betaSandwich: Example Using the RSqBetaSandwich Function

Ivan Jacob Agaloos Pesigan

Confidence intervals for multiple correlation are generated using the RSqBetaSandwich() 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 <- RSqBetaSandwich(std_mvn, alpha = 0.05)
adf <- RSqBetaSandwich(std_adf, alpha = 0.05)
hc3 <- RSqBetaSandwich(std_hc3, alpha = 0.05)

Methods

summary

Summary of the results of RSqBetaSandwich().

summary(mvn)
#> Call:
#> RSqBetaSandwich(object = std_mvn, alpha = 0.05)
#> 
#> Multiple correlation with MVN standard errors:
#>        est     se       t df p   2.5%  97.5%
#> rsq 0.8045 0.0328 24.5344 42 0 0.7383 0.8707
#> adj 0.7906 0.0351 22.5014 42 0 0.7197 0.8615
summary(adf)
#> Call:
#> RSqBetaSandwich(object = std_adf, alpha = 0.05)
#> 
#> Multiple correlation with MVN standard errors:
#>        est     se       t df p   2.5%  97.5%
#> rsq 0.8045 0.0287 28.0431 42 0 0.7466 0.8624
#> adj 0.7906 0.0307 25.7193 42 0 0.7285 0.8526
summary(hc3)
#> Call:
#> RSqBetaSandwich(object = std_hc3, alpha = 0.05)
#> 
#> Multiple correlation with HC3 standard errors:
#>        est     se       t df p   2.5%  97.5%
#> rsq 0.8045 0.0313 25.6916 42 0 0.7413 0.8677
#> adj 0.7906 0.0336 23.5627 42 0 0.7229 0.8583

coef

Calculate R-squared and adjusted R-squared.

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

vcov

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

vcov(mvn)
#>             rsq         adj
#> rsq 0.001075300 0.001152107
#> adj 0.001152107 0.001234400
vcov(adf)
#>              rsq          adj
#> rsq 0.0008230557 0.0008818454
#> adj 0.0008818454 0.0009448343
vcov(hc3)
#>              rsq         adj
#> rsq 0.0009806163 0.001050660
#> adj 0.0010506603 0.001125707

confint

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

confint(mvn, level = 0.95)
#>         2.5 %    97.5 %
#> rsq 0.7383498 0.8707027
#> adj 0.7196605 0.8614672
confint(adf, level = 0.95)
#>         2.5 %    97.5 %
#> rsq 0.7466296 0.8624229
#> adj 0.7285317 0.8525960
confint(hc3, level = 0.95)
#>         2.5 %    97.5 %
#> rsq 0.7413304 0.8677221
#> adj 0.7228540 0.8582736

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