betaSandwich: Example Using the RSqSandwich Function

Confidence intervals for multiple correlation are generated using the RSqSandwich() function from the betaSandwich package. In this example, we use the data set and the model used in betaSandwich: Example Using the BetaHC Function.

library(betaSandwich)

df <- betaSandwich::nas1982

Fit the regression model using the `lm()` function.

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = df)

Estimate the standardized regression slopes and the corresponding sampling covariance matrix.

Multivariate Normal-Theory Approach

std_mvn <- BetaN(object)

Asymptotic Distribution-Free Approach

std_adf <- BetaADF(object)

HC3

std_hc3 <- BetaHC(object, type = "hc3")

Estimate the multiple correlation coefficients (R-squared and adjusted R-squared) and the corresponding sampling covariance matrix.

mvn <- RSqSandwich(std_mvn, alpha = 0.05)
adf <- RSqSandwich(std_adf, alpha = 0.05)
hc3 <- RSqSandwich(std_hc3, alpha = 0.05)

Methods

summary

Summary of the results of RSqSandwich().

summary(mvn)
#> Call:
#> RSqSandwich(object = std_mvn, alpha = 0.05)
#> 
#> R-squared and adjusted R-squared with MVN standard errors:
#>        est     se       z p   2.5%  97.5%
#> rsq 0.8045 0.0517 15.5608 0 0.7032 0.9059
#> adj 0.7906 0.0554 14.2713 0 0.6820 0.8991
summary(adf)
#> Call:
#> RSqSandwich(object = std_adf, alpha = 0.05)
#> 
#> R-squared and adjusted R-squared with MVN standard errors:
#>        est     se       z p   2.5%  97.5%
#> rsq 0.8045 0.0519 15.4910 0 0.7027 0.9063
#> adj 0.7906 0.0556 14.2073 0 0.6815 0.8996
summary(hc3)
#> Call:
#> RSqSandwich(object = std_hc3, alpha = 0.05)
#> 
#> R-squared and adjusted R-squared with HC3 standard errors:
#>        est     se       z p   2.5%  97.5%
#> rsq 0.8045 0.0573 14.0286 0 0.6921 0.9169
#> adj 0.7906 0.0614 12.8662 0 0.6701 0.9110

coef

Calculate R-squared and adjusted R-squared.

coef(mvn)
#>       rsq       adj 
#> 0.8045263 0.7905638
coef(adf)
#>       rsq       adj 
#> 0.8045263 0.7905638
coef(hc3)
#>       rsq       adj 
#> 0.8045263 0.7905638

vcov

Calculate the sampling covariance matrix of R-squared and adjusted R-squared.

vcov(mvn)
#>             rsq         adj
#> rsq 0.002673125 0.002864062
#> adj 0.002864062 0.003068638
vcov(adf)
#>             rsq         adj
#> rsq 0.002697266 0.002889927
#> adj 0.002889927 0.003096351
vcov(hc3)
#>             rsq         adj
#> rsq 0.003288894 0.003523815
#> adj 0.003523815 0.003775516

confint

Generate confidence intervals for R-squared and adjusted R-squared.

confint(mvn, level = 0.95)
#>         2.5 %    97.5 %
#> rsq 0.7031917 0.9058608
#> adj 0.6819911 0.8991366
confint(adf, level = 0.95)
#>         2.5 %    97.5 %
#> rsq 0.7027351 0.9063174
#> adj 0.6815019 0.8996258
confint(hc3, level = 0.95)
#>         2.5 %    97.5 %
#> rsq 0.6921245 0.9169280
#> adj 0.6701334 0.9109943

References

Dudgeon, P. (2017). Some improvements in confidence intervals for standardized regression coefficients. Psychometrika, 82(4), 928–951. https://doi.org/10.1007/s11336-017-9563-z

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., Sun, R. W., & Cheung, S. F. (2023). betaDelta and betaSandwich: Confidence intervals for standardized regression coefficients in R. Multivariate Behavioral Research, 58(6), 1183–1186. https://doi.org/10.1080/00273171.2023.2201277

Ivan Jacob Agaloos Pesigan

Fit the regression model using the lm() function.