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betaDelta: Example Using the DiffBetaDelta Function

Ivan Jacob Agaloos Pesigan

Source: vignettes/example-diff-beta-delta.Rmd
example-diff-beta-delta.Rmd

Confidence intervals for differences of standardized regression slopes are generated using the DiffBetaDelta() function from the betaDelta package. In this example, we use the data set and the model used in betaDelta: Example Using the BetaDelta Function.

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 corresponding sampling covariance matrix.

Multivariate Normal-Theory Approach 

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

Asymptotic Distribution-Free Approach 

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

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

mvn <- DiffBetaDelta(std_mvn, alpha = 0.05)
adf <- DiffBetaDelta(std_adf, alpha = 0.05)

summary

Summary of the results of DiffBetaDelta().

summary(mvn)
#> Call:
#> DiffBetaDelta(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:
#> DiffBetaDelta(object = std_adf, alpha = 0.05)
#> 
#> Difference between standardized regression coefficients with ADF 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

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

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

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

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, 1–4. https://doi.org/10.1080/00273171.2023.2201277