betaSandwich: Example Using the SCorSandwich, PCorSandwich, DeltaRSqSandwich, and FSqSandwich Functions

Confidence intervals for semipartial correlations, squared partial correlations, the improvement in R-squared, and Cohen’s f-squared are generated using the SCorSandwich(), PCorSandwich(), DeltaRSqSandwich(), and FSqSandwich() functions 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")

Semipartial correlations

summary(SCorSandwich(std_hc3, alpha = 0.05))
#> Call:
#> SCorSandwich(object = std_hc3, alpha = 0.05)
#> 
#> Semipartial correlations with HC3 standard errors:
#>            est     se      z      p   2.5%  97.5%
#> NARTIC  0.4312 0.0794 5.4303 0.0000 0.2755 0.5868
#> PCTGRT  0.3430 0.0789 4.3468 0.0000 0.1883 0.4977
#> PCTSUPP 0.2385 0.0783 3.0465 0.0023 0.0851 0.3919

Squared partial correlations

summary(PCorSandwich(std_hc3, alpha = 0.05))
#> Call:
#> PCorSandwich(object = std_hc3, alpha = 0.05)
#> 
#> Squared partial correlations with HC3 standard errors:
#>            est     se      z      p    2.5%  97.5%
#> NARTIC  0.4874 0.1095 4.4532 0.0000  0.2729 0.7020
#> PCTGRT  0.3757 0.1156 3.2500 0.0012  0.1491 0.6023
#> PCTSUPP 0.2254 0.1277 1.7647 0.0776 -0.0249 0.4757

Improvement in R-squared

summary(DeltaRSqSandwich(std_hc3, alpha = 0.05))
#> Call:
#> DeltaRSqSandwich(object = std_hc3, alpha = 0.05)
#> 
#> Improvement in R-squared with HC3 standard errors:
#>            est     se      z      p    2.5%  97.5%
#> NARTIC  0.1859 0.0685 2.7151 0.0066  0.0517 0.3201
#> PCTGRT  0.1177 0.0541 2.1734 0.0298  0.0116 0.2238
#> PCTSUPP 0.0569 0.0373 1.5233 0.1277 -0.0163 0.1300

Cohen’s f-squared and local f-squared

summary(FSqSandwich(std_hc3, alpha = 0.05))
#> Call:
#> FSqSandwich(object = std_hc3, alpha = 0.05)
#> 
#> Cohen's f-squared (fsq) and local f-squared with HC3 standard errors:
#>            est     se      z      p    2.5%  97.5%
#> fsq     4.1158 1.5009 2.7422 0.0061  1.1741 7.0575
#> NARTIC  0.9510 0.4166 2.2825 0.0225  0.1344 1.7676
#> PCTGRT  0.6019 0.2967 2.0288 0.0425  0.0204 1.1834
#> PCTSUPP 0.2909 0.2128 1.3670 0.1716 -0.1262 0.7081

Comparing covariance estimators

confint(DeltaRSqSandwich(std_mvn), level = 0.95)
#>                2.5 %    97.5 %
#> NARTIC   0.055421734 0.3163632
#> PCTGRT   0.017881671 0.2174267
#> PCTSUPP -0.008779331 0.1225237
confint(DeltaRSqSandwich(std_adf), level = 0.95)
#>                2.5 %    97.5 %
#> NARTIC   0.072394224 0.2993907
#> PCTGRT   0.025067308 0.2102410
#> PCTSUPP -0.008691312 0.1224357
confint(DeltaRSqSandwich(std_hc3), level = 0.95)
#>               2.5 %    97.5 %
#> NARTIC   0.05170296 0.3200820
#> PCTGRT   0.01155384 0.2237545
#> PCTSUPP -0.01630434 0.1300487

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.