Call:
#> PCorNB(object = nb, alpha = 0.05)
#> 
#> Squared partial correlations
#> type = "pc"
#>            est     se    R   2.5%  97.5%
#> NARTIC  0.4874 0.0995 5000 0.2809 0.6690
#> PCTGRT  0.3757 0.1084 5000 0.1597 0.5879
#> PCTSUPP 0.2254 0.1152 5000 0.0413 0.4789

Differences of Standardized Regression Coefficients

DiffBetaNB(nb, alpha = 0.05)
#> 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 0.1318 5000 -0.1483 0.3728
#> NARTIC-PCTSUPP 0.2319 0.1227 5000 -0.0053 0.4788
#> PCTGRT-PCTSUPP 0.1282 0.1284 5000 -0.1191 0.3854

Documentation

See GitHub Pages for package documentation.

References

Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. Chapman & Hall. https://doi.org/10.1201/9780429246593

National Research Council. (1982). An assessment of research-doctorate programs in the United States: Social and behavioral sciences. National Academies Press. https://doi.org/10.17226/9781

Pesigan, I. J. A. (2022). Confidence intervals for standardized coefficients: Applied to regression coefficients in primary studies and indirect effects in meta-analytic structural equation modeling [PhD thesis]. University of Macau.