betaSandwich: Example Using the DiffBetaSandwich Function

Confidence intervals for differences of standardized regression slopes are generated using the DiffBetaSandwich() 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 differences of standardized regression slopes and the corresponding sampling covariance matrix.

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

Methods

summary

Summary of the results of DiffBetaSandwich().

summary(mvn)
#> Call:
#> DiffBetaSandwich(object = std_mvn, alpha = 0.05)
#> 
#> Difference between standardized regression coefficients with MVN standard errors:
#>                   est     se      z      p    2.5%  97.5%
#> NARTIC-PCTGRT  0.1037 0.1357 0.7640 0.4449 -0.1623 0.3696
#> NARTIC-PCTSUPP 0.2319 0.1252 1.8524 0.0640 -0.0135 0.4773
#> PCTGRT-PCTSUPP 0.1282 0.1227 1.0451 0.2960 -0.1123 0.3688
summary(adf)
#> Call:
#> DiffBetaSandwich(object = std_adf, alpha = 0.05)
#> 
#> Difference between standardized regression coefficients with MVN standard errors:
#>                   est     se      z      p    2.5%  97.5%
#> NARTIC-PCTGRT  0.1037 0.1212 0.8555 0.3923 -0.1338 0.3411
#> NARTIC-PCTSUPP 0.2319 0.1181 1.9642 0.0495  0.0005 0.4633
#> PCTGRT-PCTSUPP 0.1282 0.1215 1.0555 0.2912 -0.1099 0.3664
summary(hc3)
#> Call:
#> DiffBetaSandwich(object = std_hc3, alpha = 0.05)
#> 
#> Difference between standardized regression coefficients with HC3 standard errors:
#>                   est     se      z      p    2.5%  97.5%
#> NARTIC-PCTGRT  0.1037 0.1417 0.7316 0.4644 -0.1741 0.3814
#> NARTIC-PCTSUPP 0.2319 0.1318 1.7595 0.0785 -0.0264 0.4902
#> PCTGRT-PCTSUPP 0.1282 0.1375 0.9329 0.3509 -0.1412 0.3977

coef

Calculate differences of standardized regression slopes.

coef(mvn)
#>  NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP 
#>      0.1036564      0.2318974      0.1282410
coef(adf)
#>  NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP 
#>      0.1036564      0.2318974      0.1282410
coef(hc3)
#>  NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP 
#>      0.1036564      0.2318974      0.1282410

vcov

Calculate the sampling covariance matrix of differences of standardized regression slopes.

vcov(mvn)
#>                NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP
#> NARTIC-PCTGRT    0.018408653    0.009511262   -0.008897391
#> NARTIC-PCTSUPP   0.009511262    0.015672035    0.006160773
#> PCTGRT-PCTSUPP  -0.008897391    0.006160773    0.015058164
vcov(adf)
#>                NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP
#> NARTIC-PCTGRT    0.014681407    0.006928651   -0.007752755
#> NARTIC-PCTSUPP   0.006928651    0.013938955    0.007010303
#> PCTGRT-PCTSUPP  -0.007752755    0.007010303    0.014763058
vcov(hc3)
#>                NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP
#> NARTIC-PCTGRT    0.020076382    0.009274583   -0.010801799
#> NARTIC-PCTSUPP   0.009274583    0.017370731    0.008096148
#> PCTGRT-PCTSUPP  -0.010801799    0.008096148    0.018897947

confint

Generate confidence intervals for differences of standardized regression slopes.

confint(mvn, level = 0.95)
#>                      2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.16226855 0.3695814
#> NARTIC-PCTSUPP -0.01346652 0.4772614
#> PCTGRT-PCTSUPP -0.11226950 0.3687516
confint(adf, level = 0.95)
#>                        2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.1338262589 0.3411391
#> NARTIC-PCTSUPP  0.0004975295 0.4632974
#> PCTGRT-PCTSUPP -0.1099011119 0.3663832
confint(hc3, level = 0.95)
#>                      2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.17405314 0.3813660
#> NARTIC-PCTSUPP -0.02642203 0.4902169
#> PCTGRT-PCTSUPP -0.14119483 0.3976769

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.