betaDelta: Example Using the RSqDelta, SCorDelta, PCorDelta, DeltaRSqDelta, and FSqDelta Functions

Confidence intervals for R-squared, semipartial correlations, squared partial correlations, the improvement in R-squared, and Cohen’s f-squared are generated using the RSqDelta(), SCorDelta(), PCorDelta(), DeltaRSqDelta(), and FSqDelta() functions from the betaDelta package. In this example, we use the data set and the model used in betaDelta: Example Using the BetaDelta Function.

library(betaDelta)

df <- betaDelta::nas1982

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

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

Estimate the standardized regression slopes and the sampling covariance matrix.

std_mvn <- BetaDelta(object, type = "mvn")
std_adf <- BetaDelta(object, type = "adf")

R-squared and adjusted R-squared

summary(RSqDelta(std_adf, alpha = 0.05))
#> Call:
#> RSqDelta(object = std_adf, alpha = 0.05)
#> 
#> R-squared and adjusted R-squared with ADF 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

Semipartial correlations

summary(SCorDelta(std_adf, alpha = 0.05))
#> Call:
#> SCorDelta(object = std_adf, alpha = 0.05)
#> 
#> Semipartial correlations with ADF standard errors:
#>            est     se      z     p   2.5%  97.5%
#> NARTIC  0.4312 0.0672 6.4202 0e+00 0.2995 0.5628
#> PCTGRT  0.3430 0.0689 4.9812 0e+00 0.2080 0.4780
#> PCTSUPP 0.2385 0.0701 3.4003 7e-04 0.1010 0.3759

Squared partial correlations

summary(PCorDelta(std_adf, alpha = 0.05))
#> Call:
#> PCorDelta(object = std_adf, alpha = 0.05)
#> 
#> Squared partial correlations with ADF standard errors:
#>            est     se      z      p    2.5%  97.5%
#> NARTIC  0.4874 0.0941 5.1817 0.0000  0.3031 0.6718
#> PCTGRT  0.3757 0.1021 3.6796 0.0002  0.1756 0.5759
#> PCTSUPP 0.2254 0.1157 1.9481 0.0514 -0.0014 0.4521

Improvement in R-squared

summary(DeltaRSqDelta(std_adf, alpha = 0.05))
#> Call:
#> DeltaRSqDelta(object = std_adf, alpha = 0.05)
#> 
#> Improvement in R-squared with ADF standard errors:
#>            est     se      z      p    2.5%  97.5%
#> NARTIC  0.1859 0.0579 3.2101 0.0013  0.0724 0.2994
#> PCTGRT  0.1177 0.0472 2.4906 0.0128  0.0251 0.2102
#> PCTSUPP 0.0569 0.0335 1.7001 0.0891 -0.0087 0.1224

Cohen’s f-squared and local f-squared

summary(FSqDelta(std_adf, alpha = 0.05))
#> Call:
#> FSqDelta(object = std_adf, alpha = 0.05)
#> 
#> Cohen's f-squared (fsq) and local f-squared with ADF standard errors:
#>            est     se      z      p    2.5%  97.5%
#> fsq     4.1158 1.3592 3.0281 0.0025  1.4518 6.7798
#> NARTIC  0.9510 0.3581 2.6560 0.0079  0.2492 1.6528
#> PCTGRT  0.6019 0.2620 2.2970 0.0216  0.0883 1.1155
#> PCTSUPP 0.2909 0.1928 1.5091 0.1313 -0.0869 0.6688

Comparing covariance estimators

confint(DeltaRSqDelta(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(DeltaRSqDelta(std_adf), level = 0.95)
#>                2.5 %    97.5 %
#> NARTIC   0.072394224 0.2993907
#> PCTGRT   0.025067308 0.2102410
#> PCTSUPP -0.008691312 0.1224357

References

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.