Ivan Jacob Agaloos Pesigan 2024-04-14
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()
.
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")
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
Fit the regression model using the lm()
function.
object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = df)
nb <- NB(object)
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 0.0732 5000 0.3521 0.6436
#> PCTGRT 0.3915 0.0756 5000 0.2397 0.5390
#> PCTSUPP 0.2632 0.0796 5000 0.1031 0.4156
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.
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 0.0510 5000 0.6996 0.8987
#> adj 0.7906 0.0547 5000 0.6782 0.8914
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 0.0596 5000 0.0809 0.3119
#> PCTGRT 0.1177 0.0478 5000 0.0353 0.2232
#> PCTSUPP 0.0569 0.0341 5000 0.0083 0.1373
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 0.0701 5000 0.2845 0.5585
#> PCTGRT 0.3430 0.0715 5000 0.1880 0.4725
#> PCTSUPP 0.2385 0.0717 5000 0.0910 0.3706
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 0.0979 5000 0.2820 0.6655
#> PCTGRT 0.3757 0.1076 5000 0.1651 0.5801
#> PCTSUPP 0.2254 0.1153 5000 0.0373 0.4818
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 0.1322 5000 -0.1511 0.3723
#> NARTIC-PCTSUPP 0.2319 0.1258 5000 -0.0106 0.4863
#> PCTGRT-PCTSUPP 0.1282 0.1250 5000 -0.1148 0.3775
See GitHub Pages for package documentation.
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.